# 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