Howtosignalprocessing
- What are the the disadvantage of DTFT?
- What are the necessary and sufficient condition for the existence of DTFT?
- What is the nature of DTFT of the signal?
- Is DTFT continuous or discrete?
What are the the disadvantage of DTFT?
Two computational disadvantages of the DTFT are: the direct DTFT is a function of a continuously varying frequency and the inverse DTFT requires integration. The Fourier series coefficients constitute a periodic sequence of the same period as the signal; thus both are periodic.
What are the necessary and sufficient condition for the existence of DTFT?
Sufficient Condition for Existence of the DTFT
A sequence x[n] satisfying (7.7) is said to be absolutely summable, and when (7.7) holds, the infinite sum defining the DTFT X(ej ˆω) in (7.2) is said to converge to a finite result for all ˆω.
What is the nature of DTFT of the signal?
As N approaches infinity, the time domain becomes aperiodic, and the frequency domain becomes a continuous signal. This is the DTFT, the Fourier transform that relates an aperiodic, discrete signal, with a periodic, continuous frequency spectrum.
Is DTFT continuous or discrete?
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.
