N(3) (2) Consider the discrete-time signal z(n), with a z-transform X(2) = and a ROC, which %3D includes the unit-circle, where N(2) = 142 + 5z + 02.5, and D(2) = -82 + 222 + 8z + 25. %3D (a) Find the poles and zeros of X(2). Hence, identify and draw the region of conversion ROC. (b) Find an expression for 2(n) and sketch it. Identify its properties. (c) Write an expression for the Fourier transform of z(n), which is X(ej"). Hence, plot the magnitude and phase spectra.

Power System Analysis and Design (MindTap Course List)
6th Edition
ISBN:9781305632134
Author:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Publisher:J. Duncan Glover, Thomas Overbye, Mulukutla S. Sarma
Chapter6: Power Flows
Section: Chapter Questions
Problem 6.16P
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Consider the discrete time signal x(n), wit a Z-transform X9z) = N(z)/D(z) and a ROC, which includes the unit circle

N(3)
(2) Consider the discrete-time signal z(n), with a z-transform X(2) = and a ROC, which
%3D
includes the unit-circle, where
N(2) = 142 + 5z + 02.5,
and
D(2) = -82 + 222 + 8z + 25.
%3D
(a) Find the poles and zeros of X(2). Hence, identify and draw the region of conversion ROC.
(b) Find an expression for 2(n) and sketch it. Identify its properties.
(c) Write an expression for the Fourier transform of z(n), which is X(ej"). Hence, plot the
magnitude and phase spectra.
Transcribed Image Text:N(3) (2) Consider the discrete-time signal z(n), with a z-transform X(2) = and a ROC, which %3D includes the unit-circle, where N(2) = 142 + 5z + 02.5, and D(2) = -82 + 222 + 8z + 25. %3D (a) Find the poles and zeros of X(2). Hence, identify and draw the region of conversion ROC. (b) Find an expression for 2(n) and sketch it. Identify its properties. (c) Write an expression for the Fourier transform of z(n), which is X(ej"). Hence, plot the magnitude and phase spectra.
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