A realization of the random binary wave is shown in Figure 1 above. Such waveforms are used in binary communication- a pulse of amplitude 1 is used to transmit ‘1' and a pulse of amplitude -1 is used to transmit ‘0'.

The random process { X ( t )} can be written as,

where

Mean and Variance

For any t ,

Thus mean and variance of the process are constants.

Autocorrelation Function

When are not in the same pulse interval, and hence are independent.

To find the autocorrelation function for , let us consider the case . Depending on the delay D , the points may lie on one or two pulse intervals.