Howtosignalprocessing
- What is the condition for the Existence of DTFT?
- What is DTFT and its properties?
- What are the conditions for Existence of Fourier transform?
- How do you calculate DFT from DTFT?
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.
What is DTFT and its properties?
The discrete time Fourier transform is a mathematical tool which is used to convert a discrete time sequence into the frequency domain. Therefore, the Fourier transform of a discrete time signal or sequence is called the discrete time Fourier transform (DTFT).
What are the conditions for Existence of Fourier transform?
Condition for Existence of Fourier Transform
The function x(t) has a finite number of maxima and minima in every finite interval of time. The function x(t) has a finite number of discontinuities in every finite interval of time. Also, each of these discontinuities must be finite.
How do you calculate DFT from DTFT?
The continuous variable found in the DTFT (ω) is replaced with a finite number of frequencies located at 2πk/NTs. Here Ts is the sampling rate. In other words, if we take the DTFT signal and sample it in the frequency domain at omega=2π/N, then we get the DFT of x(n).
