Hi all, I have an exercise, and i should compute the wiener-hopf equations for a symmetric zero phase wiener filter. I have started from the fact that the symmetry and the zero phase imply h[n]=h[-n] for the coefficients of the filter and I compute the following equation sum{h(l)[Rx(k-l)+Rx(l-k)+Rx(k+l)+Rx(-k-l)]}=Rxs(k)+Rxs(-k), where l=0,...,N , k=0,...,N Rx is the autocorrelation Rxs is the cross-correlation of x(input) and s(signal which is estimated). Now i must solve the above equation an i don't know how to do it, any ideas;

# Symmetric Wiener Filter

Started by ●March 21, 2007

Reply by ●March 21, 20072007-03-21

On 21 Mar, 12:23, "Wiz" <skata...@mail.gr> wrote:> Hi all, > I have an exercise, and i should compute the wiener-hopf equations for > a symmetric zero phase wiener filter. I have started from the fact that > the symmetry and the zero phase imply h[n]=h[-n] for the coefficients of > the filter and I compute the following equation > sum{h(l)[Rx(k-l)+Rx(l-k)+Rx(k+l)+Rx(-k-l)]}=Rxs(k)+Rxs(-k), where > l=0,...,N ,Never EVER use l as index in a formula. It is too easy to confuse with l. Or was it 1? One of them.> k=0,...,N Rx is the autocorrelation Rxs is the > cross-correlation > of x(input) and s(signal which is estimated). Now i must solve the above > equation an i don't know how to do it, any ideas;Set the system up on matrix form: R*h = r where R is a matrix, and r and h are vectors. Rune

Reply by ●March 22, 20072007-03-22

Rune Allnor wrote:> On 21 Mar, 12:23, "Wiz" <skata...@mail.gr> wrote: > > > Hi all, > > I have an exercise, and i should compute the wiener-hopf equations for > > a symmetric zero phase wiener filter. I have started from the fact that > > the symmetry and the zero phase imply h[n]=h[-n] for the coefficients of > > the filter and I compute the following equation > > sum{h(l)[Rx(k-l)+Rx(l-k)+Rx(k+l)+Rx(-k-l)]}=Rxs(k)+Rxs(-k), where > > l=0,...,N , > > Never EVER use l as index in a formula.Unless you can use \ell :-).

Reply by ●March 22, 20072007-03-22

On 22 Mar, 11:00, "Andor" <andor.bari...@gmail.com> wrote:> Rune Allnor wrote: > > On 21 Mar, 12:23, "Wiz" <skata...@mail.gr> wrote: > > > > Hi all, > > > I have an exercise, and i should compute the wiener-hopf equations for > > > a symmetric zero phase wiener filter. I have started from the fact that > > > the symmetry and the zero phase imply h[n]=h[-n] for the coefficients of > > > the filter and I compute the following equation > > > sum{h(l)[Rx(k-l)+Rx(l-k)+Rx(k+l)+Rx(-k-l)]}=Rxs(k)+Rxs(-k), where > > > l=0,...,N , > > > Never EVER use l as index in a formula. > > Unless you can use \ell :-).If you use LaTeX. I prefer to use a one-to-one correspondence between my maths and my code, so I stay away even from \ell in stuff that is used as basis for implemented code. Rune