This applet illustrates how an discrete fourier transformation works. The function y(x) is decomposed in it's sine a(k) and cosine b(k) components. In a second step the sines and cosines are combined again to a new function of time. Try a function with sharp edges like a rectangular function. You will see the typical ripples in the recomposition.
click the >> buttons for transformation of the signals or
- draw an own function in the first graph