Fourier Series of Aperiodic convolution of periodic functions

1. Can you perform Fourier series on aperiodic signal?
2. What is the Fourier transform of aperiodic signal?
3. How do you write a Fourier series of a periodic function?
4. Can the convolution of two periodic signals be periodic?

Can you perform Fourier series on aperiodic signal?

Fourier Transform can work on Aperiodic Signals. Fourier Transform is an infinite sum of infinitesimal sinusoids. Fourier Transform has an inverse transform, that allows for conversion from the frequency domain back to the time domain.

What is the Fourier transform of aperiodic signal?

The Fourier transform is defined and is evaluated for all standard aperiodic signals such as exponential signal, rectangular pulse, triangular pulse, etc. The IFT of some standard signals such as sinc function is also discussed. The use of Dirac Delta function is explained for evaluation of FT for periodic signals.

How do you write a Fourier series of a periodic function?

If f is continuous at x, then (f (x+) + f (x−))/2 = f (x). So f equals its Fourier series at “most points.” If f is continuous everywhere, then f equals its Fourier series everywhere. A continuous 2π-periodic function equals its Fourier series.

Can the convolution of two periodic signals be periodic?

Circular convolution, also known as cyclic convolution, is a special case of periodic convolution, which is the convolution of two periodic functions that have the same period. Periodic convolution arises, for example, in the context of the discrete-time Fourier transform (DTFT).