Noise in Linear Systems Summary

 

1.   Random signals can be described by the autocorrelation function (ACF), , or by the power spectrum, .

2.   The ACF and power spectrum are a Fourier Transform pair (this is the Wiener-Khinchine theorem).

3.   White noise has a constant power spectrum independent of frequency, and a delta-function ACF.

4.   Johnson noise (also called Nyquist noise) arises in any dissipative element. For a resistor, .

5.   The  equivalent noise bandwidth is defined as:         

6.   For a signal , the maximum SNR is given by the Matched Filter. This has  and .