# Why we need fourier transform of periodic signal although we have fourier series for periodic signal?

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.

• Did you read the section? What did it say? – learner May 16 '14 at 13:58
• 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? – robert bristow-johnson May 16 '14 at 14:50

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