handout_week14_a

handout_week14_a - Stochastic Signals and Systems Analysis...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Stochastic Signals and Systems Analysis and Processing of Random Signals Virginia Tech Fall 2008 Power Spectral Density For deterministic processes (signals), Fourier series and Fourier transform represent the frequency components as a “frequency spectrum” Frequency components refer to an average rate of change (averaged over possible realizations) The power spectral density S ( f ) of a signal x ( t ) is a function that gives the variation of density of power with frequency, which can be defined as S ( f ) = lim T →∞ 1 2 T ± ± ± ± ± Z T - T x ( t ) e - j 2 π ft dt ± ± ± ± ± 2
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Power Spectral Density Frequencies are related to autocorrelation function High autocorrelation more “memory” in process, slower changes Low autocorrelation less “memory” in process, faster changes The autocorrelation function R ( τ ) of a power signal x ( t ) is defined as the time average R ( τ ) = lim T →∞ 1 2 T Z T - T x ( t ) x ( t + τ ) dt The autocorrelation function and power spectral density of a power signal are closely related this relationship is stated formally by the Wiener-Khinchine theorem: S ( f ) = F [ R ( τ )] = Z -∞ R ( τ ) e - j 2 π f τ d τ Power Spectral Density The power spectral density
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 7

handout_week14_a - Stochastic Signals and Systems Analysis...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online