1
$\begingroup$

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?

$\endgroup$
2
1
$\begingroup$

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 $\pm \pi$.

$\endgroup$

Not the answer you're looking for? Browse other questions tagged or ask your own question.