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# Is this a finite fourier series? watch

1. so i have just been given a function in terms of cos and sin, and using eulers equations ive come out with what i believe to be a finite fourier series but not totally sure - would 1/2(sin(5t)+sin(3t)) be considered a finite fourier series?
thanks
2. (Original post by SassyPete)
so i have just been given a function in terms of cos and sin, and using eulers equations ive come out with what i believe to be a finite fourier series but not totally sure - would 1/2(sin(5t)+sin(3t)) be considered a finite fourier series?
thanks
Yes.
3. (Original post by RDKGames)
Yes.
thankyou for your quick reply - may i ask why it is? we didnt really cover finite series
4. (Original post by SassyPete)
thankyou for your quick reply - may i ask why it is? we didnt really cover finite series
Because most of the terms in the infinite series turn out to be 0, and that's what you're left with.

EDIT: Fourier series of a trig function would be finite, as it's kinda like the principle of using the Taylor series to approximate a polynomial - most terms turn out to be 0 and you end up with what you started, maybe just written differently, but you end up with finite terms.
5. (Original post by SassyPete)
thankyou for your quick reply - may i ask why it is? we didnt really cover finite series
So, I don't want to seem like a git, but you have asked this question in two previous threads, and I have replied to you about 5 times, saying that it is a finite Fourier series.

I don't understand why you keep asking the same question, and never seem to listen to the responses.
6. (Original post by RDKGames)
EDIT: Fourier series of a trig function would be finite, as it's kinda like the principle of using the Taylor series to approximate a polynomial - most terms turn out to be 0 and you end up with what you started, maybe just written differently, but you end up with finite terms.
This isn't really true. It's true for a sum of sin/cos times that are all periodic with the same period as your Fourier series, but it won't be true for, say (between 0 and 2pi), and I'm pretty (very) sure it's not true for something like between 0 and 2pi, although I can't be bothered to do the actual math to check.
7. (Original post by DFranklin)
This isn't really true. It's true for a sum of sin/cos times that are all periodic with the same period as your Fourier series, but it won't be true for, say (between 0 and 2pi), and I'm pretty (very) sure it's not true for something like between 0 and 2pi, although I can't be bothered to do the actual math to check.
Fair enough, I guess I just had some basic trig functions in my mind when writing that.

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