Shift Theorem for the DTFT
where is any integer ( ). Thus, is a right-shift or delay by samples.
The shift theorem states3.5
or, in operator notation,
Note that is a linear phase term, so called because it is a linear function of frequency with slope equal to :
The shift theorem gives us that multiplying a spectrum by a linear phase term corresponds to a delay in the time domain by samples. If , it is called a time advance by samples.
Convolution Theorem for the DTFT
Symmetry of the DTFT for Real Signals