4.5 STATISTICAL PARAMETERS

The simplest statistic to compute is the mean, which, mathematically, is in fact the arithmetic mean. For N signal samples, this is

(4.4)

This is what we commonly refer to as the average. Strictly speaking, this quantity is the sample mean because it is derived from a sample or subset of the entire population (not to be confused with the fact that a signal itself is sampled, in the signal processing sense). The symbol μ denotes the population mean, which is the mean of values if we have the entire set of possible samples available. Usually, we work with a subset of observed (sampled) values; hence, the sample mean is what we are referring to. If we take different subsets of samples, the sample mean calculated from each set itself forms a distribution which is representative of the population mean.