Shift Theorem for the DTFTWe define the shift operator for sampled signals by
where is any integer ( ). Thus, is a right-shift or delay by samples. The shift theorem states3.5
or, in operator notation,
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