Why is the range of frequency for discrete time Fourier transform $-\pi<\omega<\pi$? In my class we are taught that the range for the frequency is $-\pi&lt;\omega&lt;\pi$ for discrete time Fourier transform, however for continuous time the limit is $-\infty&lt;\omega&lt;\infty$
why is this the case?
Short intuitive explaination: In a time discrete system, the spectrum repeats itself at multiples of the sampling frequency (normalized sampling frequency is $2\pi$). Because of that, the limits of the fourier integral can be reduced from $\pm \infty$ to $\pm \pi$.