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>