Coefficients
cn in the complex Fourier series
f(t)
= ... +
c-2 e-2 i ω t +
c-1 e-i ω t + c0 + c1
ei ω t + c2 e2 i ω t +
....
are
selected using the windows at bottom. The windows at lower right record
the values of |cn| and Arg(cn) 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 |cn| or Arg(cn) .
Sliders at left also control these values.
The
window at lower left records the value of cn on the complex
plane, and the value of cn 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 cn and c-n are forced to be conjugate.
©
2008 H.
Miller and J.-M. Claus