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onsider the following discrete time system: LTI h[n] here the input output relationship is defined by the difference equation y[»] = x[n] – x[n – 2] . The Y(e/") equency response of the system is described by H(e")=- X(e/") where X(e/") and Y(e®) are the purier transforms of x[n] and y[n] respectively. ) Determine the frequency response H (e /ª ) of the above system. ) The impulse response h[n] is defined by the inverse discrete-time Fourier transform of the frequency response. Find the impulse response of the system. ) Find the magnitude and phase of the frequency response at » = 0, @ = a/ 2 and » = r. ) If the input to the above system is x[n] = 1+ ( )" + sin(7 n), determine the output y[n].

onsider the following discrete time system: LTI h[n] here the input output relationship is defined by the difference equation y[»] = x[n] – x[n – 2] . The Y(e/") equency response of the system is described by H(e")=- X(e/") where X(e/") and Y(e®) are the purier transforms of x[n] and y[n] respectively. ) Determine the frequency response H (e /ª ) of the above system. ) The impulse response h[n] is defined by the inverse discrete-time Fourier transform of the frequency response. Find the impulse response of the system. ) Find the magnitude and phase of the frequency response at » = 0, @ = a/ 2 and » = r. ) If the input to the above system is x[n] = 1+ ( )" + sin(7 n), determine the output y[n].

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Consider the following discrete time system:

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Consider the following discrete time system: LTI x[n] v[n] h[n] where the input output relationship is defined by the difference equation y[n] = x[n] – x[n – 2] . The Y (eje) frequency response of the system is described by H(e ) = where X(ej@) and Y(e) are the X(ej@) Fourier transforms of x[n] and y[n] respectively. (a) Determine the frequency response H (e je) of the above system. (b) The impulse response h[n] is defined by the inverse discrete-time Fourier transform of the frequency response. Find the impulse response of the system. (c) Find the magnitude and phase of the frequency response at @= 0, @= r|2 and @= r. (d) If the input to the above system is x[n] = 1+ (i)" + sin(7 n), determine the output y[n].
Transcribed Image Text:Consider the following discrete time system: LTI x[n] v[n] h[n] where the input output relationship is defined by the difference equation y[n] = x[n] – x[n – 2] . The Y (eje) frequency response of the system is described by H(e ) = where X(ej@) and Y(e) are the X(ej@) Fourier transforms of x[n] and y[n] respectively. (a) Determine the frequency response H (e je) of the above system. (b) The impulse response h[n] is defined by the inverse discrete-time Fourier transform of the frequency response. Find the impulse response of the system. (c) Find the magnitude and phase of the frequency response at @= 0, @= r|2 and @= r. (d) If the input to the above system is x[n] = 1+ (i)" + sin(7 n), determine the output y[n].
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