# Why is the range of frequency for discrete time Fourier transform $-\pi<\omega<\pi$? [duplicate]

In my class we are taught that the range for the frequency is $$-\pi<\omega<\pi$$ for discrete time Fourier transform, however for continuous time the limit is $$-\infty<\omega<\infty$$

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 $$\pm \pi$$.