Coefficients c_n in the complex Fourier series

f(t) = ... + c_-2 e^{-2 i ω t} + c_-1 e^{-i ω t} + c₀ + c₁ e^{i ω t} + c₂ e^{2 i ω t} + ....

are selected using the windows at bottom. The windows at lower right record the values of |c_n| and Arg(c_n) by yellow diamonds and struts. The diamond and strut for the chosen value of n are gray. A mouse click on either window at lower right sets the value of n , and also the value of either |c_n| or Arg(c_n) . Sliders at left also control these values.

The window at lower left records the value of c_n on the complex plane, and the value of c_n can be chosen by a click and drag on that window.

A slider at lower right selects a value of a parameter φ . The graphing window at the top displays the graph of Re(e^{-i φ} f(t)) . Thus if φ = 0 , the real part of f(t) is displayed, while if φ = π/2, the imaginary part of f(t) is displayed.
Red vertical lines on this window also mark t = -L and t = +L , where L = π / ω , so that 2L is the period. A cursor rollover generates crosshairs and a readout of values of t and x .

A [Reset] key resets all coefficients to zero. Above the [Reset] key is a slider setting the value of ω.

At the top, a [f(t) real] key toggles the restriction on the values of the coefficients making f(t) real valued. When it is selected, c₀ is forced to be real and c_n and c_-n are forced to be conjugate.

© 2008 H. Miller and J.-M. Claus