hw3 - BME 311 PROBLEM SET #3 DUE DATE: February 1, 2006...

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BME 311 PROBLEM SET #3 January 25, 2006 DUE DATE: February 1, 2006 Show work on separate sheets of paper. Include all hand plots, Matlab plots, and Matlab code. 1. [20] Use the Matlab function conv to determine the convolution of the following DT signals. Plot the results for each, and label all axes and title the plots. Pay attention to the time axis! (a) x [ n ] = h [ n ] = ± 1 , n = 0 , 1 , 2 0 , otherwise . (b) x [ n ] = ± 1 , n = 0 , 1 , 2 0 , otherwise and h [ n ] = ± n, n = 0 , 1 , 2 0 , otherwise . (c) x [ n ] = ± 1 , n = 0 , 1 , 2 0 , otherwise and h [ n ] = ± 0 . 5 n , 0 n 5 0 , otherwise . (d) x [ n ] = ± 1 , n = 0 , 1 , 2 0 , otherwise and h [ n ] = ± 0 . 5 | n | , - 5 n 5 0 , otherwise . 7. [15] Consider an LTI system with h ( t ) = rect( t ) = ± 1 , | t | < 0 . 5 0 , otherwise . (a) Determine y ( t ) when x ( t ) = sin( ω 0 t ). For what values of ω 0 does y ( t ) = 0? (b) Determine
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