EE341Spring2011Hw8Soln

EE341Spring2011Hw8Soln - 5 .27. (a) W(&W) will be t he...

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5.27. (a) W(&W) will be the periodic convolution of X(ei W ) with P(&W). The Fourier transforms are sketched in Figure S5.27. (b) The Fourier transform of Y(ei W ) of y[nJis Y(ei W ) = P(eiW)H(ei W ). The LTI system with unit sample response h[n] is an ideal lowpass filter with cutoff frequency 1f /2. Therefore, y(&W) for each choice of p[n] are as shown in Figure S5.27. Therefore, y[nJ in each case is: (i) = 0 '('1') [] - sin(1Tn/2) _ l-cos{1Tn/2) 1 y n - 2?m 7I'2n2 ( ir) [ J= sin(1Tn{2) _ cos(7I'n/2) 1 y n 7I'2n 2!1'n (iv) y[n] = 2 [Sin(;:/4) r (v) = ! [Sin(:I2>] -t:(e.~ ~-.i.\ L fv~ D" -Ii rr >w ltt/III) ~-lli) if,. , . . . n __ --I-~ ----v". 1 Q,-il'r ) fb-iv) Figure 85.27 Ht'WJ
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5.28. Let 6 2~ 1: X(ei )G(eJ(W-6»)d9 = 1 + e- jw
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EE341Spring2011Hw8Soln - 5 .27. (a) W(&W) will be t he...

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