How Do You Solve the PCM System Quantization Problem from Leon Couch's Book?

AI Thread Summary
The discussion focuses on solving an exercise from Leon Couch's "Communication Systems" regarding the quantization noise in a PCM binary system. The key requirement is that the quantization noise must not exceed a specified percentage of the peak power, leading to the formula for the number of bits per word: N > log2(10) * log(50/P). The user attempted to derive this by relating the signal-to-noise ratio to the quantization noise but encountered discrepancies in their calculations. Clarification is sought on the correct approach to reach the desired formula, highlighting the complexities involved in PCM quantization analysis. Understanding the relationship between signal-to-noise ratio and quantization noise is crucial for accurate solutions in PCM systems.
Domenico94
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Homework Statement


Hi everyone. I was trying to solve an exercise from the book Leon couch, communication systems, number 3.7 of the 6th edition. This is the statement:
In a PCM binary system, the quantisation noise mustn t exceed the percentage value P of the peak power. Show that the required number of bit for each word is:

N> log2(10)*log(50/P).

I tried to solve it by applying this reasoning :
The s/n ratio is equal to 3M^2 for a PCM system. Then
If N<(p/100)*s, then s/n>(100/p). Then I solve it by passing to decibel, and making the logaritm, but I obtain something quite different, and I don t undestand where I was wrong.
 
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