why is this required in PCM ?

[desperado1]

quantization process noise pcm

In order to have a uniform signal to quantization noise ratio, why the stepsize must be small for small amplitude signals and large for large amp. signals ?

 

[rramya]

step required by pcm

Hi,
As per the formula the quantization noise power which is (delta)^2/12
we can call quantization noise power as variance (white noise process with zero mean).
very slowly varying signals (will of low freq) will not have much variation in amplitude w.r.to time(where noise variance will low). Since the variance is directly proportional to delta ^2 , for low variance, the step size is small.
For fast varying signal (will have high freq) will have large variation in amplitude w.r.to time. automatically (noise)variancewill high. Hence the larger step size.


Happy learning

 

[desperado1]

Can u please elaboarate this please ?
"For a large variation in amplitude signal, why the noise variance is high ? "

 

[rramya]

In PCM we do quantizing.
For quantizing, we usually limit the amplitude of the meassage signal (speech/video) to the range -A to +A.

note : +A need not be the peak amplitude of the mesage signal.

Now the amplitude range (-A,A) is divided into L Uniformly spaced intervals.

suppose if, the signal instantaneous amplitude is in
mid level between two representation level, then the quantizer will do
1.) Either rounding so that upper representation level of that particular signal instantaneous amplitude is assumed and these quantized samples are coded and transmitted as binary pulses.
2.) Either truncation so that lower representation level is assumed at thst time and these quantized samples are coded and transmitted as binary pulses.

these approxiamtion can cause quantization noise

SO if the signal vary very much suddenly, there are two possibilities.
1.This amplitude signal at that particular instant may be very high than scaled amplitude range (-A,A) done for quantizing. so we actually do truncation and fix (assume) our signal amplitude as
+A so the quantization noise will be very high.
2.Especially, In DM , we have slope overload distortion, to minimize that distortion, we usually allot large step size for the signal that changes in dynamic range. so as per formula, large delta(step size) leads to larger quantization noise.

Hope it will you some insight.

Happy learning

 

[desperado1]

thanks a lot.............