Derive the discrete-time Fourier transform (DTFT) of the signal [1, for 0

Introductory Circuit Analysis (13th Edition)
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Question 3
(a)
Derive
the discrete-time Fourier transform (DTFT) of
the signal
(1, for 0<n<4
x[n] =-
0, otherwise
and sketch its magnitude and phase spectrum over the
interval : ωε [-π, π].
(b)
The DTFT of a discrete-time signal y[n] is given by: Y(j@) = jo. Find y[n] and its
total energy.
(c)
From the signal x[n] of part (a) above, another signal w[n] is constructed as follows:
w[n] = s[k]x[n-k] where s[n]= ES[n-10r]. Sketch the magnitude spectrum of
%3D
k=-o
r=-00
w[n] over the interval: w e[-7, 7].
Transcribed Image Text:Question 3 (a) Derive the discrete-time Fourier transform (DTFT) of the signal (1, for 0<n<4 x[n] =- 0, otherwise and sketch its magnitude and phase spectrum over the interval : ωε [-π, π]. (b) The DTFT of a discrete-time signal y[n] is given by: Y(j@) = jo. Find y[n] and its total energy. (c) From the signal x[n] of part (a) above, another signal w[n] is constructed as follows: w[n] = s[k]x[n-k] where s[n]= ES[n-10r]. Sketch the magnitude spectrum of %3D k=-o r=-00 w[n] over the interval: w e[-7, 7].
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