Hi I know what the cepstrum of a univariate ARMA model is. Does anyone know how to extend the idea to multivariate ARMA processes? Recomendations for a good textbook? MODEL: x(t) = SUM( k=1..P, a(k)x(t-k) ) + SUM( k=1..Q, b(k)w(t-k) ) where w(t) ~ N(0,S) are normally distributed multivariate random variables, and x(t) is a z by 1 vector. DEFINITION FOR UNIVARIATE CASE, z=1: Simply put, it's the fourier transform of the power spectrum. A(z) = "Z"-transf. of a(k) = SUM( k=1..P, a(k)z^(-k) ); B(z) = "Z"-transf. of b(k) = SUM( k=1..Q, b(k)z^(-k) ); H(z) = system function = B(z) / A(z) log H(z) = SUM( k=0..infinity, h(k)z^(-k) ) and h(k) are the cepstrum coefficients! USES OF CEPSTRA You can define a "cepstral distance", eg in natural language processing. It's a measure of disparity between ARMA models (in this case). ANY help at all would be grately appreciated. Thanks very much -- Franco. (also posted to: sci.stat.math, sci.stat.consult, comp.dsp, comp.ai.nat-lang)

# multivariate cepstrum

Started by ●July 13, 2004

Reply by ●July 13, 20042004-07-13

"Francis Woolfe" <franco.woolfe@ntlworld.com> wrote in message news:UyXIc.146$3E6.69@newsfe2-win.ntli.net...> Hi > > I know what the cepstrum of a univariate ARMA model is. Does anyone knowhow> to extend the idea to multivariate ARMA processes? Recomendations for agood> textbook? > > MODEL: > > x(t) = SUM( k=1..P, a(k)x(t-k) ) + SUM( k=1..Q, b(k)w(t-k) ) > > where w(t) ~ N(0,S) are normally distributed multivariate randomvariables,> and x(t) is a z by 1 vector. > > DEFINITION FOR UNIVARIATE CASE, z=1: > > Simply put, it's the fourier transform of the power spectrum. > > A(z) = "Z"-transf. of a(k) = SUM( k=1..P, a(k)z^(-k) ); > B(z) = "Z"-transf. of b(k) = SUM( k=1..Q, b(k)z^(-k) ); > > H(z) = system function = B(z) / A(z) > > log H(z) = SUM( k=0..infinity, h(k)z^(-k) ) > > and h(k) are the cepstrum coefficients! > > USES OF CEPSTRA > > You can define a "cepstral distance", eg in natural language processing. > It's a measure of disparity > between ARMA models (in this case). > > > ANY help at all would be grately appreciated. Thanks very much -- Franco. > > (also posted to: sci.stat.math, sci.stat.consult, comp.dsp, > comp.ai.nat-lang) > >They are going to be Cepstrum matrices - not coefficients with your ARMA model. Tom

Reply by ●July 14, 20042004-07-14

"Francis Woolfe" <franco.woolfe@ntlworld.com> wrote in message news:<UyXIc.146$3E6.69@newsfe2-win.ntli.net>...> Hi > > I know what the cepstrum of a univariate ARMA model is. Does anyone know how > to extend the idea to multivariate ARMA processes? Recomendations for a good > textbook?...> (also posted to: sci.stat.math, sci.stat.consult, comp.dsp, > comp.ai.nat-lang)I have seen the 2D cepstrum mentioned in the context of image processing. You might want to at sci.image.processing as well. Rune