Symmetric Wiener Filter

Started by March 21, 2007
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;

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
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 :-).
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