DFT of a function and array convolution

1. How do you find the DFT of a function?
2. Why DFT does not support linear convolution?
3. What is DFT convolution?
4. What is the function of DFT?

How do you find the DFT of a function?

The DFT formula for X k X_k Xk​ is simply that X k = x ⋅ v k , X_k = x \cdot v_k, Xk​=x⋅vk​, where x x x is the vector ( x 0 , x 1 , … , x N − 1 ) .

Why DFT does not support linear convolution?

This is because you can only process on a finite amount of data points. The problem however is that when you perform transformations into the frequency domain using the DFT, by definition a signal cannot be finite.

What is DFT convolution?

Convolution is cyclic in the time domain for the DFT and FS cases (i.e., whenever the time domain has a finite length), and acyclic for the DTFT and FT cases. ^3.6. The convolution theorem is then. (3.23) That is, convolution in the time domain corresponds to pointwise multiplication in the frequency domain.

What is the function of DFT?

The Discrete Fourier Transform (DFT) is of paramount importance in all areas of digital signal processing. It is used to derive a frequency-domain (spectral) representation of the signal.