*This preview shows
pages
1–2. Sign up to
view the full content.*

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

This ** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
This is the end of the preview. Sign up
to
access the rest of the document.