CALIFORNIA STATE UNIVERSITY, NORTHRIDGE
A DIGITAL LOUDSPEAKER
EQUALIZATION TECHNIQUE
A graduate project submitted in pmiial fulfillment of the requirements
For the degree of Master of Science in
Electrical Engineering
By
Colby J Buddelmeyer
December, 2011
The project of Colby J Buddelmeyer is approved:
Dr. Xiyi Hang
Date
Professor Benjamin F. Mallard
Date
Date
California State University, Northridge
11
DEDICATION
To my wife, Anna Pomerantz:
Thank you for your support, encouragement, and patience.
I could not have finished this journey without you.
111
ACKNOWLEDGEMENT
I would like to thank Dr. Sean Olive, Allan Devantier, and the Harman
International R & D Group for allowing me to use the HATS (Hannan Audio Test
System) as part of my project. Their work has fmihered our understanding of listening
and created tools to revolutionize speaker design. I also want to thank Tim Prenta, Vice
President of Acoustics and Kevin Bailey, Director of Mechanical Engineering at Hannan
Consumer for their support of my project. They allowed me tin1e to pursue my Masters
and gave me access to the tools and resources used to build this project. Their support
made this project possible and I am in their debt. Special thanks also to my project
advisor Dr. Ichiro Hashimoto for his mentming, encouragement, and friendship. His
teachings will greatly influence the course of my future endeavors. Much appreciation
goes out to Dr. Xiyi Hang and Professor Benjamin Mallard for evaluating my project and
being such great instructors. Thanks to Jolm Jackson for assisting me in taking
measurements and providing guidance as to their meaning. Lastly, I wish to thank Brian
Castro, Mark Glazer, James Hall, and Charles Sprinkle for sharing their knowledge of
loudspeakers and DSP.
IV
TABLE OF CONTENTS
SIGNATURE PAGE
11
DEDICATION
iii
ACKNOWLEDGMENT
lV
LIST OF FIGURES AND TABLE
Vll
LIST OF SYMBOLS
lX
ABSTRACT
X
INTRODUCTION
1
SECTION I: LOUDSPEAKER DESIGN AND CONSTRUCTION
5
SECTION II: MEASUREMENTS
12
SECTION III: EQUALIZATION PROCEDURE
19
SECTION IV: RESULTS
30
SECTION V: APPLICATIONS
35
SECTION VI: CONCLUSION
37
REFERENCES
38
v
APPENDIX A: THIELE/SMALL PARAMETER VALUES
FOR THE GTI 560 5 INCH WOOFER
41
APPENDIX B: MATLAB LOUDSPEAKER CALCULATIONS
42
APPENDIX C: LOUDSPEAKER CABINET DRAWINGS
45
APPENDIX D: SPIN-0-RAMA TEMPLATE USER INTERFACE
53
APPENDIX E: UNEQUALIZED SPEAKER MEASUREMENTS
54
APPENDIX F: MATLAB HATS2FIR.M CODE AND .DAT OUTPUT FILES
62
APPENDIX G: FIR EQUALIZED SPEAKER MEASUREMENTS
67
APPENDIX H: IIR EQUALIZED SPEAKER MEASUREMENTS
75
APPENDIX I: LOUDSPEAKER PHOTOS
83
APPENDIX J: CIRRUS LOGIC CDB47XXX DSP EVALUATION BOARD
87
Vl
LIST OF FIGURES AND TABLE
Figure 1: GTi 560 Woofer
6
Figure 2: Alignment Chart for Vented-Box Systems with QL = 7
8
Figure 3: Effective Port Length for a Flared Port
9
Figure 4: Port Design for the Project showing a length of 5 inches
10
Figure 5: Project speaker setup for horizontal measurement.
12
Figure 6: Project speaker setup for vertical measurement
13
Figure 7: Horizontal Loudspeaker Amplitude Frequency Response
(No Crossover)
15
Figure 8: Vertical Loudspeaker Amplitude Frequency Response
(No Crossover)
15
Figure 9: Key Loudspeaker Data for Un-equalized Loudspeaker including:
On-Axis Amplitude Response, Listening Window,
First Reflections, Sound Power, Directivity Index (DI)
17
Figure 10: The HATS Low Frequency Network Virtual Transfer Function
Showing the Data of the Low Pass Filter
20
Figure 11: The HATS High Frequency Network Vittual Transfer Function
Showing the Data of the High Pass Filter
21
Figure 12: HATS predicted speaker response curves with added vittual EQs
22
Figure 13: Low Frequency EQ Target Curve output fi·om HATS
23
Figure 14: High Frequency EQ Target Curve output from HATS
24
Figure 15: Low Frequency FIR filter Impulse Response
25
Vll
Figure 16: High Frequency FIR filter Impulse Response
26
Figure 17: Project Loudspeaker System Block Diagram
27
Figure 18: DSP Composer FIR System Block Diagram
28
Figure 19: DSP Composer FIR Custom Post Processing Module Routing
28
Figure 20: DSP Composer IIR
Custom Post Processing Module Implementation
29
Figure 21: DSP Composer Pass-Thm
Custom Post Processing Module Implementation
29
Figure 22: DSP Board LF Pass-Thm showing Flat Response
30
Figure 23: DSP Board HF Pass-Thm
showing Flat Response above 60Hz
30
Figure 24: DSP Board LF FIR Amplitude Response
31
Figure 25: DSP Board HF FIR Amplitude Response
31
Figure 26: DSP Board LF IIR Amplitude Response
31
Figure 27: DSP Board HF IIR Amplitude Response
31
Figure 28: Key Loudspeaker Data for FIR Equalized Loudspeaker
32
Figure 29: Key Loudspeaker Data for IIR Equalized Loudspeaker
33
Table 1: Virtual EQ Filters Applied in HATS
22
Vlll
LIST OF SYMBOLS
BR
Transducer motor strength measured in tesla-meters
Cms
Transducer mechanical compliance measured in !-!miN
f3
System Minus three decibel half-power frequency (Hz)
fs
Resonance frequency of the transducer (Hz)
Levc
Transducer voice-coil inductance in mH
Mms
Acoustic mass of the transducer diaphragm assembly including
the air load measured in grams
Q
Ratio of reactance to resistance in series circuit or reactance to resistance
in parallel circuit
Qes
Transducer electrical Q
Qms
Transducer mechanical Q
Qts
Total Q of transducer (woofer) considering all transducer resistances
Re
DC resistance of the transducer voice-coil measured in ohms
Sd
Effective surface area of the driver cone measured in cm2
Vas
Volume of air having the same acoustic compliance as the
transducer suspension measured in liters
Xmax Peak linear displacement of transducer cone measured in mm
IX
ABSTRACT
A DIGITAL LOUDSPEAKER EQUALIZATION TECHNIQUE
By
Colby J Buddelmeyer
Master of Science in Electrical Engineering
This project illustrates a method of implementing a digitally equalized
loudspeaker. A two-way loudspeaker using off-the-shelf transducers will be designed
using the best construction methods derived from the literature.
This technique will
allow the author the optimum frequency response using the available components. The
Harman Audio Test System (HATS) will be used to obtain acoustic measurements in a
4pi anechoic chamber. These measurements and their processed results using HATS will
characterize the acoustic performance of the un-equalized loudspeaker. HATS will then
be used to determine the target functions needed to equalize the loudspeaker for flat onaxis frequency response. Vectors of the target functions will be exported to MATLAB
where they are used to generate the coefficients of two 128-point FIR filters. The filter
coefficients will then be implemented into a DSP evaluation board.
An IIR
implementation using values derived from HATS will be created with tools built into the
DSP software.
A listening comparison can then be performed using FIR or IIR
equalization versus no DSP, or pass-thru, for subjective evaluation.
Anechoic
measurements will be used to verify the loudspeaker has an improved frequency response
based upon the current psychoacoustic literature.
Finally, further applications and
existing products with similar technologies will be discussed.
X
INTRODUCTION
The origin of the loudspeaker can be traced back to Alexander Graham Bell and
the telephone [1]. The first binaural sound reproduction (meaning true stereo sound)
dates back over a century to 1881, when soon after the invention of the telephone, an
experiment was conducted at the Paris Opera demonstrating the use of two separate
channels. These consisted each of a telephone transmitter, an interconnecting wire and a
telephone receiver [2]. This primitive version of a stereo loudspeaker system was far
from today's modem designs.
It was not until 1923 and the initiation of regular radio broadcasting by the British
Broadcasting Company that high quality sound reproduction actually began [3]. Higher
fidelity was demanded and improved versions of Bell's original transducer resulted in the
moving-iron loudspeaker [3]. This speaker consisted of a cone driven at its apex by an
iron armature moving in a magnetic field [3]. The speaker's name is derived from the
fact that part of the iron of the magnetic circuit moves.
By 1925, General Electric
engineers Chester W. Rice and Edward W. Kellogg presented the first moving coil
loudspeaker. Their paper entitled "Notes on the Development of a New Type of Hornless
Loud Speaker" [4] is the basis for the modem dynamic loudspeaker.
Still, there was much more work to be done. Research was devoted to both the
objective
and
subjective
(or
psychoacoustic)
measurement
of
loudspeakers.
Advancements in acoustics led to a better understanding of how to equalize a loudspeaker
using the inherent characteristics of the transducers, enclosure materials, box shape and
size, and by the use of absorbent filling materials. By the early 1960's, the electro-
1
mechanical analogies and basic design characteristics of moving coil direct radiators
were well understood. As demonstrated in his influential paper entitled "Loudspeakers"
[5], Olson and his contemporaries had substantially developed this area of research. At
the same time, inventors were beginning to understand the need for multiple transducers
to achieve true full range (20Hz - 20,000Hz) designs. These designs would require
electrical networks to separate the various frequency ranges of each transducer. Twoway, three-way and even four-way designs were created using a variety of techniques.
Unfortunately, the wide manufacturing tolerances of the transducers produced
during the 1960s often reduced the effectiveness of the crossover networks. Since the
cross over frequency is usually located in the area of the sound spectrum most sensitive
to human hearing, networks needed to be adjusted to individual transducers. This meant
elaborate networks had to be devised that allowed user adjustable components.
Fortunately, modem production processes and a better understanding of the loudspeaker
system have enabled more systematic design approaches [6]. Still these analog methods
of adjusting the fl-equency response were limited. Introducing additional components for
better control adds cost and changes the overall response of the system. The result is a lot
of trial-and-enor in design and manufacturers being forced to choose between best
response and lowest cost.
Design tools continued to progress with the creation of
standard design characteristics for system design called the Thiele/Small Parameters [7].
Fmiher work led to improved analog networks, including the famed Linkwitz-Riley
crossovers [8] [9]. Still, even experienced designers and engineers do not agree on the
best characteristics for a loudspeaker [10]. The ability for more control was needed. Into
this problem we introduce the digital (DSP) crossover.
2
Digital signal processing allows far more control of the system. A well-designed
DSP does not load the system it is being used to filter. Thus, the effects of adding a
digital filter in pass-thru mode are negligible. This fact alone makes DSP loudspeakers
much easier to design. In addition, DSP provides for unlimited order filters and the
ability to completely tailor the response of the system. While this will not make a poorly
designed speaker great, it will allow a well-designed loudspeaker to be significantly
improved.
While the theories and algorithms for digital filtering were well established by the
1970s, inadequate processing power and the high cost of DSP ICs did not allow the
technology to be widely available.
Most DSP power was reserved for Audio/Video
receivers and post processors. These devices would allow for the decoding needed in
THX, Dolby, and other digital sunound algorithms [11]. The increasing power of DSP
ICs and the reduction in cost achieved in the first decade of the 2000s have now enabled
them to be included in speakers. As speakers are increasingly self-powered, the addition
of DSPs for system equalization and other enhanced features is becoming commonplace.
This paper will show the design of a loudspeaker utilizing modern teclmiques.
The process will begin by following the best speaker box practices in order to produce a
design that has good characteristics for digital equalization. Measurements will be taken
showing the frequency response of the system without the crossover. Crossover target
functions will be created for best equalization and then implemented using a finite
impulse response (FIR) filter generated in MATLAB.
The FIR coefficients will be
programmed into a DSP and measurements for the filtered system will be taken. A
second filter using the infmite impulse response (IIR) method will also be made for
3
companson purposes.
The paper will discuss how the filtered speaker meets the
objective of improved fidelity through digital filtering based upon the cunent knowledge
of psychoacoustics. The as-built loudspeakers will also be available to the committee for
subjective listening.
Finally, the future applications of this technology will be
considered.
4
I. LOUDSPEAKER DESIGN AND CONSTRUCTION
A number of important characteristics must be considered when starting a
loudspeaker design. Typical factors that may be considered include: frequency response
(amplitude response), sound power, directivity index, harmonic distortion, spurious
noises and inter-modulation distortion, frequency shift including FM distortion, dynamic
range compression (power compression), transient distortion, phase distortion, group
delay, electro-acoustic efficiency, power handling capacity (or loudness), constancy of
performance, size (and appearance), cost, and design time [12]. The order of importance
for these priorities differs by design and has changed over the years. While the purpose
of this report is to show how to equalize a speaker using DSP, there are important first
steps that cannot be ignored. In order to successfully equalize a loudspeaker (using any
method), it must have a basic design that will allow for proper alignment. This means the
box size and tuning must produce a realizable frequency response that is useful for
further equalization with the crossover network.
Most designs begin with the selection of the transducers. For this design, the
author was restricted to using standard components that can be easily and affordably
purchased. The transducers selected were a generously donated set of JBL 560 GTi
Series speakers. This tweeter and woofer set have been designed by JBL engineers to
perfmm well together in a correctly tuned and equalized system. The GTi 560 Series is a
competition speaker system meant for automotive use. It consists of two 5 inch woofers
and two 1 inch tweeters. Many of the issues mentioned above were already solved (or
determined) by the choice of h·ansducers. Transducer design and selection is a very
important part of any speaker system. The design and characteristics of transducers is
5
1. Spider-Landing Vents:Minimize distortion from mechanical noise.
2. NomeX Spider: Provides linear force in both movement directions.
3. Nitri!e-Butylene Surround: Ensures superior longevity.
4. Copper Polepiece Cap:Provides linear inductance over the full
range of forward voice-coil travel for reduced intermodulation
distortion. Provides crystal-dear vocals and midrange, even
during heavy bass signals.
5. Polished and Flared Polepiece Vent: Provides a low-velocity inlet
and outlet for the movement of air in and out of the motor structure.
Minimizes distortion from mechanical noise.
6. Neodymium MagnetProvides high flux density. Also allows more
room for larger steel motor components to provide critical heatsink
mass for the voice coil.
7. Vented Gap Cooling Ports: Provide movement of air over the voice
coil for superior power handling.
B. Flux Stabilization Ring: Provides global stabilization of the static
magnetic field and works with the copper cap to minimize
coil inductance during inward movement of the voice coil.
9. Voice Coil: long, over-hung 2" diameter, aluminum edge-wound
voice coil provides high excursion for improved low-frequency
capability Reduces distortion at low frequencies and high input
10. Vented Voice Coil FormerMinimizes distortion from mechanical
noise.
11. Screw-Down Terminals: Ensures reliable high-quality
connections.
12. Kevlar Dustcap and Cone BodyUitrarigid Kevlar dustcap and
cone body minimize unwanted cone flexing for smooth frequency
response.
13. Cast-Aluminum Basket:Provides a rigid support for motor and
moving assembly
Figure 1: GTi 560 Woofer [13]
quite involved and beyond the scope of this report. A good starting point for further
infom1ation about transducer design can be found in Chapter 1 of the Loudspeaker
Design Cookbook [14]. Appendix A shows the Thiele/Small specifications for the GTi
560 woofer. These were used to determine the size of the box required to meet the
desired frequency specifications. The author decided to limit the target low frequency
response of the design to -3dB at 60 Hz. This was chosen to prevent distortion of the
woofer at low frequencies. In order to extend the low frequency response to achieve this
specification, the speaker was built as a vented box (more commonly known as ported).
A vented box loudspeaker incorporates an opening which allows air to move in
and out of the enclosure in response to pressure variations within the enclosure. The
technique exploits the Helmholtz resonance of the box and port system. The design of
6
vented enclosures is covered in detail in papers by Thiele and Small [15] [16]. The basic
process required for alignment as used for this design will be reproduced here. The steps
follow the procedure described in the Loudspeaker Design Cookbook pgs 56-78 [14] and
Small [16] with the exception that the project was started with a predetermined box
volume.
1. Select an appropriate woofer. The GTi 560 Woofer has a rated Qtsof 0.34 which
satisfies the requirement of Q15 = 0.2- 0.5. The measured value changed to 0.45,
which is still suitable for use in this project.
2. Typically, alignment would be chosen next. For this project, the box volume was set
at Vb = 0.38 ft 3 (10.8/iters). This was done since choosing the alignment first could
lead to the requirement of producing different sized boxes to arrive at the correct
tuning. The value was also based upon the guidance of experienced JBL engineers.
3. Choose an alignment. A flat Quasi-Third Order (QB3) alignment was selected. It is
the most common vented alignment as it yields a smaller box size and lower
given driver
for a
Qts [14].
4. Determine the
woofer.
.h
Be, f
8
,
Qts' Vas' Xmax'Sd, and Vd Thiele/Smail parameters for the
All of these are given in the woofer data sheet except for Vd which is
calculated as:
7
Note that values were adjusted for the actual driver as measured in the lab. For more
information on loudspeaker testing see chapter eight of [14]. The adjusted values are
shown in Appendix A.
5. Assume leakage loss, QL,is equal to 7.
6. Use alignment chart per Small [16] with measured values of Qts and calculated value
for a . See Appendix B for MATLAB code showing the calculations and the results.
The results of plotting the derived values on the alignment chart are shown below.
0.6
.7
.5
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I
:::::: ~
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QT
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fs
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.5 .7 1
5 7 10
0
Figure 2: Alignment Chmi for Vented-Box Systems with QL = 7 [16]
Shown with plot of project values in red
8
It can be seen from Appendix B that the calculated value of a:::0.66. We find from
Figure 2 that h:::0.87 and f3 /fs
=0.77.
We also fmd the calculated value of the
-3dB frequency for the design to be approximately 57Hz (See Appendix B).
7. Detennine the port length and diameter. Using the calculations in Appendix B we
find the important values for the pmt. These are: minimum pmt diameter of just
under 2 inches and port length of approximately 4 inches. The poli, the PSP2 made
by Precision Sound Products (http://www.psp-inc.com), has a one-inch flare on each
end to prevent air noise. The general guideline for the effective poli length is to
reduce the calculated length by half the flare radius on each end (see Figure 3). Thus,
the designed port length for the project is 5 inches (see Figure 4) resulting in an
effective length of our calculated 4 inches.
This air belongs to port
This air belongs
to outside
This air belongs
to outside
-I
I
I
I
I
I
I
I
I
I
I
f--1---1
Half of flare
radius
--~L
I
1---1---l
Effective length
__j
Figure 3: Effective Pmt Length for a Flared Pmt
9
Figure 4: Port Design for the Project showing a length of 5 inches
The alignment of the project is now complete. There are still many more items that could
be assessed to make an ideal loudspeaker. For this project, the other items considered
include: diffraction, transducer placement, directivity, and enclosure structural design.
Diffraction is the process by which the change of direction of sound takes place
[17]. Olson demonstrated that the exterior of the cabinet influences the response of the
loudspeaker. This change in response is due to the diffraction effects produced by the
surface contours of the cabinet [18]. Olson measured the performance of a great many
cabinet shapes loaded with a direct radiator loudspeaker.
The results showed that
reducing sharp boundaries on the front portion of the speaker reduces variation in
response. Thus, for this project, all comers on the loudspeaker are well rounded with no
10
sharp edges on the baffle. The next issue, transducer placement, is important to prevent
phase and directivity problems. In order to minimize this issue, the transducers were
spaced as closely together as possible. In addition, the tweeter is mounted close to the
baffle top at a distance different than its distance to the left and right sides of the box.
The purpose is to vmy the distance to the diffracting edges to create a more random phase
relationship between the primary and diffracted sound waves [18].
In addition, a
waveguide included with the GTi 560 series was used for mounting of the tweeter. The
purpose of the wave-guide is to acoustically load the tweeter and thereby narrow the
directivity pattern. The goal is to focus the acoustical energy of the tweeter and thereby
match the directivity of the woofer at the crossover point. More info on directivity
related to transducer spacing can be found in reference [19]. The final issue considered
in the cabinet design was the constmction. For ease of manufacturing and consistency of
wall density,% inch medium density fiberboard (MDF) was used for the walls and brace.
The front baffle was made extra thick (1 inch) to further stiffen the unit against the first
cabinet resonance. A brace was utilized to provide additional rigidity. The cabinet walls
were lined with one-inch thick sheets of fiberglass to reduce sound radiation and provide
improved damping. The cabinet drawings can be seen in Appendix C. See reference
[20] for more info on loudspeaker cabinet materials and constmction.
11
II. MEASUREMENTS
Measurements were taken of the raw (un-equalized) loudspeaker using the 10,000
cubic foot JBL 4pi anechoic chamber. This chamber has large 4-foot wedges, which
allow for echo-less measurements from 60Hz to over 20kHz(+/- 0.5dB, l/20 1h octave).
Additional calibration enables the chamber to be accurate down to 20Hz (+/- 0.5dB,
1/1 01h octave) [21]. The speaker was placed 2m from the measurement microphone on a
platform that rotates in 10° intervals :fi:om on-axis (0° degrees) to 350°. The height of the
rotating platform is adjusted so the reference axis (or midpoint between the tweeter and
the woofer) is centered at the conect measurement location. This same process is applied
for both the horizontal and vertical axes. Thus, 72 measurements are taken in total.
Figures 5 and 6 show the horizontal and vertical setup of the speaker in the chamber.
Figure 5: Project speaker setup for horizontal measurement.
12
Figure 6: Project speaker setup for vertical measurement
The test results have been auto-adjusted to the reference standard of lmeter so the
sensitivity can be read directly [23]. Sensitivity is a measure of the acoustic soundpressure level produced by a stated electrical input voltage [6]. The typical standard is to
measure at a distance of 1 meter with an input reference voltage of 2.83V. Loudspeaker
standards specify that measurements should be made in the far field, which is defmed as
the point where sound level decreases at -6 dB per doubling of the distance. For most
loudspeakers, a distance of 2 meters is adequate for this requirement. After taking each
measurement at 2m, the sound level that would be expected from a point source at lm is
then calculated [23].
This is the reason for the auto-adjustment of the levels.
Unfortunately, the need for separate amplification of the tweeter and woofer meant the
tests had to be performed with an un-calibrated stereo reference amplifier. A Proceed
Amp 2 was used instead of the reference Lexicon 501 mono-block amplifier typically
used in the laboratory. Thus, the SPL levels in this report are reference values only. For
13
a true comparison, the raw speaker measurements had to be acquired with the DSP board
in-line before the amplifier and set to pass-tluu mode.
We will forego an in-depth
discussion of the DSP board until Section III.
The interface for taking these measurements is called HATS or the Hmman Audio
Test System. The HATS software is a powerful sixteen channel audio analyzer that is
optimized for measuring loudspeaker and loudspeaker-room systems [22]. The HATS
analyzer utilizes a BSS BLU-32 hardware I/0 for the AID and D/A used in taking the
measurements. HATS has many built-in stimuli for audio testing and can be configured
with the BLU-32 for a diverse set of applications. More about the software can be read in
the HATS User Manual [22]. Various templates can be made in HATS for standard
acoustical tests.
For the 72 measurements described above and their conesponding
analysis, an engineering template called the Spin-0-Rama was utilized. See Appendix D
for a screenshot of the Spin-O-Rama user interface. This template runs the test and
provides objective loudspeaker output data. The horizontal and vertical must be set up
and run individually but the 36 measurements for each are automated.
The horizontal and vertical anechoic speaker measurements at 0°, 10°, 20°, 30°,
60°, 90°, 120°, and 180° are shown below. From the anechoic measurement curves, we
can see a clear discontinuity at approximately 1200 Hz.
This is where the woofer
response drops before the rise of the tweeter response. There is a clear level difference
between the tweeter and the woofer of over 10 dB.
The large peak at 2kHz in the
horizontal response is caused by the acoustic loading of the waveguide.
14
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Figure 7: Hmizontal Loudspeaker Amplitude Frequency Response (No Crossover)
HARMAN Audio Test System
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Figure 8: Vertical Loudspeaker Amplitude Frequency Response (No Crossover)
15
HATS also allows us to generate other key data used in analyzing the speaker
frequency response.
These include the listening window, early (or first) reflections,
sound power, and the directivity index (DI). The meaning of these terms and their curves
will now be explained:
Listening Window: Listening Window refers to the spatial average of the nine frequency
responses on the ±10° vertical and ±30° horizontal angular range [23]. This area of the
speaker is the most common listening area.
The spatial averaging attenuates small
acoustical interferences that have little effect on the overall sound quality and reveals
resonances which can be audible.
Early (or First) Reflections: Sounds that have been reflected only once on their way to
the listener.
The curve is an estimate of all single-bounce, first reflections in a typical
listening room. Being that it is a spatial average, a bump that appears in this curve and
also appears in other curves provides clear evidence of a resonance [23].
For more
information about the research behind this curve and its calculation see [21].
Sound Power: Sound power is meant to represent all the sounds arriving at the listening
position [23].
As such, it is a weighted average of all the horizontal and vertical
measurements. The weighting is applied to make the results representative of the human
listening experience. The sound power is a measure of the total acoustical energy
radiating through an imaginary spherical surface with radius equal to the measurement
distance [23].
16
Directivity Index: The directivity index is defined as the difference between the on-axis
curve and the sound-power curve.
The on-axis curve often has diffraction artifacts
related to the shape of the cabinet or transducers that do not appear in other
measurements. In order to prevent these artifacts from affecting the curve, the definition
has been redefined to make the DI (directivity index) the difference between the listening
window and the sound power curves. This curve is a measure of the degree of forward
bias (or directivity) in the sound radiated from the loudspeaker [23].
HARMAN Audio Test System
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N 84· Tolal Snund Power Dl
···82 FnstRefiectioRs
ah(-10123120\111·49:16MJ-C'Ox:t.onoertsendSdmgsY'~J~'HyDoo..r.'Jerts'lec.e6$'Msd.!lalfrnl_ft!:s'&HMs
Figure 9: Key Loudspeaker Data for Un-equalized Loudspeaker including:
On-Axis Amplitude Response, Listening Window, First Reflections, Sound Power,
Directivity Index (DI)
17
Figure 9 shows the key measured and calculated metrics for the project
loudspeaker. (Note that Appendix E shows the 0°, 10°, 20°, 30°, 60°, 90°, 120°, and 180°
anechoic speaker measurements and their calculated metrics in larger and separated
graphs for ease of viewing.) Here again, we see the large discontinuities observed in the
individual responses. This result makes sense as these individual responses are used in
the calculated curves. It is not possible to objectively quantify the sound character of a
loudspeaker in a single measurement. Thus, the cunent best method uses many curves
and the relationship between these curves to define the response. Section IV will discuss
this topic in greater detail. What we can understand at this point is the need for amplitude
equalization of the speaker based upon the differences in level between the tweeter and
the woofer and the loss of audio at 1200 Hz. It should be noted that items including
phase response, non-linear distortion, and other problems could also be measured and
conected. Since the human ear has shown through testing to be insensitive to speaker
phase variations, this problem will not be considered in depth [23]. Nonlinear distortion
will also not be considered as its audibility is affected by the type of distortion [25] [26].
While it is possible to conect for these issues in DSP, they will be considered outside the
scope of this project.
18
III. EQUALIZATION PROCEDURE
For this part of the project we again start by turning to HATS. HATS has the
capability to apply virtual transfer functions to the measured and calculated data.
Equalization (EQ) curves can be applied directly in HATS and the results can be seen in
real time. This is a ve1y powerful aid to the would-be loudspeaker designer as it allows
for trial-and-en·or without the need of additional measurements. Based upon the results
of the raw curves generated for the project speaker, we can conclude that adjustments are
needed to improve the overall amplitude frequency response.
The first question that needs to be asked is: "What is the ideal amplitude response
of a loudspeaker?" There is no one answer to this question. Many papers have been
written on this topic and as yet there is no definitive answer. Based upon the research of
Toole and Olive [26] [27] [28] [29], a high conelation is shown between listener
preference and loudspeakers with flat on-axis amplitude. Thus, for this project, flat onaxis amplitude was established as the optimum speaker amplitude response. With this
goal in mind, HATS can now be utilized to optimize the speaker's response. The SpinO-Rama template allows the use of a global EQ, a high fi·equency virtual transfer
function, and a low frequency virtual transfer function to create the crossover and apply
additional EQ.
The process of equalizing a speaker in HATS mimics the traditional trial and error
methods. It requires an understanding of filters, loudspeakers, and their interactions. As
stated above, the great advantage of using HATS is the ability to make adjustments and
see the results in real time without the need for physically rebuilding the crossover or
19
taking additional measurements. Still, there is no substitute for experience since the great
flexibility of the tool can allow for endless possibilities in design. Knowing what filters
to apply at the starting point is essential. Reviewing the raw data in Section II, we found
the approximate crossover frequency to be 1200Hz. At this point the Low Frequency
Network Virtual Transfer Function (LF Network VTF) window was activated and a third
order maximally flat (or Butterwmih [14]) low pass filter was created with center
frequency of 1300 Hz. Next, the High Frequency Network Vi1iual Transfer Function
(HF Network VTF) window was activated and a second order Butterwmih High Pass
filter was created with center frequency of 3000 Hz. The LF and HF Network VTF
windows are shown in Figures 10 and 11. Global EQ was not utilized for this project.
! EQs
[Hi§~~~~~~~~~}__
__ ___ __ ____ __
i ~~~-~:::~:;~ :~~~~~----~
0
i
1
i
Parametric 200Hz
1
1
iI
1
l!
i
sample Rate:
I
EQ Type:
___ _ _ _____
~~~~I~~~~;-~~=;~;J
__ v J
Low Pass
[s~it;;;;~;i;:=-..::=:::~:-;1
I
FilterType:
!
Frequency:
-~;~~]if:::.:::~=-=-==~
Filter Gain:
-- -----
:
____ _ _ _
--·---
2! Hz
.
Bandwidth:
l
IJ
Octaves
-i
Slope:
dB/Octave
A'
Order:
vi
______________ !
Overall Controls
II
Gain:
I
I
iO.OO
L. ______ ...
Delay: i~-00
:Flip Phase
A
i ms
--~_j
0
'
t_ __
0
Always On Top
Close
Apply
Figure 10: The HATS Low Frequency Network Virtual Transfer Function
Showing the Data of the Low Pass Filter
20
0
0
0
0
0
Parametric 4700Hz
Parametric 4700Hz
Parametric 21OOHz
Parametric 3700Hz
vi
Sample Rate: )4BOOO
EQ Type:
Filter Type:
IHigh Pass
IButterworth
v]
v)
~] Hz
Frequency: 13000.00
Filter Gain:
1o e:r1
Bandwidth:
II tf:
Slope:
I dB
I Octaves
dB/Octave
t.
~I
Order: 12
0 verall Controls
~I
~I
Gain: 1·7.00
Delay: 1o.oo
:Flip Phase
D
ms
D
AddEQ
II
Close
II
Always On Top
dB
DeleteEQ
Apply
I
J
Figure 11: The HATS High Frequency Network Virtual Transfer Function
Showing the Data of the High Pass Filter
For low-pass and high-pass filtering, HATS can apply Buttetwmth or LinkwitzRiley [8] [9] filters. The crossover frequencies and types used in this project were chosen
by trial-and-error to produce the best overall flat amplitude frequency response. As can
be seen in Figures 10 and 11, additional parametric EQs were applied to improve the
overall response. Table 1 shows all the filters applied including these additional EQs and
their data. The purpose of the EQs was to prevent peaks or dips apparent in the predicted
response curves. The result of applying these curves on the impmtant loudspeaker curves
is shown in Figure 12. Here we can see the on-axis has been significantly improved from
the raw data.
We also find the other curves are smooth which has been shown to
cone late well with listener preferences [23]. Remember that these curves including the
21
revised on-axis response are predicted values that are yet to be measured for verification
in the anechoic chamber.
Virtual Equalization Filters Applied in HATS
LF
VTF
HF
VTF
EQType
Filter Type
CenterFreq
(Hz)
Filter Gain
(dB)
Bandwidth
(Octaves)
Low Pass
3rd Order Butterwmth
1300
0
NIA
Paramettic
Parametric
NIA
NIA
200
900
1.5
0.2
1
Parametric
N/A
4000
-5
0.2
High Pass
2nd Order Butterworth
3000
-7
Parametric
NIA
2100
-2
NIA
0.25
-2
-4
3
0.25
0.1
Parametric
N!A
3700
Paramettic
Parametric
N/A
4700
4700
N/A
-6
0.5
Table 1: Virtual EQ Filters Applied in HATS
!HARMAN Audio Test System
I
850
000
li
!~
j]
!1
i
'"'
I
35.0-\-,:,-------,•oo-------~---,ooo~'----------,=~,----J,.,j,
Frequency (Hz)
;~373:0nAxis
Xi376:To!aiSoundPan-er
]~374:Wmdow
N377 TolaiSoundPowerOI
!..I'V375:Firs!Reftecti!!ns
)c:o!r(-11lflJ/20111:03:12A.I·C.t>octmms arx:ESe!:hgs'Cf:btJ~~ut~s'lece69Bldsd!lla\fna! Bes'mstt_pti._rl'twl_!p01_t.n3_2011-1G-16111lts
Figure 12: HATS predicted speaker response curves with added viliual EQs
22
The next step is to output the results of the virtual transfer functions for use in
creating the FIR coefficients in MATLAB. This was accomplished by exporting the HF
VTF Target and LF VTF Target Rows of the Spin-0-Rama worksheet. Figures 13 and
14 show the LF and HF virtual target curves, which are composites of the EQs shown in
Table 1. The result of expmiing the curves is two text files that contain vectors of the
frequency, magnitude, and phase of the target curves. These files could not be included
in this report due to their length.
The files were then imported into MATLAB. A
MATLAB program was written to provide the FIR coefficients of both the 128-point low
fi·equency and 128-point high frequency filters. The magnitude frequency response of
the resulting FIR filters should match those shown in Figures 13 and 14.
HARMAN Audio Test System
10.0
I
0.0-j----------
-10.0
~200
-::o.o
-35.o,.±-------,oo.------------'-----,~OOJ-------'-----~--,oooo.---l
Frequency {Hz)
W383lFVTFTa.rgel
Figure 13: Low Frequency EQ Target Curve output from HATS
23
0.0
-10.0
-20.0
-:no
-50.0
~or-~~~~~~~~~~~~~~~~~~~~~~~~~~~
urn
100
2<l
IOOll
Frequency (Hz)
lv382. HFVIFTarget
Figure 14: High Frequency EQ Target Curve output from HATS
Appendix F shows the code for the MATLAB program hats2fir.m. The code has
comments that describe each step in more detail. A general synopsis for the function of
this code is to provide the bk filter coefficients for the general FIR filter of the form:
=
M-1
I, b,x(n-k)
k=O
K
The filter was implemented by first importing the HATS generated text files into a
MATLAB data file.
The data was then read into frequency, magnitude, and phase
vectors. This data was then re-sampled and interpolated using the interpl function of
MATLAB. The complex frequency response was then created and the inverse Fourier
24
transfonn was taken using the MATLAB function ifft. Only the real part needed to be
considered. Note that the result of this technique produces the impulse response, which is
the same as the FIR coefficients [30]. The resulting impulse responses were then plotted
and are shown below in Figures 15 and 16. The .DAT files with FIR coefficients can be
seen in Appendix F.
LF Impulse Response
0.05
~ .
(j
... (i
0.04
(
0.03 .. (
Q)
<i
-o
~
.t::
c
0)
ro
v:
.
).:........................;............ ;............ :. ...........:.......... .
J)~
!":"~
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~-·
(j
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~
:
:
:
.
.
..
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.
..
...
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~
~
................. ·~.. ........... ;..............l........... -~···.. ....... .
0.01 J
0
~
:
rr<
:
:
:
:
~- ..................... -~· ........... ~ ........... -~· .......... -~ ......... .
0.02
z
~
:
-~.
lj
..
...
.
H
llll~.
0
0
0
•
f!>
-0 .01 0
20
i
40
60
80
100
120
Sample
Figure 15: Low Frequency FIR filter Impulse Response
25
140
HF Impulse Response
0.3r-----,-----~------r-----,-----~------r-----.
025 )
0.15
0.1
••••••••••
c:
0.05
'
..
•••••••••••• :
•
w
~
••
0
! .
.
..
..
• • • • • • • • •: • • • • • • • • • • • • :
0
•••••••••
-~
0
•••
0
•••••••
:.
:
•••••••••••
~:
0
:
.
••••••••••• : ••••••••••••
ro
2::
.
•••••••••••• : ••••••••••••
..
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:::::1
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0.2
Q)
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~
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:
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~
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-: • • • • • • • • • • • • :
•••••••••••
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•••••••••••
:
~
•••••••••••
••••
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~
..
.
..
-~
•••••••
0
•
••••••••••
0
..
.
0
••••••• : •••••••••
•
0
•
:
:
~
~
-0.05 D- ........ ~ ........... ·: ............ ~ ........... : ............ ~- ........... ~ : ......... .
)......... L........... t........... ~ ............~ ............ ~ ........... L......... .
:
:
:
' ......... ·l· .......... ·[ ........... j........... ·i .......... ·l· .......... ·1· ......... .
-0.1
-0.15
-0.2
0
.
i
E
~
00
.
.
.
00
100
1E
1~
Sample
Figure 16: High Frequency FIR filter Impulse Response
The fmal step is to implement the FIR coefficients into the DSP board for filtering
of the loudspeaker. Figure 17 shows the generalized system block diagram. The DSP
integrated circuit (IC) utilized for the project is the Citrus Logic CS47048C. A circuit
board was required to gain access and control the CS4 7048C I C. Since designing the
circuit fi-om scratch was considered beyond the scope of the project, the CDB47XXX
evaluation board was used to implement the filters. This board has multiple analog and
digital I/Os to the onboard CS47048C DSP IC. In a real system, only the DSP would be
utilized within the architecture of the product. Cirrus provides a software interface to the
26
IC called the DSP Composer.
The software comes with built-in signal processing
modules, and the visual interface provides for ease of design.
DSPBOARD
HFXOVER
STEREO
INPUT
LFXOVER
HFXOVER
Figure 17: Project Loudspeaker System Block Diagram
Building a project within DSP Composer requires ce1iain component blocks to be placed
within the system. Once these blocks have been included, the custom pmiion of the
design may be implemented within the Custom Post-Processing Module (or Custom
PPM) block. For the project, the custom FIR primitive was used for creation of both the
woofer and tweeter equalization. Once the component blocks are properly placed and the
system is correctly routed, all that is necessary for implementation of the FIRs is to point
the primitive to the correct file location for the FIR coefficients. The project can then be
built and tested. Figures 18 and 19 show the system design within DSP Composer for the
FIR filter design.
For comparison purposes, a second version of the project was built using the IIR
method. For this method, the EQs shown in Table 1 were created using the built-in
primitives for low pass, high pass, and parametric filtering. The user interface showing
the implementation and three of the selection windows is shown in Figure 20. Finally, as
mentioned in Section II, a pass-thru version was created for use in taking the raw
measurements. This routing of the custom PPM is shown in Figure 21. Note that a 60Hz
27
high pass filter was applied to the tweeters for DC protection. The completed designs are
now ready for attachment to the amplifier/speaker system for measurement.
(';]fQj~
. OSP Composer CS4 7XXX [FIR_01_s!ereo]
File Edit
View Mode Tools
Windows Help
(]) e:3 l5lJ ; l:f"1l fi"';> . ()Go!
D)Sy~em~
[~
• •, •
ibconnect
::bEmulation
~=---~~--~~----~~---------------------------------------------------4
Remap Audio Input
Ed Remap AuctJO Output
6) Audio In
6) Audio out
System
C::1 Decoders
;:t·
i.t:
CJ Matrix Processors
!:E CJ Vutua!izers
!± D Post Processing
:t CJ Spanning Elements
i:E C:J Graphic Elements & Blocks
User Devices
Page 1
Custom PPM
edJ1
Figure 18: DSP Composer FIR System Block Diagram
(';]fQj~
. OSP Composer· CS47XXX [FIR_01_s!ereo]
File Edit
View Mode Tools
DJCJe:3 l5lJ
S~em block
l:f"1l fi"';>
L] Remap Audio Input
6] Remap Audio Output
[S.J Audio In
:t~
~:f
:£
if.
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CJ Decoders
CJ fY!atrlx Processors
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W10dows Help
{)Gol • •
~Connect £hEmulation
r-""'----"""'---~=-----~=----------------------------------------------------1
Cu.rloM PPM.In ut.L
C:J Spanning Elements
CJ Graphic Elements &Blocks
TlHF 128 Tap FIR
CUstos PPMh utR
User Devices
---~Custom PPM
Elements
edit
flyoffs /
.
;r------------------------------------------------------------1
Compile Results J.. Fllld Results
Debug /
liUdiciout
Figure 19: DSP Composer FIR Custom Post Processing Module Routing
28
,Qi
u
Figure 20: DSP Composer IIR Custom Post Processing Module Implementation
GJ~~
• DSP Composer- CS47XXX [passthru_stereo_v6]
File
Edit
View
Mode
Tools
Windows
Help
(]!IS]£::3
(!iii]. cPU fi""'{J
i {)Go! G/)'·• ~Connect ;:hEmulation
System block
.--'--=:::_---='---......::.-=-'----_:_::..._c_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _,
['SJ
Remap Audio Input
EJ Remap Audio Outpu
fS1
Q
CJ
CJ
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iti CJ
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+ CJ
cf
lt
(vCii#iiM?PPIJI.IiiiiiJ[L'
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Decoders
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<
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i\
1\ Elements f..
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Page 1
XPage 2 I
KCompile Resu_lts_6r·.-;:~:;::in"'d"'Rc:-es"'uc;;tt-:-s-I\7- ; D " ' e " " b u " ' g c - / r _ - - - - - - - - - - - - - - - - - - - - - - 1
1 _
..
edit
Figure 21: DSP Composer Pass-Thru Custom Post Processing Module Implementation
29
IV. RESULTS
Before testing the speaker in the anechoic chamber, a measurement was taken of
the amplitude frequency response for the DSP board by itself. The measurement was
taken for the pass-thru, FIR, and IIR filter implementations. Note that the pass-thru was
taken before the measurements in Section 2 but is shown here for clarity. The results are
shown below in Figures 22-27. We expect the pass-thru curves to be flat except for the
DC filtering of the tweeter.
The FIR and IIR implementations in the DSP board should
produce a result that matches the target curves generated in HATS as shown in Figures
13 and 14.
10/23/11 21:54:56
Audio Precision
.Lin
+0 2
+0. 1
...-
--
/'
1/ \
+0
d
B
-0 1
'
-r-..
-0 2
\
-0.3
-04
20
100
50
200
500
1k
2k
5k
10k
\
20k
Hz
Figure 22: DSP Board LF Pass-Thru showing Flat Response
10/23/11 22:32:11
Audio Precision
+1 0
Ap
5
0
/
5
d
B
-1 0
'
-1 5
--.
I
I
-20
-25
-
-
-30
20
/
50
100
200
500
1k
2k
5k
10k
20k
Hz
Figure 23: DSP Board HF Pass-Thru showing Flat Response above 60Hz
30
10/23/11 21 ;56:1 5
Audio Precision
0
An
-
5
5
5
0
-22 5
,........,
"''
5
5
0
' '\.
5
-42 5
20
"
?
Hz
Figure 24: DSP Board LF FIR Amplitude Response
FREQUENCY RESPONSE
Audio Precision
10/22/11 12:58;36
0
Ao
.
,
'
'
0
.
,
/
-
/
/
6
/
/
/
'
0
,
Figure 25: DSP Board HF FIR Amplitude Response
10/23/11 21:57:47
Audio Precision
Ao
-.
.........
"\.
-27 5
'
\.
'\.
-37 5
'\.
-42 5
20
Figure 26: DSP Board LF IIR Amplitude Response
10/23/11 21:53:52
Audio Precision
-20
Lin
-22
/
-24
f--
/
-30
/
/
/
/
/
/
-42
20
Figure 27: DSP Board HF IIR Amplitude Response
31
We can see from the resulting plots that the output curves do match closely with the
target curves generated in HATS. There are some differences that could be related both
to the Audio Precision (AP) measurement spacing and for the FIR the interpolation of the
target curve. Based upon this result, the board can now be used to filter the loudspeaker
for anechoic measurements.
As shown in Figure 17, the DSP board was placed between the HATS output and
the amplifier to allow for equalization. (This was also done for the raw measurements.)
The same measurement technique described in Section II was again performed on the
speaker with both FIR and IIR filters. The resulting important metrics including on-axis,
listening window, first reflections, sound power, and directivity index are shown below in
Figures 28 and 29.
HARMAN Audio Test System
910
roo
~
700
Fl
•
m
"-
]
50.0
fu:;qusm;:y(Hl)
AI 00
OnAo::is
/"'81 Wmdow
,••62:
63
To!al SoundPO\II""er
......,B4 TolalSoundPO'I'r'llrDI
/'>•
firstR~fieclions
Figure 28: Key Loudspeaker Data for FIR Equalized Loudspeaker
32
HARMAN Audio Test System
!<!.0
IIJ.O
!1l0
40.0+-~~~~~~~~~~~~~~~~~~~~~~~~~~~~---ccJ.
23
100
100)
100D
frequenc-y {Hz)
Noo OnM:is
,~
• 81 WmdO"N
~- ••
_,..•BJ·TotaiSoundPw.-er
1M Total Sound Powar Dl
N
82: Firs\ Reflections
Figure 29: Key Loudspeaker Data for IIR Equalized Loudspeaker
The results match closely with the predicted curves from HATS (see Figure 12).
In addition, the results of using the FIR and IIR on the on-axis amplitude response and
other metrics are very much the same.
This would seem to indicate the two
implementations sound the same. Appendices G and H show the 0°, 10°, 20°, 30°, 60°,
90°, 120°, and 180° vertical and horizontal anechoic speaker measurements for the FIR
and IIR implementations. It can be noted from the amplitude response measurements that
the off-axis response does vmy between the FIR and IIR.
Subjective listening tests
conducted on the two versions did confirm a difference in timbre when listening outside
the listening window (the ±10° ve1iical and ±30° horizontal angular range).
33
Overall, the results show the use of the FIR and IIR DSP implementations
provided improvement in the objective measurements of the speaker.
The on-axis
amplitude response was modified much more closely to the ideal flat amplitude. The
other key metrics show smooth responses that correlate well with listener preferences
[24].
Subjective listening tests also noted an overall smoother sound with enhanced
midrange. Some improvements are noted. Most important is the reduction of the low-Q
bump centered at 2.7 kHz. This is noticeable in the listening window, first reflections,
and sound-power curves as a shallow peak and can be seen as a dip in the DI curve at the
same frequency. Research by Olive and Toole noted that these types of resonances can
be most noticeable in the sound quality of a loudspeaker [30]. Preventing the occunence
of these low-Q bumps can reduce coloration and provide the loudspeaker with a natural
and open sound. It should be noted that the testing and implementation of this project
was untaken with the assumption that both loudspeakers have the same Thiele/Smail
parameters and therefore would have identical amplitude response. In reality, this can
never be the case due to variation within the transducers. During testing, both speakers
were measured on-axis for a comparison and the result was very close (within ±1 dB).
Unfortunately, this data was not saved and therefore is not available for this report
34
V. APPLICATIONS
As the cost of DSP ICs decrease and loudspeakers become increasingly selfpowered, this form of equalization is becoming attractive. In addition to the reduction in
component cost and size there is also a cost savings in terms of engineering. For product
development purposes, this technique allows the ability to test new EQs on the spot
without the need of rebuilding the unit. It also provides the flexibility of infinite filtering
to easily control problems that formerly would have required time-consuming
engineering solutions. As mentioned in Section IV, most loudspeaker designs assume the
variation in transducers to be within a certain range. This assumption is not always valid
as the Thiele/Small values can vmy greatly between builds. Using this method, each
individual loudspeaker can be calibrated on the line to the reference standard.
The
frequency response of the unit can be measured and the impulse response modified to
assure the most exact match. This would allow for highly precise matching between
loudspeaker pairs.
In addition, the powerful DSPs available today would allow for
custom tailored EQs and/or control of room modes by the end-user.
This increased
flexibility would allow consumers to tailor their loudspeaker to personal taste, or remove
unwanted frequencies caused by problem room acoustics or poor recording. In today's
market, the ability to provide a customizable listening experience can set a product apart
from the competition.
Some examples of products that are already implementing this forward-looking
teclmology include:
35
•
The Genelec 8260A loudspeaker. A bookshelf speaker that is ideal for use as a
professional monitor. The user can modify the speaker's frequency response through
a series of selection switches on the rear of the unit. Altemately, the speaker can be
controlled through the Genelec Loudspeaker Manager software. The speaker may be
calibrated for best in-room response using the included microphone and AutoCal™
software [31].
•
The Meridian DSP8000 Digital Loudspeaker.
audiophile quality DSP equalized loudspeaker.
This product is an example of an
These speakers allow for digital
cmmection to prevent possibility of noise-induced hum from the analog cables. The
built-in DSP allows for custom crossovers with linear phase, steep slopes, and time
delay compensation. The speaker allows for beam steering volume control that is
adjusted to the listener's horizontal and vertical position [32].
•
The JBL OnBeat™ Loudspeaker Dock. This dock is for use with the iPod or iPad. It
utilizes DSP equalization to provide a richly detailed 360-degree soundstage [33].
The sound is quite impressive especially for the product's size, price, and uniquely
stylized appearance (which can often hinder great sound capability).
36
VI. CONCLUSION
This project demonstrates the design and construction of a loudspeaker equalized
using a digital signal processing technique. The entixe process was covered, including
best loudspeaker tuning and construction practices, measurements, equalization (both FIR
and IIR methods) and results. The project has been a success since the equalized speaker
is a significant improvement both objectively and subjectively over the un-equalized
design. The process illustrated in this paper closely matches the most current techniques
employed in indust1y.
This paper notes additional areas of research that could be
explored including reduction of noise and distortion, improved phase linearity, in-room
response control, improved directivity control, and others. During product development,
these areas would also need further exploration and consideration as part of the
equalization process.
37
REFERENCES
[1]
Offenhauser, William H. Jr. "Binaural and stereophonic sound in retrospect",
Joumal of the Audio Engineering Society, Vol. 6(2):67-69, 1958.
[2]
Smith, D.L.A. "'Hi-fi before 1939'-a personal view of the period 1923-39,"
History of Electrical Engineering, Papers Presented at the Sixteenth I.E.E. WeekEnd Meeting on the, vol., no., pp.34-39, 1-3 Jull988
[3]
Rice, Chester W.; Kellogg, Edward W. "Notes on the Development of a New
Type ofHomless Loud Speaker," American Institute of Electrical Engineers,
Transactions ofthe, vol.XLIV, no., pp.461-480, Jan. 1925
[4]
Hilliard, J.K. "The History of Stereophonic Sound Reproduction,"
Proceedings ofthe IRE, vol.50, no.5, pp.776-780, May 1962
[5]
Olson, H.F. "Loudspeakers," Proceedings of the IRE,
vol.50, no.5, pp.730-737, May 1962
[6]
Barwick, J., ed., Loudspeaker and Headphone Handbook, 2nd ed.
Focal Press, Oxford, UK, 1994: 197-219
[7]
Small, Richard H. "Direct radiator loudspeaker system analysis."
J. Audio Eng. Soc, Vol. 20(5):383-395, 1972.
[8]
Linkwitz, Siegfried H. "Active crossover networks for noncoincident drivers."
J. Audio Eng. Soc, Vol. 24(1):2-8, 1976.
[9]
Linkwitz, Siegfried H. "Passive crossover networks for noncoincident drivers."
J. Audio Eng. Soc, Vol. 26(3):149-150, 1978.
[10]
Eargle, John. "Loudspeakers", J. Audio Eng. Soc.
Vol. 25, Number 10/11, October/November 1977: 685-688.
[11]
Holman, T. "The history and future ofDSPs in consumer audio equipment-part I:
history and cunent conditions," Consumer Electronics, 2008. ICCE 2008. Digest
of Technical Papers. Intemational Conference on ,
vol., no., pp.1-2, 9-13 Jan. 2008
[12]
Murphy, David J. "Design considerations for loudspeaker systems."
In Audio Engineering Society Convention 6r, 8 1996.
[13]
Ha1man Intemational. 560/660GTiLITGTi.
Woodbury, NY, October 2007.
[14]
Dickason, Vance. The Loudspeaker Design Cookbook, 61h Ed.
Peterborough, New Hampshire: Audio Amateur Press, 2001.
38
[15]
Thiele, A. N. "Loudspeakers in Vented Boxes: Parts I and II,"
J. Audio Eng. Soc., Vol. 19, No.5, May 1971, pp 382-392
(Reprinted from a 1961 publication in Proc. IRE Australia).
[16]
Small, Richard H., "Vented-Box Loudspeaker Systems, Pari I: Small-Signal
Analysis", J. Audio Engineering Soc., Vol. 21, No. 5, pp 363-444, 1973; "Pari 2:
Large Signal Analysis" J. Audio Eng. Soc, Vol. 21 No.6, pp 438-444, 1973; "Part
3: Synthesis" J. Audio Eng. Soc, Vol. 21 No.7, pp 549-554, 1973; "Part 4:
Appendices" J. Audio Eng. Soc, Vol. 21 No.8, pp 635-639, 1973.
[17]
Everest, F. Alton. The Master Handbook of Acoustics, 4th Ed.
New York: McGraw-Hall, 2001.
[18]
Hany F. Olson. "Direct radiator loudspeaker enclosures."
J. Audio Eng. Soc, Vol. 17(1):22-29, 1969.
[19]
Beranek, Leo, L. Acoustics, 1993 Edition.
Camblidge, MA: Acoustical Society of America, 1996.
[20]
Peter W. Tappan. "Loudspeaker enclosure walls."
In Audio Engineering Society Convention 13, 10 1961.
[21]
Devantier, Allan . "Characterizing the amplitude response of loudspeaker
systems." In Audio Engineering Society Convention 113, 10 2002.
[22]
Hannan International. HATS User Manual. Northridge, CA, 20 June 2011.
[23]
Toole, Floyd E. Sound Reproduction: The Acoustics and Psychoacoustics of
Loudspeakers and Rooms. Burlington, MA: Focal Press, 2008.
[24]
Voishvillo, Alexander; Terekhov, Alexander; Czerwinski, Eugene; Alexandrov,
Sergei. "Graphing, interpretation, and comparison of results of loudspeaker
nonlinear distortion measurements."
J. Audio Eng. Soc, 52(4):332-357, 2004.
[25]
Voishvillo, Alex. "Measurements and perception of nonlinear distmiion comparing numbers and sound quality."
In Audio Engineering Society Convention123, 10 2007.
[26]
Toole, Floyd E. "Loudspeaker measurements and their relationship to listener
preferences: Part 1." J. Audio Eng. Soc, 34(4):227-235, 1986.
[27]
Toole, Floyd E. "Loudspeaker measurements and their relationship to listener
preferences: Part 2." J. Audio Eng. Soc, 34(5):323-348, 1986.
39
[28]
Olive, Sean E. "A multiple regression model for predicting loudspeaker
preference using objective measurements: Part I- listening test results."
In Audio Engineering Society Convention 116, 5 2004.
[29]
Olive, Sean E. "A multiple regression model for predicting loudspeaker
preference using objective measurements: Part II- development of the model." In
Audio Engineering Society Convention 117, 10 2004.
[30]
Lyons, Richard G. Understanding Digital Signal Processing- 3rd Ed.
Boston, MA: Pearson Education, 2011.
[30]
Toole, Floyd E.; Olive,Sean E. "The perception of sound coloration due to
resonances in loudspeakers and other audio components."
In Audio Engineering Society Convention 81, 11 1986.
[31]
Genelec. The New Genelec 8260A Three-Way DSP Loudspeaker System with
Minimum Diffraction Coaxial Teclmology. lisalmi, Finland, December 2009.
[32]
Meridian Audio. DSP8000 Digital Loudspeaker System User Guide.
Cambridgeshire, England, 2010.
[33]
Harman Consumer Inc. JBL OnBeat Users Manual.
Northridge, CA, 2011.
40
,.-...,
>
CJ:l
r:/.1
~
"d
"d
.....-
.....
Parameter
BL
RE
:tvi;r..rs
Sn
.j:::>
I->
Desciiption
Driver Motor Strength (tesla-meters)
DC Resistance of the Voice Coil (ohms)
Datasbeet Value
7.6
3.07
Acoustic Mass of Driver Diaphragm Assy including Air Load (grams)
14.84
Effective Projected Diaphragm Area
2
(Cll1 )
l\Ieasurecl Values
7.22
3.7
14.84
86.6
CMs
Driver Mechanical Compliance (llJTh'N)
86.6
312
LEvc
VAS
Driver Voice Coil Inductance (mH)
0.1
312
0.1
7.06
74
7.06
74
Fs
Vohune of Air Equal to the Driver Compliance.
Driver Free Air Resonance (Hz)
C:~;rs
(liters)
QEs
Driver Electdcal Q
0.37
0.49
QM,S
Dliver Mechanical Q
5.49
Qrs
Driver Total Q
0.34
5.49
0.45
XMA..x
Distance the Voicecoil can travelmaintaililll~_(lll~11l! "#. oftums ill the gap (lllll1)
4.87
4.87
(!)
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>
APPENDIXB
MATLAB LOUDSPEAKER CALCULATIONS
%California State University, Northridge
%MSEE Project
%A Digital Loudspeaker Equalization Technique
%By Colby Buddelmeyer
%Dec 2011
%file: Loudspeaker_Calcs.m
%Program of calculations used to determine:
%Lv port length, f3 (-3dB half power frequency), h (tuning ratio)
%alpha (system compliance ratio), dv (min port diameter)
%inputs include mfgr given transducer values
%(which are modified for measured DC Voicecoil resistance)
%and chosen box size and chosen port diameter
close all
clear all
clc
format shmi
%reference values
c = 345; %velocity of sound in air (m/s)
%Mfg supplied TIS Parameters
BL_mfgr = 7.6; %Driver Motor Strength (Tesla-Meters)
Re_mfgr = 3.07; %DC Voicecoil resistance given by mfgr
fs = 74; %Driver Free Air Resonance (Hz)
Qts_mfgr = 0.34; %Driver Total Q
Qms = 5.49; %Driver Mechanical Q
Qes_mfgr = 0.37; %Driver Electrical Q
Vas_liters = 7.06; %Volume of Air Equal to the Driver Compliance, CMS (liters)
Vas= Vas liters*10"(-3) %convert Vas to meters cubed
Xmax = 4.87e-3; %amount ofvoicecoil overhang (m)
Sd = 8.66e-3; %Effective Projected Diaphragm Area (m''2)
Cms = 3.12e-4; %Driver Mechanical Compliance (m/N)
42
~----------------------------------------------------------------~adjusted values for measured values
BL= 7.22;
Re = 3.7; ~Measured DC Voicecoil resistance
Qes = Re/(BV'2*Cms*fs*2*pi) ~Driver Electrical Q adjusted for real Re
Qts = 1/((1/Qms)+(l/Qes)) ~Driver Mechanical Q adjusted for real Re
~o----------------------------------------------------------------~Selected values:
Vb = 658; ~liters selected (658in"3 = 10.76liters)
r= 1; ~choose 2in diameter port, radius =lin
~----------------------------------------------------------------~calculated
values
Vd = (Sd)*Xmax ~Displacement volume (m"3)
alpha= Vas_liters/(Vb*(0.016387)) ~system compliance ratio
h = 0.87; ~tuning ratio from Figure 2
fb = h*fs ~box tuning frequency (Hz)
Lv = ((1.463e7*r"2)/((fb"2)*Vb))-1.463*r ~pmi length in inches
f3_fs = 0.77; ~f3/fs ratio from Figure 2
f3 = f3_fs*fs ~-3dB frequency
dv = 39.37*((411.25*Vd)/sqrt(fb))"(.5) ~minimum port diameter
43
File Output:
Qes=
0.4893
Qts =
0.4492
Vd=
4.2174e-005
alpha=
0.6548
fb=
64.380
Lv=
3.9013
f3=
56.9800
dv=
1.8304
44
APPENDIXC
LOUDSPEAKER CABINET DRAWINGS
co
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~
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APPENDIXE
UNEQUALIZED SPEAKER MEASUREMENTS
,.m,
Frequ~ntJ
(rlz)
ON AXIS
jHARMAN Audio Test System
:
1000
t[l)
10 DEGREES HORIZONTAL
54
[HARMAN Audio TeSt System ·-·- - - - - ...
i
\00.0
"'0
600
~0+-----------.---------------.---------------.----~
20
too
torn
tlml
flfqt!Ency(Hz)
?v2 Ho120
20 DEGREES HORIZONTAL
HARMAN Audio Test System
I
100.0
9J.O
ffi01----------~---------------.---------------.----~
20
um
\OJ
Frequency (Hz)
.'"v3 Ho1II
30 DEGREES HORIZONTAL
55
tlml
I
1000!
900
70.0
60.0
~·+-----~~-----------.~----------------------------.-----------------------------.-------~
>J
100
1000
10000
Frequm:y(Hz)
60 DEGREES HORJZONTAL
HARMAN Audio Test System
100.0
000
100
1000
10000
;-:;,.9 HorOO
__ j
90 DEGREES HORJZONTAL
56
·--------·-------···---·-·-·HD.O
00.0
"-
]
~
1if.
70.0
'"'
flfqu~ncy
(Hz)
vv12: Hor120
120 DEGREES HORIZONTAL
·HARMAN Audio Test System
'"'"
000
~
e
000
"]
i
£
~
70.0
Frequent)· (Hz)
NJB·Hmlf:O
180 DEGREES HORIZONTAL
57
--------·---"]
l HARMAN Audio Test-Sy-cstc-em
____ . - - - - - - -
~
100.0
''"
600
-----"-;--~-~
910+-'--'-----(
20
tOCu
100
\OOJJ
Frequer.cy{Hz)
l'v37-Ver0
0 DEGREES VERTICAL
HARMAN Audio Test System
100.0
?.
§ roo
,_
~
J
1
70.0
roo
000+-----~-L--~------~------------------------------.-----------------------------.-------~
20
100
l()J]
\OOJJ
Frequeney(Hl)
.rv33 VerlO
10 DEGREES VERTICAL
58
iHARMANAu-dio Te:-::-st;:-;s;;cyc:c;stc:cem=---·---~~~- --
---
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100.0
roo
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.
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-
.
. .
-
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700
600
IOOJ
100
IOOOJ
Frequency {Hz)
.rv39: Ver20
20 DEGREES VERTICAL
HARMAN Audio Test System
1000
roo
.
'5
A
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•
m
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100
Frequsncy(Hz)
;;,;.40 Vu3J
30 DEGREES VERTICAL
59
[HARMAN AUdio Test System ____ - - - - - 1
--------------· -- ---------·----=l
1oo.o
i
roo
700
""
Frequency (Hz)
'""
/V43 Ver60
60 DEGREES VERTICAL
HARMAN Audio Test System
100.0
"'"
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1
70(]
~
Frequ~ncy
(Hz)
90 DEGREES VERTICAL
60
'"""
l HARMAN Audio Test System
!<10
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Fn;quency(Hz}
....V>l9 Vsr120
120 DEGREES VERTICAL
HARMAN Audio Test System
100.0
9)0
~
~
000
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]
j
l
70_0
100
10000
180 DEGREES VERTICAL
61
APPENDIXF
MATLAB HATS2FIR.M CODE AND .DAT OUTPUT FILES
%hats2fir.m
%ECE698C -Fall 2011
%Master's Project
%Student: Colby Buddelmeyer
%Create HF Target FIR Coefficients
close all
clear all
clc
fs=48000;
% fs
ny=fs/2;
%nyquist
%block size
N=2/\9;
%FIR crop length
N2=2/\7;
f1 =(1 :N)'/N*ny;
%hats data
pathin = 'C:\target_curves\'; %path for input txt file
filename= 'HF VTF Target.txt'; %filename
%
datal= impmidata([pathin filename],'\t',5); %5 header lines
datatemp = datal.data;
%
f2=datatemp(:,l); % freq (Hz)
A2=datatemp(:,2); %Mag (dB)
phi2=datatemp(:,3);% phase (deg)
% resample
Al =interpl(f2,A2,fl);
phil =interpl(f2,phi2,fl );
%->H
[Hre Him]= pol2cmi( pi.*phil./180, lO.A(Al./20) ); %polar-> rectangular
H=complex(Hre,Him);
%cmplx
H=[H;conj(flipud(H(2:N-l)))];
%conjugate, flip
% -> generate HF impulse response (FIR coeffiecients)
h=real(ifft(H));
% check plots
figure
62
stem(h(l :N2))
grid
title('HF Impulse Response')
xlabel('Sample')
ylabel('Magnitude')
% export FIR coefficients for Cinus DSP
filename= 'HF_VTF_Target.dat';
fid = fopen(filename,'w');
for i=l:N2
fprintf(fid,'%1.1 Of\n',h(i));
end
fprintf( fid, '\n');
fclose(fid);
%-------------------------------------------------------------%
%-------------------------------------------------------------%
%Create LF Target FIR Coefficients
clear all
clc
fs=48000;
%fs
ny=fs/2;
%nyquist
N=2/\9;
%block size
N2=2/\7;
% FIR crop length
fl =(1 :N)'/N*ny;
%hats data
pathin = 'C:\target_curves\'; %path for input txt file
filename= 'LF VTF Target. txt'; %filename
%
datal = importdata([pathin filename ],'\t',5);
%5 header lines
datatemp = datal.data;
%
f2=datatemp(:,l); % freq (Hz)
A2=datatemp(:,2); %Mag (dB)
phi2=datatemp(: ,3); % phase (de g)
% resample
Al =interp 1(f2,A2,fl );
phil =interp 1(f2,phi2,fl );
%->H
[Hre Him]= pol2cmi( pi.*phil./180, lO.A(Al./20) ); %polar-> rectangular
H=complex(Hre,Him);
%cmplx
H=[H;conj(flipud(H(2:N-l)))];
%conjugate, flip
63
% -> generate LF impulse response (FIR coeffiecients)
h=real(ifft(H));
% check plots
figure
stem(h(l :N2))
grid
title('LF Impulse Response')
xlabel('Sample')
ylabel('Magnitude')
% export FIR Coefficients for Ci1rus DSP
filename= 'LF_VTF_Target.dat';
fid = fopen(filename,'w');
for i=l:N2
fprintf(fid,'%1.1 Of\n',h(i));
end
fprintf(fid,'\n');
fclose(fid);
64
HATS OUTPUT TARGET CURVE .TXT FILES
LF_VTF_Target.dat (contains FIR coefficients for Low Frequency Target Curve):
-0.0014371930
0.0005736167
0.0048760779
0.0107297409
0.0171225662
0.0234335915
0.0293040343
0.0345282788
0.0389745121
0.0425390030
0. 0451311956
0.0466813097
0.0471591215
0.0465925885
0.0450776150
0.0427744660
0.0398909660
0.0366564325
0.0332925363
0.0299875963
0.0268794141
0.0240492608
0.0215267595
0.0193029688
0.0173474878
0.0156251099
0.0141083696
0.0127838796
0. 0116521938
0.0107225509
0.0100049019
0.0095019275
0.0092033373
0.0090838270
0.0091049360
0.0092200233
0.0093808845
0.0095442938
0. 0096769869
0.0097581491
0.0097791912
0.0097412547
0.0096513669
0.0095183447
0.0093494326
0.0091483397
0.0089148926
0.0086460909
0.0083380369
0.0079880738
0.0075965159
0. 0071675388
0.0067090756
0.0062318353
0.0057477596
0.0052683401
0.0048031913
0.0043591714
0.0039401654
0.0035474810
0.0031806658
0.0028384840
0.0025197946
0.0022241357
0.0019519238
0.0017042869
0.0014826340
0.0012881190
0. 0011211597
0.0009811356
0.0008663276
0.0007740932
0.0007012124
0.0006443078
0.0006002365
0.0005663699
0. 0005407198
0.0005219088
0.0005090201
0.0005013866
0.0004983799
0.0004992550
0.0005030783
0.0005087459
0.0005150740
0.0005209272
65
0.0005253481
0.0005276521
0.0005274692
0.0005247262
0.0005195792
0. 0005123211
0.0005032837
0.0004927601
0.0004809581
0.0004679906
0.0004538961
0.0004386768
0.0004223436
0.0004049510
0.0003866161
0.0003675183
0.0003478825
0.0003279521
0.0003079582
0.0002880960
0.0002685087
0.0002492842
0.0002304625
0.0002120480
0.0001940261
0.0001763771
0.0001590883
0.0001421575
0.0001255918
0.0001094045
0.0000936075
0.0000782071
0.0000632013
0.0000485795
0.0000343241
0. 0000204115
0.0000068162
-0.0000064870
-0.0000195211
-0.0000323049
-0.0000448533
-0.0000571773
HF_ VTF_ Target.dat (contains FIR coefficients for High Frequency Target Curve):
0.2611634915
-0.1540284657
-0.0937479214
-0.0487930964
-0.0198679423
-0.0041980410
0.0026036764
0.0048599982
0.0057164909
0.0067312048
0.0080885351
0.0091875410
0.0093002656
0.0080584655
0.0056362179
0.0026477489
-0.0001342738
-0.0020792705
-0.0029000282
-0.0026909445
-0.0018189818
-0.0007396454
0. 0001795724
0.0007604451
0.0010166386
0.0010796901
0.0010939592
0. 0011345108
0.0011792485
0. 0011390284
0.0009230744
0.0005029596
-0.0000567162
-0.0006150688
-0.0010095383
-0.0011244437
-0.0009425352
-0.0005544039
-0.0001245188
0.0001730203
0.0002247990
0.0000217562
-0.0003357722
-0.0006804503
-0.0008420111
-0.0007161973
-0.0003067303
0.0002735440
0.0008440338
0.0012215171
0. 0012850727
0.0010205693
0.0005223763
-0.0000411597
-0.0004894791
-0.0006927144
-0.0006145709
-0.0003200767
0.0000528794
0.0003469441
0.0004432825
0.0003042796
-0.0000169821
-0.0003992997
-0.0006985737
-0.0008015809
-0.0006657524
-0.0003325166
0.0000901355
0.0004670799
0.0006831563
0.0006836059
0.0004880584
0.0001814250
-0.0001207424
-0.0003135977
-0.0003393479
-0.0002047816
0.0000246336
0.0002524654
0.0003869036
0.0003738457
0.0002151661
-0.0000343289
-0.0002885630
-0.0004613206
-0.0004971387
-0.0003888007
-0.0001779696
0.0000613435
0.0002504471
0.0003327853
0.0002923120
0.0001564890
-0.0000154607
-0.0001564750
66
-0.0002150025
-0.0001727270
-0.0000494340
0.0001059948
0.0002345950
0.0002888308
0.0002490235
0.0001292654
-0.0000291598
-0.0001730469
-0.0002563686
-0.0002561097
-0.0001787174
-0.0000563568
0.0000655600
0.0001451704
0.0001586746
0.0001071654
0.0000152344
-0.0000795762
-0.0001406496
-0.0001454431
-0.0000928132
-0.0000025224
0.0000929687
0.0001602777
0.0001769059
0. 0001389549
0.0000611940
-0.0000285780
-0.0001000813
-0.0001312123
APPENDIXG
FIR EQUALIZED SPEAKER MEASUREMENTS
:HARMAN Audio Test System
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120 DEGREES VERTICAL
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74
10000
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APPENDIXH
IIR EQUALIZED SPEAKER MEASUREMENTS
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(Hz)
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180 DEGREES VERTICAL
82
"""
APPENDIX I
LOUDSPEAKER PHOTOS
83
84
85
86
APPENDIXJ
CIRRUS LOGIC CDB47XXX DSP EVALUATION BOARD
87