Dtft in matlab

1. What is DTFT used for?
2. What is DTFT equation?
3. Is DTFT same as DFT?

What is DTFT used for?

In mathematics, the discrete-time Fourier transform (DTFT) is a form of Fourier analysis that is applicable to a sequence of values. The DTFT is often used to analyze samples of a continuous function.

What is DTFT equation?

The DTFT of the convolution sum of two signals x1[n] and x₂[n] is the product of their DTFTs, X₁(e^jω) and X₂(e^jω). That is: y [ n ] = x 1 [ n ] * x 2 [ n ] ⇔ Y ( e j ω ) = X 1 ( e j ω ) X 2 ( e j ω ) .

Is DTFT same as 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.