theorem 17.59 Wiener–Khinchin
open in the book ·
parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2177
· p. 696
Rests on
-
depends_on
definition 17.58
Stationary process and power spectral density
¶
- depends_on definition 17.56 Correlation ¶
- depends_on definition 17.29 Fourier transform; the treatise convention ¶
- depends_on definition 17.29 Fourier transform; the treatise convention ¶ ↺
-
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-36 ¶
Supports
- depends_on proposition 17.61 Mean-square response of a damped resonator ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
depends_on |
→ | Stationary process and power spectral density | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2187 |
depends_on |
→ | Fourier transform; the treatise convention | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2187 |
depends_on |
→ | Fourier inversion | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2187 |
depends_on |
← | Mean-square response of a damped resonator | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2267 |
proves |
← | ch:15-fourier-integral-transforms@proof-36 | declared | parts/02-mathematical-methods/15-fourier-integral-transforms.tex:2190 |