090223%20HomeWork5

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

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Unformatted text preview: 1 ECE 700 Digital Signal Processing Home Work 5 Due 3/4/09 1. (Scaling function ) Let ( t ) be an orthogonal scaling function with CTFT ( ). Let the corresponding wavelet be ( t ) with CTFT ( ). Starting with the two scale equation for ( t ) and ( t ), show that ( 2 ) ( ) ( ) ( 2 ) ( ) ( ) j j j H e j j G e j = = 2. (Sinc Wavelets) Let sin( ) ( ) t t t = Show that a) - Z { ( ), } t n n is an orthogonal set. b) Use the results from problem 1 to compute ( ) 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....
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090223%20HomeWork5 - 1 ECE 700 Digital Signal Processing...

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