N = 5 Given the values of the following discrete-time signal x[n] of length n 0 1 2 4 x[n] 1 2 3 4 5 a) Please determine the DFT X[k] of the input signal x[n], in coefficient exponential -jbkk form (e.g. as a sum of a e N terms). You do not need to calculate the final complex values for each of the X[k] (e.g. do not calculate X[1] = 0.5+ j0.5). 4πk b) Find the DFT G[k] based on the DFT you found in Part (a), where G[k] = e¯ 5 X[k] in coefficient exponential form (you do not need to calculate the final complex values for G[k]). c) Find discrete-time signal g[n], where g[n] is the inverse DFT transformed version of the signal G[k] in Part (b). Determine the circular shift value m for the resulting signal g[n] = x[n-m]mod N
N = 5 Given the values of the following discrete-time signal x[n] of length n 0 1 2 4 x[n] 1 2 3 4 5 a) Please determine the DFT X[k] of the input signal x[n], in coefficient exponential -jbkk form (e.g. as a sum of a e N terms). You do not need to calculate the final complex values for each of the X[k] (e.g. do not calculate X[1] = 0.5+ j0.5). 4πk b) Find the DFT G[k] based on the DFT you found in Part (a), where G[k] = e¯ 5 X[k] in coefficient exponential form (you do not need to calculate the final complex values for G[k]). c) Find discrete-time signal g[n], where g[n] is the inverse DFT transformed version of the signal G[k] in Part (b). Determine the circular shift value m for the resulting signal g[n] = x[n-m]mod N
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ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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![1.
N = 5
Given the values of the following discrete-time signal x[n] of length
n
0
1
2
3
4
x[n]
1
2
3
4
5
a) Please determine the DFT X[k] of the input signal x[n], in coefficient exponential
.bk
-
form (e.g. as a sum of a · e N terms). You do not need to calculate the final complex
values for each of the X[k] (e.g. do not calculate X[1] = 0.5 + j0.5).
.4πk
-
= e 5 X[k]
b) Find the DFT G[k] based on the DFT you found in Part (a), where G[k]
in coefficient exponential form (you do not need to calculate the final complex values for
G[k]).
c) Find discrete-time signal g[n], where g[n] is the inverse DFT transformed version of
the signal G[k] in Part (b). Determine the circular shift value m for the resulting signal
g[n] = x[n-m] mod N](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F670cd716-78ea-4bd2-aa02-b6fca7de8b87%2F3deefd0e-8a38-4c06-801e-4718160635b8%2Fmu7p8t_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1.
N = 5
Given the values of the following discrete-time signal x[n] of length
n
0
1
2
3
4
x[n]
1
2
3
4
5
a) Please determine the DFT X[k] of the input signal x[n], in coefficient exponential
.bk
-
form (e.g. as a sum of a · e N terms). You do not need to calculate the final complex
values for each of the X[k] (e.g. do not calculate X[1] = 0.5 + j0.5).
.4πk
-
= e 5 X[k]
b) Find the DFT G[k] based on the DFT you found in Part (a), where G[k]
in coefficient exponential form (you do not need to calculate the final complex values for
G[k]).
c) Find discrete-time signal g[n], where g[n] is the inverse DFT transformed version of
the signal G[k] in Part (b). Determine the circular shift value m for the resulting signal
g[n] = x[n-m] mod N
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