The DFT specifies the relationship between a time-domain signal and its frequency-domain representation.
Many general relationships between these two representations can be derived from Eq. (1) (see link for details).
For example, if a time-domain signal is time-shifted by an amount (resulting in a signal ), its frequency-domain representation is simply multiplied by a phase shift term of
:
This result is referred to as the “Shift Theorem”, given by a corresponding “transform pair”:
(3)
Note that the phase shift term has unity magnitude (
) and so, a time-shift produces no change in the magnitude response of the corresponding frequency-domain representation.