In the definitions given in the previous slide for quantities such as and the signal is available in digital form and stored in a computer. Many of these integrals can instead be evaluated in terms of the probability density function of the signal . The advantages of this approach are:

1. can be determined using hardware (instruments) and,

2. is a usually a smooth function of its argument and hence integrals involving can be accurately calculated by high order numerical integration formulas.

However, the difficulty of having a long enough signal for is now transferred to waiting for a long enough time to determine . The accuracy with which is measured depends on the choice of the window and total time .

In general, for small values a large value of time is required for satisfactory convergence of the limit process arising in the definition of . In terms of the mean and RMS values are defined as follows:

For signals that do not have a zero mean

The th order moment of a signal with a zero mean is defined as