c) For a periodic function y(t) with period T, its Fourier series may be represented in complex form as y(t) = Σ 8=18 inwt derive a formula for Cn. Cne where w 2π/T and all c, are complex constants defined for n integer. i. Show that if y(t) is a real function satisfying y where the bar denotes the complex conjugate. ii. Using the fact that 2π fotot e ei(n-m)t dt = { 0 2π y, then cn = Cn for all integers n, if m= n if m #n
c) For a periodic function y(t) with period T, its Fourier series may be represented in complex form as y(t) = Σ 8=18 inwt derive a formula for Cn. Cne where w 2π/T and all c, are complex constants defined for n integer. i. Show that if y(t) is a real function satisfying y where the bar denotes the complex conjugate. ii. Using the fact that 2π fotot e ei(n-m)t dt = { 0 2π y, then cn = Cn for all integers n, if m= n if m #n
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:c)
For a periodic function y(t) with period T, its Fourier series may be represented in complex
form as
y(t) = Σ
n=-x
where w 2π/T and all cn are complex constants defined for n integer.
derive a formula for Cn.
i. Show that if y(t) is a real function satisfying y = y, then cn = Cn for all integers n,
where the bar denotes the complex conjugate.
ii. Using the fact that
C2π
Cneinwt
ei(n-m)t dt =
{
2π
0
if m= n
if m #n
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