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Design of a deconvolution filter

Started by axr0284 January 22, 2006
Hi,
 I am really new to this so bear with me. I got a homework assignment for
a course called analytical topics and I was wondering if anybody could
help me figure it out. I don't need a complete answer but just some
pointers of where to begin with this problem and how to proceed. Thank you
very much for any information. The setup is as follows:

I am given an fir filter:
y(k)=sum[u(k-i)h(k)] for i=0 to i=n-1
In terms of discrete time convoution
y=h*u

Design a deconvolution filter which has fir form
z(k)=sum[y(k-i)g(k)] for i=0 to i=m-1

I need to find g so that the filter output is approximately the channel
input delayed by D samples, i.e z(k) approximately equal to u(k=D)
(g*h)(D) = 0 for k not equal to D
(g*h)(D) = 1 for k equal to D

It is also given that the least square equalizer is the g that minimizes
the sum-of -squares error:
[(g*h)(D)-1]^2+sum[((g*h)(k))^2] for k not equal to D

FIND THE LEAST SQUARES EQUALIZER g OF LENGTH m=20 WITH DELAY D=12

I am also given a vector h=[ 0.3571;-0.5714;0.7143;0.7143;-0.5714;0.3571]
and a vector y that contains 105 elements and it states that u={1,-1} and
k starts at 0.

Thanks a lot for any answer.
Amish


"axr0284" <axr0284@rit.edu> wrote in message
news:lK-dnbKzaKFXuknenZ2dnUVZ_sCdnZ2d@giganews.com...
> Hi,
> Thanks a lot for any answer. > Amish > >
Yeh right - you want us to do your homework? Dream on!
> >"axr0284" <axr0284@rit.edu> wrote in message >news:lK-dnbKzaKFXuknenZ2dnUVZ_sCdnZ2d@giganews.com... >> Hi, > >> Thanks a lot for any answer. >> Amish >> >> > >Yeh right - you want us to do your homework? Dream on! > > > >
If you had read the whole thread, I did not ask for an answer just pointers of where to start with this. Amish
Look for discrete-time Wiener filter.
You need to solve the Yule-Walker equations (a.k.a. normal equations) for
the given setup.
Emre

>Hi, > I am really new to this so bear with me. I got a homework assignment
for
>a course called analytical topics and I was wondering if anybody could >help me figure it out. I don't need a complete answer but just some >pointers of where to begin with this problem and how to proceed. Thank
you
>very much for any information. The setup is as follows: > >I am given an fir filter: >y(k)=sum[u(k-i)h(k)] for i=0 to i=n-1 >In terms of discrete time convoution >y=h*u > >Design a deconvolution filter which has fir form >z(k)=sum[y(k-i)g(k)] for i=0 to i=m-1 > >I need to find g so that the filter output is approximately the channel >input delayed by D samples, i.e z(k) approximately equal to u(k=D) >(g*h)(D) = 0 for k not equal to D >(g*h)(D) = 1 for k equal to D > >It is also given that the least square equalizer is the g that minimizes >the sum-of -squares error: >[(g*h)(D)-1]^2+sum[((g*h)(k))^2] for k not equal to D > >FIND THE LEAST SQUARES EQUALIZER g OF LENGTH m=20 WITH DELAY D=12 > >I am also given a vector h=[
0.3571;-0.5714;0.7143;0.7143;-0.5714;0.3571]
>and a vector y that contains 105 elements and it states that u={1,-1}
and
>k starts at 0. > >Thanks a lot for any answer. >Amish > > >