# HW4_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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Department of Electrical and Computer Engineering ECE 410 Digital Signal Processing Homework 4 Wednesday, September 17, 2008 Prof. Bresler, Prof. Jones Due by September 24, 2008 Problem 1 (10 points) Complete the following signal ﬂow diagram for 8-point, radix-2 decimation-in-time FFT algorithm, and use it to compute the DFT of the 8-pt sequence x [ n ] = {- 1 , - 4 , - 2 , - 3 , 1 , 4 , 2 , 3 } by hand . Specify the value of the input sequence, output sequence, and the signal values after each stage, i.e. , at all the points marked by the solid circles in the diagram. Problem 2 (10 points) The sequence x [ n ] = cos ± π 8 n ² , -∞ < n < was obtained by sampling a continuous-time signal x c ( t ) = cos(Ω 0 t ) , -∞ < t < at a sampling rate of 1024 samples/sec. What are three possible values of Ω 0 that can result in the same sequence of x [ n ]? Problem 3

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HW4_FA08 - UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN...

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