Hi Rune, I am very aware of the phase unwrapping problem. There can also be the huge problem of identifying what is what in the ceptrum. The breathtaking example for echo cancelling in O&S is an extremely ideal case. Schafer's thesis addressed multiple echos and (IIRC) filtered echoes that quickly compilcated things. Also, having a null in the spectrum and filling it with noise to avoid taking log(0), as someone suggested, should not be expected to give the right unwrapped phase. It is a difficult technique to use for many applications. Dirk Dirk Bell DSP Consultant Rune Allnor wrote:> dbell skrev: > > Hi Emre, > > > > IIRC from >20 years ago, there was an approach to cepstral > > deconvolution of f(n), n>=0, where there were nulls in the spectrum, > > that multiplied f(n) with a decaying exponential g(n)=e^(-an), for > > n>=0, a>0. Again, IIRC, the multiplication shifted the zeroes away > > from the unit circle so the the nulls were no longer present AND > > modified the cepstrum in a very predictable way. IIRC the cepstrum > > could then be modified, inverted, and the scaling by g(n) removed. > > > > I think you can work through the math (I did at the time), but I > > believe I saw this in Ron Schafer's MS (or is it S.M.?) disertation. > > I wouldn't be surprised if this was investigated by Schafer; I know > Oppenheim has written a thesis over cepstrum processing. > > However, nulls is only one of the problems with cepstra. Another > big problem is phase unwrapping. > > In order to extract the interesting pulse shapes, one needs to > both unwrap the phase of the spectrum unambiguously, and also > keep the FT pair of the log magnitude and unwrapped phase > in sync with the requirements to causal signals. > > Not very easy. > > Rune
spectral factorization using cepstral deconvolution
Started by ●December 23, 2006
Reply by ●December 26, 20062006-12-26
Reply by ●December 26, 20062006-12-26
dbell skrev:> Hi Rune, > > I am very aware of the phase unwrapping problem. There can also be the > huge problem of identifying what is what in the ceptrum. The > breathtaking example for echo cancelling in O&S is an extremely ideal > case. Schafer's thesis addressed multiple echos and (IIRC) filtered > echoes that quickly compilcated things. > > Also, having a null in the spectrum and filling it with noise to avoid > taking log(0), as someone suggested, should not be expected to give the > right unwrapped phase. > > It is a difficult technique to use for many applications.I saw that cepstra had been tested for deconvoltion of seismic signals in the mid '70s. The results could not have been good; the only way I know about this is from the table of contents from a book that went out of print ages ago. Some times I think that "advanced DSP" is more about finding explanations why some technique doesn't work, rather than use the techniques in applications. Rune
Reply by ●December 27, 20062006-12-27
dbell wrote:> Also, having a null in the spectrum and filling it with noise to avoid > taking log(0), as someone suggested, should not be expected to give the > right unwrapped phase.Yes, adding a noise floor should not be expected give the right unwrapped phase. However, the one experiment I tried with a series of decreasing noise floors did make the phase look as if it were converging somewhere. Whether or not it was converging to the right value, I don't know, but it did help me find some very low (if not provably minimum) impulse responses for a given frequency response. IMHO. YMMV. -- rhn A.T nicholson d.0.t C-o-M