Non Sinusoidal Waveforms

Can be repetitive or non-repetitive.

Repetitive Waveforms

The Fourier series represents them as a sum of sinusoidal components with discrete frequencies $n\omega_0$ for $n = 0, 1, 2, \ldots$

Non-Repetitive Waveforms

Waveforms that do not repeat over time. Can be modelled as a repetitive function with period $T \to \infty$.

As $T \to \infty$, the fundamental frequency $\omega_0 = 2\pi/T \to 0$ and the spacing between harmonics also $\to 0$:

The discrete harmonic spectrum becomes a continuous spectrum. Summation over discrete harmonics becomes an integral over a continuous frequency variable. The Fourier transform is the result of this limiting process.