Set Homework 2
ACM 126b, Spring 2009 Assigned Tuesday, 4/20/2009. Due 5 pm, Monday, 5/3/2009 to Sheila Shull, Firestone 217. Please refer to the homework guide when preparing your work. This assignment covers transform coding and block cosine bases. (1) (Audio coding). Read Section 8.4 of Mallat's book to learn about lapped orthogonal projectors, local cosine bases, and the method for discretizing the transform. (a) Write a Matlab function that decomposes an input signal in a discrete local cosine basis with equal-length windows. The window width should be a parameter of the function. You may use the simple window 0 defined on page 419. To deal with the boundaries, just extend the input signal by zero. (b) Use your Matlab function to make a timefrequency plot of the handel signal, akin to Figure 8.19(b) of Mallat. You'll have to determine an appropriate window width. (c) Now, let's develop a nonlinear approximation method for audio signals. Step 1. Compute the local cosine coefficients of the input signal with windows of width W . Step 2. Discard all coefficients below a threshold T . (d) Why can we compute the 2 approximation error the in coefficient space without reconstructing the signal? (e) For the handel signal, plot the nonlinear approximation error (in 2 ) as a function of both the window width W and the threshold T . Identify a good window width W . (f) Make a log-log plot of the nonlinear approximation error as a function of the threshold with window width W . What does this plot tell us? (g) To create a transform coder, we replace Step 2 with a discretization. Step 2 . Quantize the coefficients uniformly with bin width 2- . Make the zero bin twice as wide as the others. (h) For the handel signal, make a semilog plot of the transform coding error as a function of the bin width 2- using windows of ...