for a random signal (AR) y(k)=-a1y(k-1)-a2y(k-2)-...-any(k-n)+e(k) (e(k) is white noise) I am a bit confused - I understood the YW normal equations were of the form Ra = b where R is the correlation matrix a=[a1,a2...an] is the parameter vector and b=[-r(2),-r(3)...-r(n)] However I see many web refs to the above which has the same except b=[sigma^2,0,0...0] where sigma^2 is the variance of y eg http://www.cbi.dongnocchi.it/glossary/YuleWalker.html ? Naebad

# Yule Walker Equations for LPC

Started by ●January 8, 2006

Reply by ●January 9, 20062006-01-09

You get the Yule-Walker equations by multiplying the equation with itself and taking the expectations. The multiplication yields the following kind of products y(k-m)y(k-r) , which on taking the expectation give you the coefficients of the correlation matrix. y(k-m)e(k), On expectation...this just goes to 0. Signal and noise are supposed to be uncorrelated. One term with e(k)e(k)...This gives you the sigma^2 (noise power) on expectation. Work it out. You should be able to get it. Raja naebad wrote:> for a random signal (AR) > > y(k)=-a1y(k-1)-a2y(k-2)-...-any(k-n)+e(k) (e(k) is white noise) > > I am a bit confused - I understood the YW normal equations were of the > form > > > Ra = b > > where R is the correlation matrix > > > a=[a1,a2...an] is the parameter vector and > > b=[-r(2),-r(3)...-r(n)] > > However I see many web refs to the above which has the same except > > b=[sigma^2,0,0...0] > > where sigma^2 is the variance of y eg > > http://www.cbi.dongnocchi.it/glossary/YuleWalker.html > > ? > > Naebad