Summation limits in DFT

1. What are twiddle factors of the DFT?
2. What is L and N in DFT?
3. How do you calculate DFT coefficient?
4. What is linearity property of DFT?

What are twiddle factors of the DFT?

A twiddle factor, in fast Fourier transform (FFT) algorithms, is any of the trigonometric constant coefficients that are multiplied by the data in the course of the algorithm. This term was apparently coined by Gentleman & Sande in 1966, and has since become widespread in thousands of papers of the FFT literature.

What is L and N in DFT?

We have an L-sample-long sequence, x(n) , representing the analog continuous-time signal x(t) . The goal is to find a set of sinusoids which can be added together to produce x(n) . As discussed above, the DFT is based on sampling the DTFT, given by Equation 1, at equally spaced frequency points.

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 ) .

What is linearity property of DFT?

Linearity. The transform of a sum is the sum of the transforms: DFT(x+y) = DFT(x) + DFT(y). Likewise, a scalar product can be taken outside the transform: DFT(c*x) = c*DFT(x). These follow directly from the fact that the DFT can be represented as a matrix multiplication.