Treatise of Physics

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proposition 17.86 The DFT is exact for a band-limited periodic signal

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:3017 · p. 705

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proposition 17.86: The DFT is exact for a band-limited periodic signal17.86definition 17.84: Discrete Fourier transform17.84definition 17.1: Fourier coefficients and Fourier series17.1proposition 17.85: Inversion and Parseval for the DFT17.85proof : ch:15-fourier-integral-transforms@proof-53prooftheorem 17.87: Cooley–Tukey17.87definition 17.25: Multiple Fourier series17.25lemma 17.6: Dirichlet kernel17.6lemma 17.2: Orthogonality of the harmonics17.2lemma 17.15: A polynomial whose partial sum spikes at the origin17.15proposition 17.4: Least squares and Bessel's inequality17.4proposition 17.10: Smoothness and coefficient decay17.10proposition 17.16: An explicit continuous function with a divergent Fourier series17.16theorem 17.3: Euler–Fourier coefficient formulas17.3theorem 17.47: Poisson summation17.47theorem 17.80: Sampling theorem17.80proof : ch:15-fourier-integral-transforms@proof-52proof

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depends_on → Discrete Fourier transform declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:3024
depends_on → Fourier coefficients and Fourier series declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:3024
depends_on → Inversion and Parseval for the DFT declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:3024
proves ← ch:15-fourier-integral-transforms@proof-53 declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:3027