# If the cosine function is periodic, why does it have a Fourier Transform? [duplicate]

As far as I understand Fourier Transforms are for non-periodic signals and Fourier Series for periodic signals.

So why is it we can take the Fourier Transform of a cosine when it is a periodic function, assuming the above paragraph is correct?

• Note that nothing prevents you from finding the Fourier Series of a non-periodic signal in the interval $T$. The series will converge in $T$. Likewise, as long as the integrals make sense, you can the FT of any signal you want. I recall there's a nice explanation in Paul Nahin's "The Science of Radio" if you can get ahold of it. – MBaz Sep 18 '19 at 2:06

First, it can be shown that the continuous-time Fourier transform can be obtained from the continuous-time Fourier series by letting the period $$T$$ go to infinity.