A decomposition of a signal into constituent frequencies, mapping functions from time domain to frequency domain.
transforms a function f(t) into F(w) by integrating against complex exponentials
inverse Fourier transform reconstructs the original signal from its spectrum
FFT (Fast Fourier Transform):: the O(n log n) algorithm enabling practical computation
convolution theorem:: convolution in time domain equals multiplication in frequency domain
Foundation of signal processing, audio analysis, image compression, and wave physics
spectral analysis reveals hidden periodicities in data, connecting to statistics
Central to quantum mechanics (momentum-position duality) and differential equations (solving PDEs)
Related:: calculus, linear algebra, information theory, optimization