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Let x[n] = 1, for n = 0,1,2,3 and x[n] = 2 for n = 4,5,6,7. The signal length is N = 8. (a) Let WN = e. Find W^, for n = 0,1,2,3 and plot them on the complex plane. (b) Using decomposition-in-time FFT, find the DFT X[k]. (c) From X[k] in Part (b), find x[n] using the duality and the decomposition-in- frequency FFT. Hint: the duality is: rx[n] = ± [DFT(X*[k])]*.

Let x[n] = 1, for n = 0,1,2,3 and x[n] = 2 for n = 4,5,6,7. The signal length is N = 8. (a) Let WN = e. Find W^, for n = 0,1,2,3 and plot them on the complex plane. (b) Using decomposition-in-time FFT, find the DFT X[k]. (c) From X[k] in Part (b), find x[n] using the duality and the decomposition-in- frequency FFT. Hint: the duality is: rx[n] = ± [DFT(X*[k])]*.

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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Let x[n] = 1, for n = 0,1,2,3 and x[n] = 2 for n = 4,5,6,7. The signal length is N = 8. (a) Let WN = e. Find W^, for n = 0,1,2,3 and plot them on the complex plane. (b) Using decomposition-in-time FFT, find the DFT X[k]. (c) From X[k] in Part (b), find x[n] using the duality and the decomposition-in- frequency FFT. Hint: the duality is: rx[n] = ± [DFT(X*[k])]*.
Transcribed Image Text:Let x[n] = 1, for n = 0,1,2,3 and x[n] = 2 for n = 4,5,6,7. The signal length is N = 8. (a) Let WN = e. Find W^, for n = 0,1,2,3 and plot them on the complex plane. (b) Using decomposition-in-time FFT, find the DFT X[k]. (c) From X[k] in Part (b), find x[n] using the duality and the decomposition-in- frequency FFT. Hint: the duality is: rx[n] = ± [DFT(X*[k])]*.
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