DFT of Transient vs. Analytical Solution

1. What is the difference between DFT and IDFT?
2. Why do we need discrete Fourier transform?
3. How do you calculate DFT coefficient?
4. Which sequence is applied for DFT?

What is the difference between DFT and IDFT?

The DFT allows one to convert a set of digital time samples to its frequency domain representation. In contrast, the IDFT can be used to invert the DFT samples, allowing one to reconstruct the signal samples x(k) directly from its frequency domain form, X(m).

Why do we need discrete Fourier transform?

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.

How do you calculate DFT coefficient?

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 ) .

Which sequence is applied for DFT?

In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency.