6.1 Principle of Averaging

In practice, it is frequently the case that a signal of limited duration is repeated in time several or many times, always after a certain not necessarily constant period; such a signal is called a repetitive signal. Should such a received signal be corrupted by additive noise, it is possible, after receiving more repetitions, to improve the signal to noise ratio by averaging. We utilise the fact that, for every time instant t _l from the beginning of the finite useful signal, there exist more measurements of the corrupted signal values (i.e. of the mixture of the signal and noise for the time instants t _k = t _{0 i} + t _l, which have a constant distance from the beginnings of repetitions, t _{0 i}). While the signal component value is identical in all the measurements, the noise assumes different values and, if it is generated by a stationary stochastic process with a zero mean, it will tend to disappear in the calculated average of all the measurements. The signal value, on the contrary, naturally remains untouched by the averaging. Such measurements and calculations should be done independently in parallel for a set of time instants t _l, l = 0, 1, ... N - 1, separated by a suitably selected sampling period T, thus providing estimates of sampled signal values. Note that the term average should be understood in the more general sense...