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Superposition and the <strong>Frequency</strong> <strong>Response</strong>Example: Three Inputs with• The input is• The frequency response is• The input frequencies areHe j0He j 4He j 3• Thusb k= 1– 11xn 10 4 --n+--= + cos + 3 --n –--48cos 3 4– 1 – e jˆ –= + e j2ˆHe jˆ–e jˆ– 1 + 2cosˆ>> w = 0:pi/200:pi;>> H = 1 - exp(-j*w) + exp(-j*2*w);>> subplot(211)>> plot(w,abs(H))>> grid>> hold>> plot([pi/4 pi/4],[0 3],'r')=ˆ k = 0 43 = e – j0 – 1 + 2cos0 = 1 = e – j 4 – 1 + 2cos 4 = 0.4142e – j 4 = e – j 3 – 1 + 2cos 3 = 0yn = 10 1 + 4 0.4142 cos --n +-- –-- 4 8 4= 10 + 1.6569 cos --n –-- 4 8ECE 2610 Signals and Systems 6–8
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