Audio Signal Processing and Coding

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)

1. Design a uniform PCM quantizer with four levels.
2. 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 ±σ_x 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.