Howtosignalprocessing
What is the DTFT of a constant?
Discrete Time
This function then periodically repeats with period 2π (as it must to be a DTFT). What this says is that a constant in the time domain is concentrated at zero frequency in the frequency domain (which should not be surprising). We can verify this answer easily by evaluating the inverse DTFT.
Is DTFT always continuous?
The DTFT itself is a continuous function of frequency, but discrete samples of it can be readily calculated via the discrete Fourier transform (DFT) (see § Sampling the DTFT), which is by far the most common method of modern Fourier analysis.
Why is DTFT continuous?
DTFT is continuous because the original time-domain signal that you sampled has well behaved transform which means it doesn't envolve impulses in the transformed domain (fourier domain). Because DTFT is just repeated version of the actual FT at every intervals. The DTFT itself is a continuous function of frequency.
