definition 17.79 Band-limited function

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definition 17.79: Band-limited function17.79definition 17.29: Fourier transform; the treatise convention17.29corollary 17.81: Sampling periodises the spectrum; aliasing17.81theorem 17.80: Sampling theorem17.80corollary 17.49: Lattice sums and the reciprocal lattice17.49definition 17.58: Stationary process and power spectral density17.58definition 25.52: Wigner function25.52example 17.31: The three standard pairs17.31lemma A.584: Fourier injectivity in n variablesA.584lemma 17.35: Multiplication formula17.35proposition 17.90: Hankel transform as the axially symmetric Fourier transform17.90proposition 17.68: The Laplace transform is a Fourier transform17.68proposition 17.30: Elementary properties17.30proposition 28.60: A wave packet translates at v_g and spreads at a rate set by the curvature of \omega(k)28.60proposition 10.39: Fourier reduction on the line10.39theorem 17.53: Convolution theorem17.53theorem 17.32: Fourier inversion17.32theorem 17.78: Causality implies dispersion relations17.78theorem 17.36: Plancherel17.36theorem 17.47: Poisson summation17.47theorem 17.104: Projection-slice theorem17.104theorem 17.59: Wiener–Khinchin17.59proof : ch:15-fourier-integral-transforms@proof-51proofdefinition 17.1: Fourier coefficients and Fourier series17.1theorem 17.34: Parseval's identity for series17.34corollary 17.107: How many projections17.107proof : ch:15-fourier-integral-transforms@proof-50proof

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depends_on Fourier transform; the treatise convention declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2827
depends_on Sampling periodises the spectrum; aliasing declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2918
depends_on Sampling theorem declared parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2845