Dr.subhash techinecal campus
Junagadh.
Subject: AUDIO & VIDEO SYSTEM
based on..
“SAMPLING & QUANTIZATION
PROCESS”
Guided By: Prof.N.Y.Chavda
Submitted By:
Dodiya Pankaj k. (140833111017)
Koshiya Hardik l. (140833111018)
Varu Akash a.
(140833111021)
Sakariya Brijesh v. (140833111022)
Outline
• Analog To Digital Converter
• Review of sampling
–
–
–
–
–
Nyquist sampling theory: frequency and time domain
Alliasing
Bandpass sampling theory
Natural Sampling
Aperture Effect
• Quantization
– Quantization.
– Quantization Error.
– Companding.
Claude Elwood Shannon, Harry Nyquist
Sampling Theory
• In many applications it is useful to represent a
signal in terms of sample values taken at
appropriately spaced intervals.
• The signal can be reconstructed from the
sampled waveform by passing it through an ideal
low pass filter.
• In order to ensure a faithful reconstruction, the
original signal must be sampled at an appropriate
rate as described in the sampling theorem.
– A real-valued band-limited signal having no spectral
components above a frequency of FM Hz is determined
uniquely by its values at uniform intervals spaced no
greater than (1/2FM) seconds apart.
Sampling Block Diagram
• Consider a band-limited signal f(t) having no
spectral component above B Hz.
• Let each rectangular sampling pulse have unit
amplitudes,
seconds in width and occurring at
fs(t)
interval of T seconds.
f(t)
A/D
conversion
T
Sampling
Sampling
Sampled waveform
Signal waveform
0
0
1
201
1
201
Impulse sampler
0
1
201
Impulse Sampling
with increasing sampling time T
Sampled waveform
Sampled waveform
0
0
1
1
201
Sampled waveform
201
Sampled waveform
0
0
1
201
1
201
Introduction
Let g (t ) denote the ideal sampled signal
g ( t ) 

 g (nT )  (t  nT )
n  
s
s
where Ts : sampling period
f s  1 Ts : sampling rate
EE 541/451 Fall 2006
(3.1)
Interpolation
If the sampling is at exactly the Nyquist rate, then
 t  nTs 

g (t )   g (nTs ) sin c
n  
 Ts 

Under Sampling, Aliasing
Avoid Aliasing
• Band-limiting signals (by filtering)
before sampling.
• Sampling at a rate that is greater
than the Nyquist rate.
f(t)
Anti-aliasing
filter
A/D
conversion
T
Sampling
fs(t)
Practical Interpolation
Sinc-function interpolation is theoretically perfect but it can
never be done in practice because it requires samples from
the signal for all time. Therefore real interpolation must
make some compromises. Probably the simplest realizable
interpolation technique is what a DAC does.
Natural sampling
(Sampling with rectangular waveform)
Signal waveform
Sampled waveform
0
0
1
1
201
401
601
801
1001
1201
1401
1601
1801
201
401
2001
Natural sampler
0
1
201
401
601
801
1001 1201 1401 1601 1801 2001
601
801
1001
1201
1401
1601
1801
20
Bandpass Sampling
• A signal of bandwidth B, occupying the frequency
range between fL and fL + B, can be uniquely
reconstructed from the samples if sampled at a
rate fS :
fS >= 2 * (f2-f1)(1+M/N)
where M=f2/(f2-f1))-N and N = floor(f2/(f2-f1)),
B= f2-f1, f2=NB+MB.
Time Division Multiplexing
• Entire spectrum is allocated for a channel (user) for a limited
time.
• The user must not transmit until its
k1
k2
k3
k4
k5
k6
next turn.
• Used in 2nd generation
c
Frequency
f
t
• Advantages:
– Only one carrier in Time
the medium at any given time
– High throughput even for many users
– Common TX component design, only one power amplifier
– Flexible allocation of resources (multiple time slots).
Quantization
• Scalar Quantizer Block Diagram
Quantization Procedure
Quantization Error
Quantization Type
Mid-tread
Mid-rise
Quantization Noise
Quantization Noise
• What happens if no. of representation
level increases?
• >64 distortion is significant
• Quantization
error
is
uniformly
distributed in interval (-∆/2 to ∆/2).
• The Avg. Power of Quantizing error qe
Companding
• Process of uniform Quantization is not
possible.
• Example: Speech, Video.
• The variation in power from weak signal to
powerful signal is 40 db.
• So Ratio 1000:1
• Excursion in Large amplitude occurs less
frequently.
• This Scenario is cared by Non- Uniform
Quantization.
Non-uniform Quantizer
F: nonlinear compressing function
F-1: nonlinear expanding function
F and F-1: nonlinear compander
X
y
F
Example
F: y=log(x)
Q
^
y
F-1
^
x
F-1: x=exp(x)
We will study nonuniform quantization by PCM example next
A law and  law
Input-Output characteristic
of Compressor