1 / 13

Power spectral density . frequency-side,  , vs. time-side, t

Power spectral density . frequency-side,  , vs. time-side, t /2 : frequency (cycles/unit time). Non-negative Unifies analyses of processes of widely varying types. Examples. Spectral representation . stationary increments - Kolmogorov.

Télécharger la présentation

Power spectral density . frequency-side,  , vs. time-side, t

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Power spectral density. frequency-side, , vs. time-side, t /2 : frequency (cycles/unit time) Non-negative Unifies analyses of processes of widely varying types

  2. Examples.

  3. Spectral representation. stationary increments - Kolmogorov

  4. Frequency domain approach. Coherency, coherence Cross-spectrum. Coherency. R MN() = f MN()/{f MM() f NN()} complex-valued, 0 if denominator 0 Coherence |R MN()|2 = |f MN()| 2 /{f MM() f NN()| |R MN()|2 1, c.p. multiple R2

  5. Proof. Filtering. M = {j }  a(t-v)dM(v) =  a(t-j ) Consider dO(t) = dN(t) -  a(t-v)dM(v)dt, (stationary increments) where A() =  exp{-iu}a(u)du fOO () is a minimum at A() = fNM()fMM()-1 Minimum: (1 - |RMN()|2 )fNN() 0  |R MN()|2 1

  6. Proof. Coherence, measure of the linear time invariant association of the components of a stationary bivariate process.

  7. Empirical examples. sea hare

  8. Muscle spindle

  9. Spectral representation approach. Filtering. dO(t)/dt =  a(t-v)dM(v) =  a(t-j ) =  exp{it}dZM()

  10. Partial coherency. Trivariate process {M,N,O} “Removes” the linear time invariant effects of O from M and N

More Related