Audio Signal Processing and Coding

COMPUTER EXERCISES

3.7. Design a DPCM coder for a stationary random signal with power spectral density . Use a first-order predictor. Give a block diagram and all pertinent equations. Write a program that implements the DPCM coder and evaluate the MSE at the receiver. Compare the SNR (for the same data) for a PCM system operating at the same bit rate.

3.8. In this problem, you will write a computer program to design a vector quantizer and generate a codebook of size [L × N]. Here, L is the number of codebook entries and N is the codebook dimension.

Step 1

Generate a training set, T_in, of size [Ln × N], where n is the number of training vectors per codevector. Assume L = 16, N = 4, and n = 10. Denote the training set elements as t_in(i, j), for i = 0, 1, … , 159 and j = 0, 1, 2, 3. Use Gaussian vectors of zero mean and unit variance for training.

Step 2

Using the LBG algorithm [Lind80], design a vector quantizer and generate a codebook, C, of size [L × N], i.e., [16 × 4]. In the LBG VQ design, choose the distortion threshold as 0.001. Label the codevectors as c(i, j), for i = 0, 1, … , 15 and j = 0, 1, 2, 3.

Table 3.6. Segmental and overall SNR values for a test signal within and outside the training sequence for different number of codebook entries, L, different codebook dimensions, N, and ε = 0.001.

Figure 3.23. Four-bit VQ design specifications for Problem 3.9.

Step 3

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