Lecture 16 Random Signals and Noise (III). Fall 2008 NCTU EE Tzu-Hsien Sang. 1. 1. 1. 1. Outline. Terminology of Random Processes Correlation and Power Spectral Density Linear Systems and Random Processes Narrowband Noise. Linear Systems and Random Processes.
Mean = mx; auto-correlation = RX().
RX(t1,t2) = (t1-t2) = () andSX(f) = 1 (constant).
(1) X(t) Gaussian, H() stable, linear Y(t) Gaussian.
(2) X(t) Gaussian and WSS X(t) is SSS.
(3) Samples of a Gaussian process, X(t1), X(t2), …, are uncorrelated They are independent.
(4) Samples of a Gaussian process, X(t1), X(t2), …, have a joint Gaussian pdf specified completely by the set of means and auto-covariance function .
It is just a way to describe a band-limited noise with the bandwidth of an ideal band-pass filter.