Theorem: For any
and any integer
,
Proof:
The shift theorem is often expressed in shorthand as
The shift theorem says that a delay in the time domain corresponds to a linear phase term in the frequency domain. More specifically, a delay of samples in the time waveform corresponds to the linear phase term multiplying the spectrum, where .^{7.14}Note that spectral magnitude is unaffected by a linear phase term. That is, .