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**Unformatted text preview: **UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN Department of Electrical and Computer Engineering ECE 410 Digital Signal Processing Homework 12 Wednesday, November 12, 2008 Prof. Bresler, Prof. Jones Due by November 19, 2008 Problem 1 (20 points) Design a length-7, symmetric ramp FIR filter h [ n ] ,n = 0 , 1 ,..., 6 with desired frequency re- sponse D ( ω ) = | ω | (before the linear phase shift) by hand. Use the window design method with a simple truncation ( i.e. , rectangular/boxcar) window and give the filter coefficients as your answer. Using Matlab, plot separately the magnitude and phase of H ( ω ), using at least 1000 points between- π and π . Also plot the ideal desired magnitude response | D ( ω ) | on the same plot as the actual response. Problem 2 (20 points) Use the frequency sampling method respectively to design a length-101 type-1 GLP FIR high- pass filter having cutoff frequency ω c = 3 π/ 4 and generalized linear phase. (a) Find an expression for the filter coefficients { h n } 100 n =0 . (b) Use Matlab to evaluate H d ( nπ 512 ), for n =- 512 ,- 511 ,..., 511. Plot the magnitude and phase responses, respectively, and analyze the plots to see if they are what you expected.responses, respectively, and analyze the plots to see if they are what you expected....

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