Why can Fourier series be used on a non-repetitive function?

1. Can we use Fourier series for non periodic signals?
2. Why Fourier series is only applicable for periodic signals?
3. Is Fourier series only for periodic functions?
4. What are the necessary conditions of a function to have Fourier series?

Can we use Fourier series for non periodic signals?

Fourier series is defined for periodic signals and the Fourier transform can be applied to aperiodic (occurring without periodicity) signals.

Why Fourier series is only applicable for periodic signals?

Fourier series is just a means to represent a periodic signal as an infinite sum of sine wave components. A periodic signal is just a signal that repeats its pattern at some period. The primary reason that we use Fourier series is that we can better analyze a signal in another domain rather in the original domain.

Is Fourier series only for periodic functions?

The Fourier series is always a periodic function, even if original function s(x) wasn't.

What are the necessary conditions of a function to have Fourier series?

For the Fourier Series to exist, the following two conditions must be satisfied (along with the Weak Dirichlet Condition): In one period, f(t) has only a finite number of minima and maxima. In one period, f(t) has only a finite number of discontinuities and each one is finite.