Implementing Multirate Filters
in FLEX Devices
T E C H N I C A L
B R I E F
J A N U A R Y
2
1 9 9 6
Finite impulse response (FIR) filters are used in many digital signal processing (DSP) systems to perform signal preconditioning, low-pass filtering, and anti-aliasing functions. Modifications of the FIR
filter allow it to perform multirate filtering, including decimation and interpolation. Multirate filters
are digital filters that change the sampling rate of a digitally represented signal. These filters convert
one set of input samples to another set of data that represents the same analog signal sampled at a
different rate. A system incorporating multirate filters can process data sampled at various rates. The
two types of multirate filtering processes are decimation and interpolation. Decimation reduces the
sample rate of a signal to eliminate redundant information and compact the data, allowing more information to be stored, processed, or transmitted. Interpolation increases the sample rate of a signal
to fill in missing information between samples of a signal.
Applications for multirate filters include:
•
•
•
•
•
•
Digital reconstruction/anti-alias filters for digital audio
Down-sampling a system that employs over-sampling
Image resizing
Narrow-band spectra calculation for vibration analysis
Sample-rate conversion between digital audio systems
Sub-band coding for vocoder speech processing
One example of sample-rate conversion aligns two digital systems of unequal sample frequency
(i.e., DAT at 48 kSps to CD at 44.1 kSps). The signal is first up-sampled (interpolated) to a common
multiple, filtered, and then down-sampled (decimated) to the required sampling rate. This results in
a sample rate conversion that retains the fidelity of the original signal.
Decimating Filter for Sample Rate Reduction
Decimation is commonly used in digital systems that employ over-sampling techniques. Many DSP
systems employ over-sampling (i.e. 8x) for purposes such as noise shaping. The final stages of lowpass filtering and decimation are combined into a decimating filter that converts the oversampled
rate back to the original rate.
A decimating filter only computes every nth result, where n is the decimation factor. Decimating
filters are created by simply discarding any unwanted results from a regular FIR filter. For example,
if the input data rate is 100 MHz, to decimate the data rate by 2, the output data rate is only
50 MHz. See Figure 1. However, this implementation is inefficient. The low-pass FIR filter must run
at the XIN data rate (i.e., 100 MHz), which wastes half of the computations performed by the FIR
filter.
Figure 1. Typical Decimating Filter
XIN = 100 MHz
Low-Pass
FIR Filter
100 MHz
Keep Only
Every Other
Sample
50 MHz
M-TB8-DSP3-01
®
Figure 2 shows the shift register section of a 16-tap, decimate-by-2 FIR filter. This filter only computes every other result (i.e., the data skips every other register). Therefore, most of the filter runs at
the output rate rather than the input rate, saving about 50% of the power consumed by the full-speed
filter. The filter in Figure 2 also permits a faster input sample rate. For example, if the input data
rate is 100 MHz, only the T flipflop must run at the 100-MHz rate—the rest of the FIR filter runs at
50 MHz.
Figure 2. FLEX Decimating Filter
Repeating Decimating Filter Block
x(n)
D
Q
EN
D
Repeating
Decimating
Filter Block
Q
EN
Repeating
Decimating
Filter Block
Repeating
Decimating
Filter Block
50 MHz
TFF
VCC
100 MHz
D
Q
s(1)
s(2)
s(3)
s(4)
s(5)
s(6)
s(7)
s(8)
Interpolating Filter
An interpolating filter (i.e., an up-sampling filter) performs the opposite function of a decimating
filter: it increases the sample rate by a factor of n. One way to perform interpolation is to add extra
zero-value samples between each input data sample. See Figure 3. The data stream (with the zeros) is
sent through a low-pass filter; this output data rate is at a higher sample rate than the input data rate.
Figure 3. Stuffing Zeros into the Data Stream
Input Data Stream
Sampling Period
Divided by Two
(Period = T)
T
T
2
Figure 4 shows the interpolating filter block diagram.
Figure 4. Interpolating Filter
T
Zero
Stuffer
T
2
Low-Pass
Filter
T
2
Because much of the input data to the low-pass filter is zero, the shift register is always sparsely
populated. Figure 5 shows an example of an interpolating filter where the data is up-sampled by two.
One input to each of the symmetric tap adders is always zero. Therefore, the adder is not necessary.
Copyright © 1996 Altera Corporation. Altera and FLEX are trademarks and/or service marks of Altera Corporation in the United States and other countries. Other brands or products are trademarks of their respective holders.
The specifications contained herein are subject to change without notice. All rights reserved.
®
Figure 5. Up-Sampling Data by Two
0
x(1)
0
x(2)
0
x(3)
0
x(4)
8
8
0
x(n)
8
0
x(8)
8
8
8
0
x(7)
8
8
0
x(6)
8
x(5)
8
8
s(1) = x(1)
8
s(2) = x(8)
s(3) = x(2)
8
8
8
s(4) = x(7)
s(5) = x(3)
8
s(6) = x(6)
8
s(7) = x(4)
s(8) = x(5)
AN 73 (Implementing FIR Filters in FLEX Devices) provides further details on the optimization of
decimation and interpolation functions. This application note illustrates the ease of converting a
FLEX FIR filter into a decimation or interpolation filter by simply re-routing the shift register. This
methodology provides great flexibility, enabling one FLEX device to be reconfigured for normal,
decimation, and interpolation modes.
DSP Design Kit Available from Altera
FLEX devices provide the high performance of custom DSP solutions without sacrificing flexibility.
Altera’s DSP Design Kit includes customizable building blocks for implementing DSP functions.
These building blocks include fully parallel FIR filters with parameterized features. DSP functions are
optimized for Altera FLEX architectures to allow customization for fitting specific design parameters.
The documents listed below provide more detailed information. Part numbers are in parentheses.
Product Information Bulletins
PIB 23 Digital Signal Processing in FLEX
Devices (A-PIB-023-01)
Application Notes
AN 73 Implementing FIR Filters in FLEX
Devices (A-AN-073-01)
You can request these documents from:
• Altera Express fax-back service at (800) 5-ALTERA
• World-Wide Web at http://www.altera.com
• Your local Altera sales representative
Copyright © 1996 Altera Corporation. Altera and FLEX are trademarks and/or service marks of Altera Corporation in the United States and other countries. Other brands or products are trademarks of their respective holders.
The specifications contained herein are subject to change without notice. All rights reserved.
®