## Power Theorem

The*power theorem*for Fourier transforms states that the

*inner product*of two signals in the time domain equals their inner product in the frequency domain.

The

*inner product*of two spectra and may be defined as

(B.21) |

This expression can be interpreted as the inverse Fourier transform of evaluated at :

(B.22) |

By the convolution theorem (§B.7) and flip theorem (§B.8),

(B.23) |

which at gives

(B.24) |

Thus,

(B.25) |

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Flip Theorems