DFT application will show the steps inside a Discrete Fourier Transform. DFT may help you grasp the concept. The easiest way to see it is to program one frequency into this application.

You can see the amplitude cancel when it is off the reference frequency. You can also add several frequencies to see the resulting waveform. May be interesting if your studying Fourier Transforms. Input signals have 48db S/N. Results are 768db S/N. (Of course, you'll never know because of the low resolution output).