Howtosignalprocessing
- What are the the disadvantage of DTFT?
- What is the condition for the existence of DTFT?
- Why we use DFT instead of DTFT?
- What is the difference between DTFT DFT and FFT?
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 is the condition for the existence of DTFT?
So existence means simply that the sum that defines a DTFT does not blow up. This is easy to prove for absolutely summable sequences. If you take the magnitude of the DTFT at any point omega, this is equal to the sum for n that goes from minus infinity to plus infinity of x[n] times e to the- j omega n in magnitude.
Why we use DFT instead of DTFT?
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.
What is the difference between DTFT DFT and FFT?
DTFT gives a higher number of frequency components. DFT gives a lower number of frequency components. DTFT is defined from minus infinity to plus infinity, so naturally, it contains both positive and negative values of frequencies. DFT is defined from 0 to N-1; it can have only positive frequencies.
