February 2007
Intermediate to advanced
464 pages
14h 40m
English
Content preview from Audio Signal Processing and Coding
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PROBLEMS
3.1. Derive the PCM 6 dB per bit rule when the quantization error has a uniform probability density function.
3.2. For a signal with Gaussian distribution (zero mean and unit variance)
- Design a uniform PCM quantizer with four levels.
- Design a nonuniform four-level quantizer that is optimized for the signal PDF. Compare with the uniform PCM in terms of SNR.
3.3. For the PDF 
, determine the mean, the variance, and the probability that a random variable will fall within ±σx of the mean value.
Figure 3.22. An example PDF.
3.4. For the PDF, p(x), given in Figure 3.22, design a four-level PDF-optimized PCM and compare to uniform PCM in terms of SNR.
3.5. Give and justify a formula for the number of bits in simple vector quantization with N × 1 vectors and L template vectors.
3.6. Give in terms of L and N the order of complexity in a VQ codebook search, where L is the number of codebook entries and N is the codebook dimension. Consider the following cases: (i) a simple VQ, (ii) a multi-step VQ, and (iii) a split VQ. For (ii) and (iii), use configurations given in Figure 3.12 and Figure 3.14, respectively.
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