Question

7. Determine the system function, magnitude response, and phase response of the fol- lowing systems and use the pole-zero pattern to explain the shape of their magnitude response (a) y[n] = 1(x(n]-x(n-1), ln -2

no need for pole-zero plot

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Answer #1

y[n]) = }(x[n] - x[n-11) Apply DTFT. Y(elº) = x (ed) - e-bºx(ev) Y(e) 1 16-ja H (e%) = (1-eso) h(n) = }[7(n)-3(n-1)] The magH (es)= }(1-220) n(n) = }[(n)-8(n-2)] The magnitude of H (em) is. |H (el)= The phase of H (ei®) is, ZH (et“)=0° +180° – tanH (e)) = (1+2+1° -e719-e350) h(n) = 3 [3(n) +8(n-1)-8(n-2)-8(n-3)] The magnitude of H (em) is, |H (16) = 4 + 4 4 =0 The phas(d) y [n] = {(x[i]+x[n-1) - ([n–3]+x[n–4]) Apply DTFT. Yle%) = x(e1)+-5° X(eº) -Le** X (e)0) -- */ X (el) H (e) = {1+** -e39

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