Periodic Signals

Abstract

The fact that the great majority of functions which may usefully be considered as signals are functions of time lends justification to the treatment of signal theory in terms of time and of frequency. A periodic signal will therefore be considered to be one which repeats itself exactly every T seconds, where T is called the period of the signal waveform; the theoretical treatment of periodic waveforms assumes that this exact repetition is extended throughout all time, both past and future. Portions of such continuous periodic waveforms are illustrated in figure 2.1. In practice, of course, signals do not repeat themselves indefinitely. Nevertheless, a waveform such as the output voltage of a mains rectifier prior to smoothing^8,16 does repeat itself very many times, and its analysis as a strictly periodic signal yields valuable results. In other cases, such as the electrocardiogram, the waveform is quasi-periodic and may usefully be treated as truly periodic for some purposes. It

is worth noting that a truly repetitive signal is of very little interest in a communications channel, since no further information is conveyed after the first cycle of the waveform has been received. One of the main reasons for discussing periodic signals is that a clear understanding of their analysis is a great help when dealing with aperiodic and random ones.