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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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