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I was going through some of the basics of fourier series and fourier transform. And I came across one topic "Fourier transform of periodic signal". But I am not able to understnad why we need to go for fourier transform because we already have fourier series to take care of periodic signal.

Any help is appreciated.

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    $\begingroup$ Did you read the section? What did it say? $\endgroup$
    – learner
    May 16, 2014 at 13:58
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    $\begingroup$ suppose you have a problem where both periodic and non-periodic signals are combined or affect each other in some way. say, for example, a periodic signal is multiplying an aperiodic signal. how would you then deal with it? $\endgroup$
    – robert bristow-johnson
    May 16, 2014 at 14:50

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If you take the Fourier transform of a periodic signal, you'll arrive at the same result that you would if you had computed the signal's Fourier series. Its spectrum will consist of discrete lines that correspond directly with the terms in the Fourier series. As an example, note the following Fourier transform pair:

$$ \cos(\omega_0 t) \Leftrightarrow \pi \left(\delta(\omega - \omega_0) + \delta(\omega+\omega_0)\right) $$

If you computed the complex Fourier series of $\cos(\omega_0 t)$, you would find exactly two nonzero coefficients: those that correspond to frequencies $\omega_0$ and $-\omega_0$.

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