Radio Receiver Design
This reference focuses on understanding and designing radio receivers and systems, presenting the characteristics of individual receiver components and their interaction in cascade.
TABLE OF CONTENTS Radio Receiver Design
Chapter 9: Appendix
9.1 Gaussian or Normal Statistics
Gaussian Probability Density Function
The equation for the general Gaussian probability density function (GPDF) is
| (9.1) |  |
where
| ? | = | the mean or average, |
| ? | = | the standard deviation, |
| x | = | the variable under consideration. |
The Gaussian distribution is also referred to as a normal distribution. It is common to speak of a Gaussian or normal distribution with mean ? and standard deviations. Thermal noise is almost universally assumed to be a zero mean process. The mean value of the noise is zero, i.e., the noise has no DC component because it has been passed through a capacitor. The GPDF for thermal noise is
| (9.2) |  |
Normalized Gaussian Probability Density Function
For the sake of calculation, we sometimes assume that the mean of the GPDF in Equation 9.1 equals zero and that the standard deviation equals 1. These assumptions produce the normalized Gaussian probability density function (NGPDF). The equation for the NGPDF is
| (9.3) |  |
where z = the normalized value of x.
Figure 9-1 shows the normalized Gaussian probability density function. Figure 9-2 illustrates the area A(z) and tail functions T(s) of the Gaussian PDF. Figure 9-3 shows the area and tail functions.
Figure 9-1: The normalized Gaussian probability density function (NGPDF).
Figure 9-2: The NGPDF and associated areas. The area under the curve from 0 to z is denoted by A(z). The area under the curve from z to infinity is denoted as T(z).
Figure 9-3: The area and...
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