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Homework_9

# Homework_9 - 1 EE113 Homework 9 Problem 14.5 Consider the...

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1 EE113 Homework 9 Problem 14.5 Consider the following sequences: (a) x ( n )= sin ( π 3 n ) n . (b) y ( n )= e j π 4 · sin ( π 4 n ) n . (c) w ( n )= e j π 4 n · sin ( π 6 n ) n . (d) z ( n )= x ( n ) y ( n ) from parts (a) and (b). Find the DTFTs of the following variations: (a) x (2 n ) . (b) y (2 n ) . (c) w (3 n ) . (d) z (2 n ) . (e) cos( π 3 n ) x (2 n ) . (f) ( - 1) n y (2 n ) . (g) sin( π 4 n ) n y ( n ) . Problem 14.10 Let x ( n )=cos parenleftBig π 4 n parenrightBig · sin ( π 8 ( n - 1) ) n - 1 Find the DTFTs of the following sequences: (a) x (4 n ) . (b) ( - 1) n 2 · x (3 n ) . (c) n 2 x (2 n ) . (d) x ( - n +1) . (e) x ( - 3 n ) . (f) ( - 1) n 1 · x ( n +2) · sin ( π 2 ( n - 1) ) . Problem 14.13 Let x ( n )= sinc ( π 3 n ) . Plot the DTFT of y ( n )=( - 1) n x ( - n +2)cos parenleftBig π 6 n - π 3 parenrightBig September 28, 2011 DRAFT

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2 Problem 14.25 Consider the sequence x ( n ) = 0 . 5 n u ( n ) . Evaluate the following quantities without finding X ( e ) : (a) X ( e j 0 ) . (b) X ( e ) . (c) 1 2 π integraltext π π X ( e ) . (d) 1 2 π integraltext π π | X ( e ) | 2 . Problem 15.17 Given the four pole-zero distributions shown in Fig. 15.17, which ones correspond to low-pass, high-pass, band-pass, or band-stop filters? Problem 15.25 Find the frequencies that are present in the sequences
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Homework_9 - 1 EE113 Homework 9 Problem 14.5 Consider the...

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