EGR 544 Communication Theory
4. Coding Techniques for Analog Signal
Z. Aliyazicioglu Electrical and Computer Engineering Department Cal Poly Pomona
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Z. Aliyazicioglu Electrical and Computer Engineering Department Cal Poly Pomona
Coding Techniques for Analog Source • There are several analog source coding techniques • Most of the coding techniques are applied speech and image coding Three type of analog source encoding • Temporal Waveform coding :design to represent digitally the time-domain characteristic of the signal • Spectral waveform coding: signal waveform is sub divided into different frequency band and either the time waveform in each band or its spectral characteristics are encoded. • Model-based coding: Based on the mathematical model of source.
Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 2
1
Temporal Waveform Coding Most common used methods: • Pulse-code modulation (PCM) • Differential pulse-code modulation (DPCM) • Delta modulation(DM) Pulse-code modulation (PCM) Let’s have continuous source function x (t ) and each sample taken from x (t ) is xn at sampling rate fs ≥ 2W, where W is the highest frequency in x (t ) . In PCM, each sample is quantized to one of 2R amplitude level, where number of binary digits used to represent each sample. The bit rate will be Rfs [bit/s] Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 3
Pulse-code modulation (PCM) • The quantized value will be xn and xn = xn − qn
qn quantization error
• Assume that a uniform quantizer is used, then PDF of quantization error is 1 p( q) = ∆ 0
if −
∆ ∆ ≤q≤ 2 2 o.w.
∆ is step size and obtained ∆ = 2− R
Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 4
2
Pulse-code modulation (PCM) Mean square value of the quantization error (or noise) power is ∆/2
E ( q2 ) = ∫
−∆ / 2
q 2 p( q) dq =
1 2 1 −2 R 2 ∆ = 12 12
Mean square value of the quantization error power in dB
E ( q 2 ) dB = 10log
1 2 1 ∆ = 10log 2 −2 R = −10.8 − 6 R [dB] 12 12
Quantization noise decreases by 6dB/bit Quantization noise for 8 bit -58.8 dB It can be measured by signal-to-quantization noise ratio (SQNR) in dB SQNR = 10log
P (average power of source signal) [dB] E(q 2 )
If source is sinusoidal Cal Poly Pomona
SQNR = −1.76 + 6.02 R [dB]
Electrical & Computer Engineering Dept.
EGR 544-2 5
Pulse-code modulation (PCM) • The non-uniform quantizer characteristic can be obtained by passing the signal through a non-linear device the compress the signal amplitude • For example: µ-law compressor: A Logarithmic compressor input-output function
y =
log(1 + µ x ) log(1 + µ )
µ is a parameter that gives desired compression µ=225 selected for USA and Canada. µ=225 , it will drop quantization noise power about –77dB for 7 bit quantization Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 6
3
Example of µ -law
µ=20
µ=100 Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 7
Differential pulse-code modulation (DPCM) • The differences between samples are expected to be smaller than the actual sampled amplitude value. • The simple solution is to encode the differences between successive samples rather than the samples themselves. • Fever bits require to represent the differences
Let xn denote the current sample from the source and let xn denote the predicted value of xn, defined as p
xˆn = ∑ ai xn −1 i =1
• xn is weighted linear combination of the past p samples and {ai} are the predicted coefficient that are selected to minimize the error between xn and xn
Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 8
4
Differential pulse-code modulation (DPCM) • The mean square error between xn and xn is given 2 p ε p = E (e ) = E xn − ∑ ai xn−i i =1 2 n
p
p
i =1
i =1
= E ( xn2 ) − 2∑ ai E ( xn xn −i ) + ∑
p
∑ a a E( x i
j =1
x
n −i n − j
j
)
• Selecting {ai } to minimize the MSE Assume that source output is stationary and φ(m) shows the autocorrelation function of xn p
p
i =1
i =1
ε p = φ (0) − 2∑ aiφ (i ) + ∑ • To minimize εp set
j =1
i
j
p
∑ a φ (i − j ) = φ ( j ) i =1
Cal Poly Pomona
p
∑ a a φ (i − j )
i
Electrical & Computer Engineering Dept.
EGR 544-2 9
Differential pulse-code modulation (DPCM) • If autocorrelation function is not known, it may be estimated as
The quantized sample xn differs from the input xn by quantization error qn
To low-pass filter
Decoder
Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 11
Delta Modulation en = ( xn − xˆn ) To transmitter
Predicted (estimated) value
qn = en − en
xˆn = xn−1 = xˆn −1 + en −1 xˆn = xn−1 + qn−1
= en − ( xn − xˆn ) Source Encoder Output
Source Decoder Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 12
6
Delta Modulation Equivalent realization of Delta modulation To transmitter
Source Encoder
Output
Source Decoder Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 13
Delta Modulation • The performance of the DM encoder is limited by two types of distortion • Slope overload distortion • Step size is too small • Granular noise • Step size is to large Granular noise
Slope-overload distortion
Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 14
7
Delta Modulation •
Alternative solution is variable step size: Step size is increased when the waveform has steep slope and decreased when the waveform has a relatively small slope
• One of the method is called continuous variable slope delta modulation (CVSD) If en , en−1 ,and en−2 has same sign
∆ n = α∆ n −1 + k1 Granular noise
Otherwise
∆ n = α∆ n −1 = k2 where
0 0
k =1
The difference between xn and xˆn
The filter coefficients {ak } can be selected to minimize the mean square error
p
en = xn − xˆn = xn − ∑ ak xn −k k =1
Cal Poly Pomona
Electrical & Computer Engineering Dept.
EGR 544-2 21
Encoding methods for Speech signal • Speech signal band limits 200-3200Hz. • Sampling frequency 8000samples/s for all encoder except DM Encoding method
Quantization
Coder
Transmission rate(bits/s)
PCM Log PCM DPCM ADPCM DM ADM
Linear Logarithmic Logarithmic Adaptive Binary Adaptive Binary
![FOVEATED [1] and region-of-interest [2] coding techniques](https://kipdf.com/img/300x300/foveated-1-and-region-of-interest-2-coding-techniq_5b336a2d097c47757b8b45c6.jpg)
