(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)

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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(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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