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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

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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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
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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