If I were to find the general Fourier Series expression for a function that is defined for example in the [-pie, pie] or [-2pi, 2pi] intervals. What is my L? Do I directly take L as pi or 2pi, or do I have to divide by 2 such that 2L = pi, therefore, L = pi/2? I have seen so many examples online where the period was given as f(t+2) so the solution was 2L = 2, therefore, L = 1.. But I have also seen questions like f(t) = -5t when 0< t <1 10-5t 1< t <2 What is my L going to be in this case? Is it going to be different when I'm dealing with Odd/Even functions?
If I were to find the general Fourier Series expression for a function that is defined for example in the [-pie, pie] or [-2pi, 2pi] intervals. What is my L? Do I directly take L as pi or 2pi, or do I have to divide by 2 such that 2L = pi, therefore, L = pi/2? I have seen so many examples online where the period was given as f(t+2) so the solution was 2L = 2, therefore, L = 1.. But I have also seen questions like f(t) = -5t when 0< t <1 10-5t 1< t <2 What is my L going to be in this case? Is it going to be different when I'm dealing with Odd/Even functions?
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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If I were to find the general Fourier Series expression for a function that is defined for example in the [-pie, pie] or [-2pi, 2pi] intervals. What is my L? Do I directly take L as pi or 2pi, or do I have to divide by 2 such that 2L = pi, therefore, L = pi/2?
I have seen so many examples online where the period was given as f(t+2) so the solution was 2L = 2, therefore, L = 1.. But I have also seen questions like
f(t) = -5t when 0< t <1
10-5t 1< t <2
What is my L going to be in this case?
Is it going to be different when I'm dealing with Odd/Even functions?
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