Scientific Computing

This module illustrates the *twiddle factors* (i.e., complex roots
of unity) that play a fundamental role in the discrete Fourier
transform. For a given integer *n*, the *n*th root of unity
is given by *ω*_{n} = cos(2 *π*
⁄ *n*) − *i* sin(2 *π* ⁄ *n*) =
*e*^{−2π i ⁄ n}*n*, *m*, and *k*, the value of
*ω*_{n}^{mk} is plotted in the
complex plane.

The user selects values for *n* and *m* from the menus and
clicks the plus and minus buttons to increment or decrement *k*.
As *k* changes, the twiddle factor moves around the unit circle in
jumps of equal size.

**Reference:** Michael T. Heath, *Scientific Computing,
An Introductory Survey*, 2nd edition, McGraw-Hill, New York,
2002. See Section 12.1, especially Figure 12.1.

**Developers:** Evan VanderZee and Michael Heath