## 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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The Continuous-Time Impulse

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Flip Theorems