Fourier coefficients

Fourier coefficients are values that tell us how much of a specific basic sound (or "wave") is present in a complex signal or pattern. Imagine a complicated musical tone made up of many simpler notes; Fourier coefficients help identify and measure each of those individual notes. They are calculated through a mathematical process called Fourier analysis, which breaks down complex signals into a sum of basic waves called sine and cosine functions. These coefficients essentially describe the strength and contribution of each basic wave to the overall shape or pattern of the original signal.