Source: Wikipedia. Pages: 192. Chapters: Nyquist Shannon sampling theorem, Discrete cosine transform, Discrete Fourier transform, Bessel function, Dirac delta function, Autocorrelation, Laplace's equation, Convolution, Topological group, Banach algebra, List of Fourier-related transforms, Frequency spectrum, Haar measure, Laplace transform, Fourier transform spectroscopy, Convolution theorem, Harmonic function, Basis function, Periodic function, Whittaker Shannon interpolation formula, Fundamental frequency, Laplace operator, Modified discrete cosine transform, Fourier optics, Spherical harmonics, LTI system theory, Window function, Pontryagin duality, Multiplier, Discrete-time Fourier transform, Modulus of continuity, Sobolev space, Almost periodic function, Carleson's theorem, Ewald summation, Relations between Fourier transforms and Fourier series, Poisson summation formula, Analytic signal, Reciprocal lattice, Fractional Fourier transform, Solid harmonics, Spin-weighted spherical harmonics, Short-time Fourier transform, Uncertainty principle for the short-time Fourier transform, Riesz Thorin theorem, Discrete Hartley transform, Linear canonical transformation, SigSpec, Discrete sine transform, Chirplet transform, Homogeneous distribution, Peter Weyl theorem, Bilinear time frequency distribution, Metaplectic group, Bloch wave MoM method, Marcinkiewicz interpolation theorem, Spectral leakage, Orthonormal basis, Paley Wiener theorem, Overlap-add method, FBI transform, Unit circle, Fourier inversion theorem, DFT matrix, Poisson kernel, Interpolation space, Littlewood Paley theory, Motions in the time-frequency distribution, List of cycles, Parametrix, A derivation of the discrete Fourier transform, Parseval's theorem, Number-theoretic transform, Compact group, Overlap-save method, Set of uniqueness, Multitaper, Convolution power, Instantaneous phase, Dirichlet problem, S transform, Tube domain, Projection-slice theorem, Fourier transform on finite groups, Shapiro polynomials, Regressive discrete Fourier series, Wiener Khinchin theorem, Spectral concentration problem, Triple correlation, Periodogram, Arithmetic complexity of the discrete Fourier transform, Parseval's identity, Sine and cosine transforms, Schwartz space, Fast Fourier Transform Telescope, Hausdorff Young inequality, Generalized Fourier series, Trigonometric polynomial, Spectrum continuation analysis, Fourier integral operator, Cone-shape distribution function, Bicoherence, Calderón Zygmund lemma, Bispectrum, Final value theorem, Wirtinger's inequality for functions, Oscillatory integral operator, Choi Williams distribution function, Plancherel theorem, Autocovariance, List of Fourier analysis topics, Gabor atom, Fourier operator, Friedel's law, Van der Corput lemma, S plane, Conjugate Fourier series, Balian Low theorem, Superoscillation, Indirect Fourier transform, Algebraic analysis, Non-uniform discrete Fourier transform, Microlocal analysis, Photon Doppler velocimetry, Segal Shale Weil distribution, Discrete weighted transform, Space-time Fourier transform, Modulated complex lapped transform, Metaplectomorphism. Excerpt: The Fourier transform is a mathematical operation that decomposes a signal into its constituent frequencies. Thus the Fourier transform of a musical chord is a mathematical representation of the amplitudes of the individual notes that make it up. The original signal depends on time, and therefore is called the time domain representation of the signal,...
