> >>>> Because if you ain't applying a filter to the purpose for which it is > >>>> designed > > >>> If you can't figure out how to use convolutions and match filtering to > >>> determine magnitudes of noisy signals you need to start a thread > >>> entitled "A Scholarly Enumeration of Filters& Their Purposes." > > >>> Maybe you can get it in Wikipedia! > > >>> Bret Cahill > > >> Wiki is a bit weak on iterative deconvolution algorithms. > > >> The sort of thing you are asking about, or rather a version that > >> actually works in practice was invented in 1974 by Hogbom as the CLEAN > >> algorithm for radio astronomy. His original paper is online at: > > >>http://www.astro.rug.nl/~vdhulst/SignalProcessing/Project1_data/clean... > > >> Variants of this algorithm are still used today in aperture synthesis > >> although I prefer other deconvolution algorithms myself. > > > In match filtering the deconvolution step to recover the original > > [filtered]wave form isn't complicated. Just take the square root in > > the frequency domain, IMSQRT in Excel. > > Anyone who says deconvolution isn't complicated demonstrably does not > have the first clue about the subject of signal processing.
The issue here is the special kind of convolution used in match filtering.
If you want to change the issue to convolutions generally feel free to start another thread.
> Convolution > is easy but deconvolution is usually
Does this include the convolution of a function with itself?
Remember, no dodging.
> a very difficult inverse problem.
Unless the convolution is of a signal with a kernel or a kernel with itself.
In that case the deconvolution just requires taking the square root in the frequency domain.
> > Of course, if the magnitude of the kernel is different than the > > magnitude of the signal -- the general case -- then the magnitude of > > the recovered signal will be the sqrt of the product of the 2 > > magnitudes.
> > If you want to get the original magnitude of the signal just square > > the mag. of the filtered signal and then divide by the mag. of the > > kernel, or, to keep errors equal, divide by the kernel match filtered > > with itself. > > > This was done 7 decades ago, wasn't it? > > Your description is so vague and woolly that
that anyone with an even a junior level applied math background should be able to show it on Excel.
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