Make up the derivation of Eq. (8.4) Wrect (@p) +2 ΣWrect(t)e-ipt = e-ipT(N-1)/2N sin(@pT/2) sin(@pT/2N) (8.4) k=0 for DFT of rectangular window by using the formula for the sum of a geometrical series with the first term of 1 and a geometric ratio of e-ipT/N. Then, plot the DFT.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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H1.
Make up the derivation of Eq. (8.4)
N-1
Wrect(@p) == Wrect(t)e-i@pth
=
e-ipT(N-1)/2N sin(@pT/2)
sin(@pT/2N)
(8.4)
N
k=0
for DFT of rectangular window by using the formula for the sum of a geometrical series
with the first term of 1 and a geometric ratio of e-ipT/N. Then, plot the DFT.
Transcribed Image Text:Make up the derivation of Eq. (8.4) N-1 Wrect(@p) == Wrect(t)e-i@pth = e-ipT(N-1)/2N sin(@pT/2) sin(@pT/2N) (8.4) N k=0 for DFT of rectangular window by using the formula for the sum of a geometrical series with the first term of 1 and a geometric ratio of e-ipT/N. Then, plot the DFT.
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