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The periodic function 7(x) obeys T(x+2) = T(x) and T(z) = >={¹,₂ -1 Its Fourier transform is given by ao = 0, a2+1 = (-1) (2k+1) › @2k = 0 and b Fill in the Fourier coefficients for periodic (Q(x) = Q(x+2π)) function Q(x) = { ¹₁ 0 0,n>0 □mn = cos(mx) cos(nx)dx for all m,n 5mn = cos(mx) sin(nx) dx □mn = 1 Σmn 8mninen = Σk |CK|² □mn=f(n-m)z dz 0 |x|< π/2 */2 ≤|2|< * = 0 for k integer.

The periodic function 7(x) obeys T(x+2) = T(x) and T(z) = >={¹,₂ -1 Its Fourier transform is given by ao = 0, a2+1 = (-1) (2k+1) › @2k = 0 and b Fill in the Fourier coefficients for periodic (Q(x) = Q(x+2π)) function Q(x) = { ¹₁ 0 0,n>0 □mn = cos(mx) cos(nx)dx for all m,n 5mn = cos(mx) sin(nx) dx □mn = 1 Σmn 8mninen = Σk |CK|² □mn=f(n-m)z dz 0 |x|< π/2 */2 ≤|2|< * = 0 for k integer.

Advanced Engineering Mathematics
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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The periodic function 7(x) obeys T(x+2) = T(x) and T(z) = >={¹,₂ -1 Its Fourier transform is given by ao = 0, a2+1 = (-1) (2k+1) › @2k = 0 and b Fill in the Fourier coefficients for periodic (Q(x) = Q(x+2π)) function Q(x) = { ¹₁ 0<x<* -1 * ≤ x < 2 ag= ,b₁ = ,b3 = Which of the below are valid properties of the Kronecker delta 8mn for m, n integer? [Tick all that apply- □mn=sin(mx) sin(nx)dx form > 0,n>0 □mn = cos(mx) cos(nx)dx for all m,n 5mn = cos(mx) sin(nx) dx □mn = 1 Σmn 8mninen = Σk |CK|² □mn=f(n-m)z dz 0 |x|< π/2 */2 ≤|2|< * = 0 for k integer.
Transcribed Image Text:The periodic function 7(x) obeys T(x+2) = T(x) and T(z) = >={¹,₂ -1 Its Fourier transform is given by ao = 0, a2+1 = (-1) (2k+1) › @2k = 0 and b Fill in the Fourier coefficients for periodic (Q(x) = Q(x+2π)) function Q(x) = { ¹₁ 0<x<* -1 * ≤ x < 2 ag= ,b₁ = ,b3 = Which of the below are valid properties of the Kronecker delta 8mn for m, n integer? [Tick all that apply- □mn=sin(mx) sin(nx)dx form > 0,n>0 □mn = cos(mx) cos(nx)dx for all m,n 5mn = cos(mx) sin(nx) dx □mn = 1 Σmn 8mninen = Σk |CK|² □mn=f(n-m)z dz 0 |x|< π/2 */2 ≤|2|< * = 0 for k integer.
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