090223%20HomeWork5

# 090223%20HomeWork5 - 1 ECE 700 Digital Signal Processing...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 ECE 700 Digital Signal Processing Home Work 5 Due 3/4/09 1. (Scaling function ) Let φ ( t ) be an orthogonal scaling function with CTFT ( ). Φ Ω Let the corresponding wavelet be ψ ( t ) with CTFT ( ). Ψ Ω Starting with the two scale equation for φ ( t ) and ψ ( t ), show that ( 2 ) ( ) ( ) ( 2 ) ( ) ( ) j j j H e j j G e j Ω Ω Φ Ω = Φ Ω Ψ Ω = Φ Ω 2. (Sinc Wavelets) Let sin( ) ( ) t t t π φ π = Show that a) φ- ∈ Z { ( ), } t n n is an orthogonal set. b) Use the results from problem 1 to compute ϖ ϖ ( ) and G( ). j j H e e c) Take the inverse DTFT of your results from part b to compute h [ n ] and g [ n ]. 3. (Haar wavelets) Consider expanding the function f ( t ) shown below using the Haar wavelets. What are the wavelet coefficients in this case? 1, 0 1 ( ) 0, otherwise t f t ≤ < = 2 Part II (MATLAB Exercises) For the MATLAB exercises below, download the ZIP file HW5MATLAB.zip from Carmen, and unzip it in a directory of your choice. This directory will need to be on Carmen, and unzip it in a directory of your choice....
View Full Document

## This note was uploaded on 04/18/2009 for the course ECE 700 taught by Professor Un during the Winter '09 term at Ohio State.

### Page1 / 3

090223%20HomeWork5 - 1 ECE 700 Digital Signal Processing...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online