The periodic function T(1) obeys T(x+2) = T(x) and |I| 0,n>0 mn= cos(mr) sin(nx)dx □ Σmn Smn²in²n = Σ₂ |CK|² -T T(x) = {¹
The periodic function T(1) obeys T(x+2) = T(x) and |I| 0,n>0 mn= cos(mr) sin(nx)dx □ Σmn Smn²in²n = Σ₂ |CK|² -T T(x) = {¹
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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Question
![The periodic function T(z) obeys T(x+2) = T(x) and
T(r)
=
Its Fourier transform is given by ao = 0, a2k+1 = (−1)k-
=
*(2k+1), ak
Fill in the Fourier coefficients for periodic (Q(x) = Q(x + 2π)) function
Q(x) = {
0<x<T
T≤ x < 2π
ao
a3
, b₁
, b3
Which of the below are valid properties of the Kronecker delta 8mn for m, n integer? [Tick all that apply-points will be deducted for wrong answers]
5mn = sin(mx) sin(nx)dx for m > 0,n > 0
□ Smn = 1
Smn
=
cos(mx) cos(nx) dx for all m,n
л
ग
□mn=21/ei(n-m)z dz
8mn =
cos(mr) sin(nx)dr
□ Σmn 8mncn²n = Σk|ck|²
-π
|x| <T/2
-1 π/2 < x < T
0 and bl =
0 for k integer.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53ce1657-b18a-4e5a-99aa-3e87bdade9e3%2F45c80dc0-0bb3-45c7-b512-209402dfee7c%2Fbon1pjs_processed.png&w=3840&q=75)
Transcribed Image Text:The periodic function T(z) obeys T(x+2) = T(x) and
T(r)
=
Its Fourier transform is given by ao = 0, a2k+1 = (−1)k-
=
*(2k+1), ak
Fill in the Fourier coefficients for periodic (Q(x) = Q(x + 2π)) function
Q(x) = {
0<x<T
T≤ x < 2π
ao
a3
, b₁
, b3
Which of the below are valid properties of the Kronecker delta 8mn for m, n integer? [Tick all that apply-points will be deducted for wrong answers]
5mn = sin(mx) sin(nx)dx for m > 0,n > 0
□ Smn = 1
Smn
=
cos(mx) cos(nx) dx for all m,n
л
ग
□mn=21/ei(n-m)z dz
8mn =
cos(mr) sin(nx)dr
□ Σmn 8mncn²n = Σk|ck|²
-π
|x| <T/2
-1 π/2 < x < T
0 and bl =
0 for k integer.
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