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Re: Re: maximum entropy method for deconvolution

• To: mathgroup at smc.vnet.net
• Subject: [mg75489] Re: [mg75469] Re: maximum entropy method for deconvolution
• From: Sseziwa Mukasa <mukasa at jeol.com>
• Date: Thu, 3 May 2007 03:40:15 -0400 (EDT)
• References: <200704281000.GAA09123@smc.vnet.net><f146p6$mcq$1@smc.vnet.net> <200705020749.DAA04907@smc.vnet.net>

On May 2, 2007, at 3:49 AM, dantimatter wrote:

>
> Thanks to all for the help, and a special thanks to Guillermo Sanchez
> for the Modeling and Simulation notebook.  I'm finding that my answer
> is still 'unpleasant'.

I'm not sure what you mean by unpleasant.

> Could it be that the convolution of a function
> with a step-function is something that simply cannot be deconvolved?

In general, yes.

> That perhaps there's information lost in the convolution and it could
> never be recovered?

Yes because the spectrum of a step function is sinc function which of  
course means you're multiplying by 0 in the frequency domain at the  
nodes of the sinc.

There are approximate methods for this problem since it's equivalent  
to finding a "good" pseudoinverse to a singular Toeplitz matrix  See  
http://www.math.ucdavis.edu/~strohmer/papers/1995/str1695.html for a  
case in which the inverse can be found.

If you ever stumble on a good solution for a non-bandwidth limited  
signal please let me know.

Regards,

Sseziwa

• References:
  • Re: maximum entropy method for deconvolution
    • From: dantimatter <dantimatter@gmail.com>