What are Fourier series and Fourier transform?

Fourier series are mathematical representations that decompose periodic functions into sums of sine and cosine functions, allowing for the analysis of their frequency components. The Fourier transform extends this concept to non-periodic functions, transforming them into a continuous spectrum of frequencies. Both tools are fundamental in signal processing, physics, and engineering, enabling the study of waveforms and the analysis of signals in the frequency domain. They facilitate the understanding of complex functions by breaking them down into simpler, oscillatory components.