Confuse between fourier transform and fourier series formula?

Find from the first principles the fourier transform of the function F(t)=e of power a[t] where a is a positive constant.

Answer:
Go to the Wikipedia article on fourier series, and it will tell you how to generate a list of coeficient that you can use with sine and cosine functions to approximate a function.

The fourier transform, on the other hand, is a mathematical transformation (the integration function) that gives you the frequency components of a periodic function.

If you have a measurement over .2 seconds (5 hz) of periodic data (for example) with sampling of up to 0.001 seconds (1000 HZ) you can determine the power spectrum by performing a fourier transform.

It's easier to understand how the two are related if you use them for a couple of problems.

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