Fourier series (cont.)

In depth
In-depth

 

If, as is always the case in practice, the channel has a finite bandwidth, then we can expect to receive a non-perfect replica of the input time domain waveform, unless all of its Fourier series components fall within the available channel bandwidth.

The output response of a channel passing only the first three frequency components of the square wave is shown here and clearly demonstrates the change caused by restricted bandwidth on the time domain waveform. This example also shows, however, that the 1, 0, 1, 0, 1, 0, ... data stream can still easily be detected without all the constituent frequency components of the original square wave, and in fact correct demodulation is possible if only the fundamental component is passed by the channel.