Howtosignalprocessing
- What is DTFT spectrum?
- What is the relationship between DTFT and is a transform?
- What is spectrum of sampled signal?
- What is the relation between DTFT and DFT?
What is DTFT spectrum?
The spectrum of the DTFT is continuous, so either f or ω can be used. The common choice is ω, because it makes the equations shorter by eliminating the always present factor of 2π. Remember, when ω is used, the frequency spectrum extends from 0 to π, which corresponds to DC to one-half of the sampling rate.
What is the relationship between DTFT and is a transform?
Also, if r = 1, then the discrete time Fourier transform (DTFT) is same as the Z-transform. In other words, the DTFT is nothing but the Z-transform evaluated along the unit circle centred at the origin of the z-plane.
What is spectrum of sampled signal?
The sampled signal has a spectrum that is periodic at the sampling frequency (20 Hz) and has an even symmetry about 0.0 Hz, as well as symmetry about the sampling frequency, fs. Since the sampled spectrum is periodic, it goes on forever and only a portion of it can be shown.
What is the relation between DTFT and DFT?
DFT (Discrete Fourier Transform) is a practical version of the DTFT, that is computed for a finite-length discrete signal. The DFT becomes equal to the DTFT as the length of the sample becomes infinite and the DTFT converges to the continuous Fourier transform in the limit of the sampling frequency going to infinity.
