LAB_4 - ECE425 LAB 4 FALL 2006 HAAR VS. DFT ANALYSIS...

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ECE425 LAB 4 FALL 2006 HAAR VS. DFT ANALYSIS INTRODUCTION: Efficient representation of a signal (i.e., “good” representation with minimum resources) can depend strongly on the choice of basis functions. We have known about DFT analysis for a long time, and recently we have looked at wavelet analysis in terms of Haar Wavelets or Haar Functions. Here we want to develop tools for computing these transforms, for reducing the number of coefficients, and for computing the resulting error. 1. THE DFT AS A MATRIX: Here we will be looking at length 16 real-valued signals. In Matlab, we easily compute the DFT of such a signal using fft . Another way is to develop a 16x16 matrix D such that the DFT of a signal x is X=Dx. Find this matrix and see if it gives the same answer as fft for a variety of test signals. 2. THE HAAR TRANSFORM AS A MATRIX: We have recently looked at Haar Functions or Haar Wavelets, and have seen that the Haar coefficients can be computed using a matrix, or using a filter bank. For this lab, we
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LAB_4 - ECE425 LAB 4 FALL 2006 HAAR VS. DFT ANALYSIS...

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