Non-infinite time domains makes things quite complicated. If, for example, the function is zero (or any other constant value) everywhere except some fixed segment on the time axis, such as the segment depicted on your image, the spectrum will be

*continuous*(and rather wide, in that case). It is calculated as

*Fourier transform*https://en.wikipedia.org/wiki/Fourier_transform[^].

If the function is

*strictly periodical*("strictly" also implies infinite domain in time), the spectrum is

*discrete*and is calculated as the

*Fourier series*: https://en.wikipedia.org/wiki/Fourier_series[^].

Note that a spectrum consists of the points which are characterized not just with frequency, but frequency/phase, which, apparently also can be expressed as a complex number.

The case of the sine function on an infinite time domain I mentioned fist is just the special case of strictly periodic function, which is trivial and makes the discrete spectrum of just one line at the frequency 1/t and some phase.

http://en.wikipedia.org/wiki/Sine_wave

If the 'Draw method is called repeatedly, are you aware it could be speeded up by a factor of at least #100 ? Why aren't you using the Paint Event ?