Understanding the twiddle factors

1. What is twiddle factor?
2. How do you calculate twiddle factors?
3. What are properties of twiddle factor?
4. Why do we use twiddle factors?

What is twiddle factor?

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.

How do you calculate twiddle factors?

In Figure 1 the twiddle factors are shown as e^–j2πQ/N, where variable Q is merely an integer in the range of 0 ≤ Q ≤ (N/2)–1. To simplify this blog's follow-on figures, we'll use Figures 1(c) and 1(d) to represent the DIF and DIT butterflies.

What are properties of twiddle factor?

The twiddle factors are inversely symmetric about the origin. This means that only the first half (0 to pi) of the twiddle factors contain all the necessary information as the second half is just an inverse of the first half.

Why do we use twiddle factors?

Why do we use twiddle factors? We use the twiddle factor to reduce the computational complexity of calculating DFT and IDFT. Alternatively, we can also say that the twiddle factor has periodicity/a cyclic property.