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

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SUMMARY

The discussion focuses on solving a quantization problem in Pulse Code Modulation (PCM) systems as presented in Leon Couch's "Communication Systems," specifically exercise 3.7 from the 6th edition. The required number of bits per word is determined by the formula N > log2(10) * log(50/P), where P represents the maximum allowable quantization noise as a percentage of peak power. A participant attempted to derive this using the signal-to-noise ratio (S/N) relationship of 3M² for PCM but encountered discrepancies in their calculations, indicating a misunderstanding in applying logarithmic transformations.

PREREQUISITES
  • Understanding of Pulse Code Modulation (PCM) systems
  • Familiarity with signal-to-noise ratio (S/N) calculations
  • Knowledge of logarithmic functions and their properties
  • Basic concepts of quantization noise in communication systems
NEXT STEPS
  • Study the derivation of the S/N ratio in PCM systems
  • Learn about quantization noise and its impact on signal quality
  • Explore logarithmic transformations in mathematical proofs
  • Review examples of PCM system design and bit allocation
USEFUL FOR

Students and professionals in electrical engineering, particularly those focusing on communication systems, signal processing, and digital communications.

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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