Appendix D. Mean, Variance, and Standard Deviation

In our studies, we're often forced to consider noise functions. These are descriptions of noise signals that we cannot explicitly describe with a time-domain equation. Noise functions can be quantified, however, in a worthwhile way using the statistical measures of mean, variance, and standard deviation. Although here we only touch on the very broad and important field of statistics, we will describe why, how, and when to use these statistical indicators, so that we can add them to our collection of signal analysis tools. First we'll determine how to calculate these statistical values for a series of discrete data samples, cover an example using a continuous analytical function, and conclude this appendix with a discussion of the probability density functions of several random variables that are common in the field of digital signal processing. So let's proceed by sticking our toes in the chilly waters of the mathematics of statistics to obtain a few definitions.