> > >> I wasn't gonna comment any more but there is this question: > > > >> For a matched filter you start with a replica of the signal of interest. > > >> You use this to operate on a noisy/perturbed version of the signal. > > > >> Then you operate some more. > > > > If you just want the magnitude of the signal multiple passes probably > > > won't be any better than one filtering. > > > > The reason for this is the noise that was -- or maybe wasn't -- > > > filtered ends up in the frequencies and phase angles of the "noise > > > free" signal altering the magnitude. > > > > Additional passes will make the signal look more like the original > > > clean but the magnitude will always be off somewhat _even if you > > > correct for it each pass by comparing it to the magnitude of the > > > "replica" match filtered with itself_. > > > > This could be easily demonstrated on Excel. > > > >> Then you operate some more.... > > > >> And, in the end you get the replica which you started with???? > > > > Not if you correct for differences in the magnitude of the template > > > with the magnitude of the filtered signal. > > > > As long as you do that each time the magnitudes will be different. > > > > Anything more than once is probably a waste of time, however, because > > > the error will remain. > > > >> How is that useful? > > > > In the example shown on my page the convolution wasn't much better > > > than not filtering at all. > > > > The additional step of recovering the original signal -- the > > > deconvolution --reduced the error from noise by 2/3rds. > > > >> You already have the replica. That's what you > > >> started with. Extracting the replica from itself seems useless. > > > > The template won't generally be the same magnitude as the match > > > filtered signal. > > > > Bret Cahill > > > You already agreed about the magnitude with one pass. > > Going beyond that..... you say that you are getting a version of the > > replica which is beyond getting the magnitude. > > I am not disputing that one bit. > > But, I still ask, what is that good for? > > Said another way: > > - if you have the replica > > - if you can extract the best estimate of magnitude with a classical > > matched filter (still subject to calibration of course) > > What is left to know? > > Why do you think that the traditional match filter output will give > the same estimate of magnitude as the deconvolution of that output? > > The deconvolution step reverses some of the low pass filtering effect > of match filtering so you'll get different results depending on the > noise and signal frequencies.
By taking the square root of each frequency, the deconvolution step tends to level magnitudes in the frequency domain. Whatever noise or signal frequencies that were low magnitude in the convolution will be amplified in the deconvolution and vice versa.
More work is necessary to determine what the deconvolution step does to filtered snr in high or low SNR w/ signal bandwidth noise.