All about the differential pulse code modulation and adaptive pulse code modulation which is one the classification of pulse code modulation(digital communications).
3. Short Review of PCM
Short review of PCM
For the samples that are
highly correlated,when
encoded by PCM,will
leave Redundant
information behind.
Cause for Redundancy
●High Correlation b/w
conjugation bits.
●When sampled at a rate
slightly greater that Nyquist
rate.(fs>2W)
Where W is maximum
frequency of the analog i/p
signal.
Redundant bits
means Extra bits.
5. High correlation with reference to
DPCM.
During the process of quantization
the signal doesnot change rapidly from one samples to the next sample.
With the result that the difference b/w adjacent samples has variance that is
smaller than the variance of the signal itself.
I.e;variance (difference b/w adjacent sample) < variance (digitalized signal)
So at this case the samples obtained are called as highly correlated samples.
7. The above figure shows a continuing time signal x(t) denoted by a dotted line.
This signal is sampled by flat-top sampling at intervals Ts, 2Ts, 3Ts…nTs.
The sampling frequency is selected to be higher than the Nyquist rate.
These samples are encoded by using 3-bit (7 levels) PCM.
The samples are quantized to the nearest digital level as shown by small circles
in the above figure.
The encoded binary value of each sample is written on the top of the samples.
Just observe the above figure at samples taken at 4Ts, 5Ts, and 6Ts are
encoded to the same value of (110). This information can be carried only by one
sample value. But three samples are carrying the same information means
redundant.
Now let consider the samples at 9Ts and 10Ts, the difference between these
samples only due to the last bit and first two bits are redundant since they do not
change.
9. Solution
DPCM(differential pulse code modulation)
To process this Redundant Information and to
have better output,it is a wise decision to take
the predicted sampled values ,assumed from its
previous output and summarize them with the
original quantised values.And such process is
called as DPCM.
DPCM is a derivative of standard PCM.
10. Differential pulse code modulation (DPCM) is a
procedure of converting an analog into a digital signal
in which an analog signal is sampled and then the
difference between the actual sample value and its
predicted value (predicted value is based on previous
sample or samples) is quantized and then encoded
forming a digital value.
DPCM Reduces the bit rate.
DPCM code words represent differences between
samples unlike PCM where code words represented a
sample value.
11. DPCM analysis
The signals at each point are named as −
x(nTs) is the sampled input
xˆ(nTs) is the predicted sample
e(nTs) is the difference of sampled input and predicted output, often called as prediction
error
v(nTs)is the quantized output
u(nTs)is the predictor input which is actually the summer output of the predictor output
and the quantizer output
12. Quantizer Output is represented as −
v(nTs)=Q[e(nTs)]
=e(nTs)+q(nTs)
v(nTs)= e(nTs)+q(nTs) eqn 1
Where q (nTs) is the quantization error
Predictor input
u(nTs)=xˆ(nTs)+v(nTs) eqn 2
u(nTs)=xˆ(nTs)+e(nTs)+q(nTs) (from eqn 1)
predictor output quantizer output
Result :Predictor input is the sum of
quantizer output and predictor output,
The same predictor circuit is used in the
decoder to reconstruct the original input.
13. DPCM Reciever The block diagram of DPCM
Receiver consists of
a decoder
a predictor
a summer circuit
The input given to the decoder is
processed and that output is summed up with
the output of the predictor, to obtain a better
output.
In the absence of noise, the encoded
receiver input will be the same as the
encoded transmitter output.
14. Prediction gain
Variance of message signal assumed to
be zero mean.
Variance of prediction error
Variance of
quantization
error
15. ADPM
Adaptive differential pulse-code modulation (ADPCM) is a variant
of differential pulse-code modulation (DPCM) that varies the size of the
quantization step,(variation of step size depends upon amplitude levels)
to allow further reduction of the required data bandwidth for a given signal-to-
noise ratio.
Also reduces the bit rate.
ADPCM implemented using forward
Logic for
adaptive
prediction
Or backward estimation.
In forward estimation,unquantized
sample of i/p signal is used to obtain
the step size.
in backward estimation,quantizer
o/p samples are used to obtain step
size.
16. Advantages and Applicationsof ADPCM
Advantages
1)bit rate less
2)Bcz of backward estimation,problems of delay
and requriements of buffer are reduced .
Applications
Voice coding at 32kpbs
Secure transmission over radio channels.
