theorem 17.57 Wiener–Khinchin, finite-energy form

open in the book · parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2129 · p. 696

Rests on

depends_on definition 17.56 Correlation ¶
depends_on theorem 17.53 Convolution theorem ¶
- depends_on definition 17.50 Convolution ¶
- depends_on definition 17.29 Fourier transform; the treatise convention ¶
- depends_on proposition 17.51 Algebra of convolution ¶
  - depends_on definition 17.50 Convolution ¶ ↺
  - proves proof ch:15-fourier-integral-transforms@proof-32 ¶
- depends_on theorem 17.32 Fourier inversion ¶
  - depends_on definition 17.29 Fourier transform; the treatise convention ¶ ↺
  - depends_on equation 17.42 eq:ft-gaussian ¶
  - proves proof ch:15-fourier-integral-transforms@proof-20 ¶
- proves proof ch:15-fourier-integral-transforms@proof-34 ¶
proves proof ch:15-fourier-integral-transforms@proof-35 ¶

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type	direction	node	provenance	where
`depends_on`	→	Correlation	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2138
`depends_on`	→	Convolution theorem	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2138
`proves`	←	ch:15-fourier-integral-transforms@proof-35	declared	parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2141