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(d) Let {Xo, X₁,..., Xn-1} be a finite realization of a time series with fast fourier transform (FFT) {X(wo),..., X(wn-1)}. Show that the inverse FFT is given by n-1 Xt= ΣX (wk) eiwxt, nk=0 1 Wk 2πk n and k = 0, 1,..., n-1.

(d) Let {Xo, X₁,..., Xn-1} be a finite realization of a time series with fast fourier transform (FFT) {X(wo),..., X(wn-1)}. Show that the inverse FFT is given by n-1 Xt= ΣX (wk) eiwxt, nk=0 1 Wk 2πk n and k = 0, 1,..., n-1.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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(d) Let {Xo, X₁,..., Xn-1} be a finite realization of a time series with fast fourier transform (FFT) {X(wo),..., X(wn-1)}. Show that the inverse FFT is given by X₁ = = EX (wn) etwat, Xt n k=0 Wk = 2πk n and k = 0, 1,..., n - 1.
Transcribed Image Text:(d) Let {Xo, X₁,..., Xn-1} be a finite realization of a time series with fast fourier transform (FFT) {X(wo),..., X(wn-1)}. Show that the inverse FFT is given by X₁ = = EX (wn) etwat, Xt n k=0 Wk = 2πk n and k = 0, 1,..., n - 1.
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