- Consider the discrete-time signal (n), which is absolutely summable, and has the following z-transform given by : bez-

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Consider The Discrete Time Signal N Which Is Absolutely Summable And Has The Following Z Transform Given By Bez 1 (38.57 KiB) Viewed 41 times

- Consider the discrete-time signal (n), which is absolutely summable, and has the following z-transform given by : bez- 0 X (2) = 4 ko and bo = 0, b = 84, b2 = 272, by = 108, be = 72, 0o = 144, a1 = 408, 42 = 625, a3 = 492,24 = 144. (i) Find the poles and zeros of X(z). Hence, determine and sketch the ROC of X(z). Does it include the unit-circle? 2 (ii) Determine the partial fraction expansion of X(). Hence, identify the terms belonging to the causal and non-causal parts of the signal. (iii) Write an expression for a(n) identifying the causal part (n), and non-causal part #2(n) of r(n) (iv) Plot (n) and find its energy (v) Plot the magnitude and phase spectra of the signal. (b) A real-valued signal, which is absolutely summable, which has the following irrational - transform X(z) = X(2) - X:( - ), where X() = - (1 (1 - 1-2/23/2 (i) Expand X: () and hence express X) using a power series expansion method. (ii) From the above step, find (n), the inverse z-transform of X(2) its ROC. (III) Plot 3(1), showing only 8 significant number of terms. (iv) Find the energy of (n). (v) Determine and plot the magnitude of Fourier transform.