# In this problem, we compare the performance of a DPCM system

# In this problem, we compare the performance of a DPCM system

In this problem, we compare the performance of a DPCM system with that of an ordinary PCM system using companding. For a sufficiently large number of representation levels, the signal-to-(quantization) noise ratio of PCM systems, in general, is defined by 10 1og10 (SNR) O = a + 6n dB where 2n is the number of representation levels. For a companded PCM system using the µ-law, the constant a is itself defined by a = 4.77 — 20 1og10 (log (1 + µ)) dB, for a DPCM system on the other hand, the constant a lies in the range —3 < a=””>< 15=”” dbs.=”” the=”” formulas=”” quoted=”” herein=”” apply=”” to=”” telephone-quality=”” speech=”” signals.=”” compare=”” the=”” performance=”” of=”” the=”” dpcm=”” system=”” against=”” that=”” of=”” the=”” µ-companded=”” pcm=”” system=”” with=”” µ=”255″ for=”” each=”” of=”” the=”” following=””>

(a) The improvement in (SNR) O realized by DPCM over companded PCM for the same number of bits per sample.

(b) The reduction in the number of bits per sample required by DPCM, compared to the companded PCM for the same (SNR) O.