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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.

 
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Chapter One. Discrete Sequences and Systems

Chapter Two. Periodic Sampling

Chapter Three. The Discrete Fourier Transform

Chapter Four. The Fast Fourier Transform

Chapter Five. Finite Impulse Response Filters

Chapter Six. Infinite Impulse Response Filters

Chapter Seven. Specialized Lowpass FIR Filters

Chapter Eight. Quadrature Signals

Chapter Nine. The Discrete Hilbert Transform

Chapter Ten. Sample Rate Conversion

Chapter Eleven. Signal Averaging

Chapter Twelve. Digital Data Formats and Their Effects

Chapter Thirteen. Digital Signal Processing Tricks

Appendix A. The Arithmetic of Complex Numbers

Appendix B. Closed Form of a Geometric Series

Appendix C. Time Reversal and the DFT

Appendix D. Mean, Variance, and Standard Deviation

Appendix E. Decibels (dB and dBm)

Appendix F. Digital Filter Terminology

Appendix G. Frequency Sampling Filter Derivations

Appendix H. Frequency Sampling Filter Design Tables

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Understanding Digital Signal Processing
Understanding Digital Signal Processing (2nd Edition)
ISBN: 0131089897
EAN: 2147483647
Year: 2004
Pages: 183
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