## 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.

*Step 3*

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