KnowraFourier coefficientLinked fromLinked fromThe 11 pages that link to Fourier coefficient, each with the reason it gives.All 11Broader topic 5Related 5Narrower topic 1Fourier seriesBroader topic: Each coefficient sets the amplitude and phase of one harmonic in the series.Orthonormal basisRelated: Inner products with basis vectors provide the coefficients of an expansion.Poisson summation formulaRelated: Each dual-lattice sample is a Fourier coefficient of the periodized function, up to normalization.Bessel's inequalityRelated: Inner products with orthonormal vectors are generalized Fourier coefficients.Parseval's identityBroader topic: The identity adds the squared magnitudes of these coefficients to recover total energy.Parseval's theoremBroader topic: The theorem assembles the magnitudes of these coefficients into the function’s norm.Riemann–Lebesgue lemmaRelated: The circle version asserts that these coefficients vanish as frequency grows.Fejér's theoremBroader topic: The coefficients determine the partial sums that Fejér averaging combines.Dirichlet–Jordan testRelated: The partial sums in the theorem are assembled from these coefficients.Dini testBroader topic: The test concerns the convergence of the partial sums formed from these coefficients.F. and M. Riesz theoremNarrower topic: The theorem's hypothesis specifies which indexed coefficients must vanish.