Fourier Analysis is like a way of looking at a wave. We can use it to study how a wave is made up out of lots of different vibrations. It works by breaking down a wave into simpler pieces, ones that make it easier for us to understand and work with. For example, imagine a complex wave like an ocean wave with many bumps and dips. Fourier Analysis helps us understand the wave by breaking it down into lots of simpler waves that make up the original bigger wave. Each of these smaller waves is called a frequency, and when we put the different frequencies together, we can create the original wave. It is like a recipe; the different frequencies are like ingredients and by mixing them together in just the right way, we can make up the wave.

Basis vector,
Bispectrum,
Characteristic function (probability theory),
Conjugate Fourier series,
Fourier-related transforms,
Fourier–Bessel series,
Generalized Fourier series,
Laplace transform,
Mellin transform,
Non-uniform discrete Fourier transform,
Number-theoretic transform,
Orthogonal functions