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# Homework_10 - 1 EE113 Homework 10 Problem 17.3 Let x(n =(n...

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1 EE113 Homework 10 Problem 17.3 Let x ( n ) = δ ( n + 2) δ ( n ) + δ ( n 2) . (a) Determine its DTFT. (b) Sample the DTFT to obtain the 6-point DFT of x ( n ) . (c) Obtain the same 6-point DFT using (17.20). (d) Obtain the same 6-point DFT using (17.21). Does aliasing in time occur? Problem 17.8 Find the inverse DFTs of the DFT sequences defined below over one period, 0 k 5 : (a) X ( k ) = (1 , 0 , 1 , 0 , 1 , 0) . (b) Y ( k ) = e jπk · X ( k ) . (c) Y ( k ) = e - j π 3 k · X ( k ) . (d) Y ( k ) = sin ( π 3 k ) · X ( k ) . In each case, plot | x ( n ) | and x ( n ) . Problem 17.16 Determine the N-point DFT of the sequences (a) x ( n ) = sin(2 n ) · cos 2 ( n ) . (b) x ( n ) = cos( n ) · sin 2 ( n ) . Problem 17.21 Figure 17.22 shows a 4-point DFT. Give two sequences x ( n ) whose 4-point DFTs agree with the figure. Problem 18.11 Let x ( n ) = { 1 , 2 , 1 , 1 2 } . (a) Find the 4-point DFT of ( 1) n · x ( n ) . (b) Find the 4-point DFT of e - j 3 π 2 n · x ( n ) . Problem 18.17 Compute the circular convolution cos parenleftbigg 2 πn N parenrightbigg cos parenleftbigg 4 πn N parenrightbigg September 28, 2011 DRAFT

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2 where both sequences are limited to the interval 0 n N 1 .
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Homework_10 - 1 EE113 Homework 10 Problem 17.3 Let x(n =(n...

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