COMP 150 MDC - Fall 2016 - Homework 6

Due Thursday, 27 October, 2016 in class

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  1. (This is a modified version of Problem 3 from Chapter 9.) Specify the decision boundaries and representation levels for an optimal 3-bit uniform quantizer for a source that has Laplacian distribution with mean 3 and variance 4. What is the loading factor and mean square error for your quantizer?
  2. Find a nonuniform quantizer for the above source with lower mean square error.
  3. (This is a modified version of Problem 6 from Chapter 9.) For the companding quantizer of Example 9.6.1, what are the outputs for the following inputs:

    -0.8, 1.2, 0.5, 0.6, 3.2, -0.3

    Compare your results with a uniform quantizer with the same number of levels and comment on the difference. (The compressor function is 2x on [-1, 1], (2x+4)/3 for x values in [1, 4] and (2x-4)/3 for x values in [-4, -1].)
  4. (This is a modified version of Problem 9 from Chapter 9.)
    1. Plot the rate-distortion function for a Gaussian source with mean zero and variance 2.
    2. Assuming fixed-length codewords, compute the rate and distortion for 1, 2, and 3-bit pdf-optimized nonuniform quantizers for this source. Mark these points on the above graph as x's.
    3. For the 2 and 3-bit quantizers, assume that the quantizer outputs are entropy coded. Plot the corresponding points on the above graph as o's.