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Deconvolution problem

Started by niuer October 8, 2008
Hi guys,
   I have a theoretical relationship that variable z = convolution(x, y ).
I now have vectors of z and x and I am trying to deconvolute them to get
vector y. I tried to to FFT to solve for y. The problem is that I also got
some oscillation in the y vector while there should be none. The shape of
the vectors z and x all look like bell shape and they look pretty smooth.
They are close to zero(but no zeros there) at the tails. Anybody has any
idea how should I fix this problem, either using filter or other method?

Thanks for your advice,
Neil


Neil wrote:
> Hi guys, > � �I have a theoretical relationship that variable z = convolution(x, y ). > I now have vectors of z and x and I am trying to deconvolute them to get > vector y. I tried to to FFT to solve for y. The problem is that I also got > some oscillation in the y vector while there should be none. The shape of > the vectors z and x all look like bell shape and they look pretty smooth. > They are close to zero(but no zeros there) at the tails. Anybody has any > idea how should I fix this problem, either using filter or other method? > > Thanks for your advice, > Neil
If the frequency domain approach via FFT doesn't work for you, try time domain inversion via Wiener SysID Filter. Remember that (assuming that x[n] = y[n] = 0 for n <0) z[n] = sum_k=0^n x[k] y[n-k] or written out: z[0] = x[0] y[0] z[1] = x[0] y[1] + x[1] y[0] z[2] = x[0] y[2] + x[1] y[1] + x[2] y[0] ... and so on. This is linear in the unknown y, and you can use least- squares (for noisy observations z) or minimax (for smooth z) inversion techniques to find y. Regards, Andor
>Neil wrote: >> Hi guys, >> =A0 =A0I have a theoretical relationship that variable z =3D
convolution(=
>x, y ). >> I now have vectors of z and x and I am trying to deconvolute them to
get
>> vector y. I tried to to FFT to solve for y. The problem is that I also
go=
>t >> some oscillation in the y vector while there should be none. The shape
of
>> the vectors z and x all look like bell shape and they look pretty
smooth.
>> They are close to zero(but no zeros there) at the tails. Anybody has
any
>> idea how should I fix this problem, either using filter or other
method?
>> >> Thanks for your advice, >> Neil > >If the frequency domain approach via FFT doesn't work for you, try >time domain inversion via Wiener SysID Filter. Remember that (assuming >that x[n] =3D y[n] =3D 0 for n <0) > >z[n] =3D sum_k=3D0^n x[k] y[n-k] > >or written out: > >z[0] =3D x[0] y[0] >z[1] =3D x[0] y[1] + x[1] y[0] >z[2] =3D x[0] y[2] + x[1] y[1] + x[2] y[0] >... > >and so on. This is linear in the unknown y, and you can use least- >squares (for noisy observations z) or minimax (for smooth z) inversion >techniques to find y. > >Regards, >Andor >
Thanks for your reply. I don't have DSP background, do you know any good reference on 'Wiener SysID Filter'? and I don't understand the '3D' in your formula. Would you please explain more? thanks for your time. Neil
On 8 Okt., 16:16, "niuer" <iam...@gmail.com> wrote:
> >Neil wrote: > >> Hi guys, > >> =A0 =A0I have a theoretical relationship that variable z =3D > convolution(= > >x, y ). > >> I now have vectors of z and x and I am trying to deconvolute them to > get > >> vector y. I tried to to FFT to solve for y. The problem is that I also > go= > >t > >> some oscillation in the y vector while there should be none. The shape > of > >> the vectors z and x all look like bell shape and they look pretty > smooth. > >> They are close to zero(but no zeros there) at the tails. Anybody has > any > >> idea how should I fix this problem, either using filter or other > method? > > >> Thanks for your advice, > >> Neil > > >If the frequency domain approach via FFT doesn't work for you, try > >time domain inversion via Wiener SysID Filter. Remember that (assuming > >that x[n] =3D y[n] =3D 0 for n <0) > > >z[n] =3D sum_k=3D0^n x[k] y[n-k] > > >or written out: > > >z[0] =3D x[0] y[0] > >z[1] =3D x[0] y[1] + x[1] y[0] > >z[2] =3D x[0] y[2] + x[1] y[1] + x[2] y[0] > >... > > >and so on. This is linear in the unknown y, and you can use least- > >squares (for noisy observations z) or minimax (for smooth z) inversion > >techniques to find y. > > >Regards, > >Andor > > Thanks for your reply. > I don't have DSP background, do you know any good reference on 'Wiener > SysID Filter'?
Any book on adaptive / optimal filters, or more generally, statistical signal processing.
> and I don't understand the '3D' in your formula. > Would you please explain more?
That's funny. Everytime I type "=" it seems to show up as "=3D" in your newsreader. I've been posting many "="'s here in this group, and you are the first one to attach a 3D, so I assume that this a problem of your reader software. Essentially, I just wrote out the convolution sum and noted that it is linear in the unknown variable and suggeste how to solve for the variable. What's not clear? Regards, Andor
Andor wrote:

   ...

> That's funny. Everytime I type "=" it seems to show up as "=3D" in > your newsreader. I've been posting many "="'s here in this group, and > you are the first one to attach a 3D, so I assume that this a problem > of your reader software.
Do you have an ASCII table? $3D = decimal 61; the code for '='. Do you notice some lines ending in '20'? Jerry -- Engineering is the art of making what you want from things you can get. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095; ** Posted from http://www.teranews.com **