Fourier Series

Let's say y(x)= B.sin(π.x)

How can i find the complex exponential fourier series of y(x) and the trigonometric fourier series of y(x)?

I need a real good explanation about this because i can't get it how much i try.

by ManWithWhite
June 10, 2020

For a classical Fourier Series, you need the period and then, find the coefficients for each terms in sinus and in cosines for each multiple of the given period. You already have that answer since you already have the sum: Each coefficients is zero, except for sin( pi*x) having its coefficient equals to B. You are expecting too much work, while it is super easy :-) For other signal, that could be harder, though, but for a pure sinus, or cosine, that is already given for ... free.

by vanderghast
June 14, 2020

Sorry i still could not get it. Do you have any links for me? That topic is really makes me cry. Despite my understanding, i believe you just explained it very good.

by ManWithWhite
June 14, 2020

You can try the classical approach with https://www.youtube.com/watch?v=iSw2xFhMRN0, which is about solving an infinite number of equations having an infinite number of unknowns (the coefficients). We cannot use Gaussian elimination, as usual. But using "orthogonal" functions with integration over a period (note that for a given equation, how the multiplication, then the integration, bring all terms equal to zero, except one term which then allows us to compute the coefficients, one by one).

by vanderghast
June 14, 2020

I couldn't understand but thanks for your effort my friend.

by ManWithWhite
June 16, 2020
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