(1) (a) Consider the discrete-time signal (n), which has the following Fourier-transform given by X (ed) - Nel) D(jw) wh

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1 A Consider The Discrete Time Signal N Which Has The Following Fourier Transform Given By X Ed Nel D Jw Wh 1 (36.49 KiB) Viewed 36 times

(1) (a) Consider the discrete-time signal (n), which has the following Fourier-transform given by X (ed) - Nel) D(jw) where N(e) brejk 9 k=0 4 D(ed) -Σ aze اينات I=0 and bo = 0, bi = 84, b2 = 272. b3 = 108, ba = 72. ao = 144, a 408, Q2 = 625, 23 = 492,04 = 144. = (1) Find the poles and zeros of X (z). Hence, determine and sketch the ROC of X (2). Does it include the unit-circle? (ii) Determine the partial fraction expansion of X(z). Hence, identify the terms belonging to the causal and non-causal parts of the signal. (ii) Write an expression for :(n) identifying the causal part 11(n), and non-causal part 12(n) of r(n). (iv) Plot (n) and find its energy. (v) Plot the magnitude and phase spectra of the signal.