john wrote:> Jerry Avins wrote:...>>Minimum phase was implicit in the question. The phase response that >>one derives from a magnitude response is always minimum phase. To reverse >>the process, one must travel the same path.> So what about the ideal LPF example I gave? Does it work?No. It specifies phase and amplitude independently. Such a specification is almost never minimum phase. An ideal low-pass is clearly not one of the rare exceptions. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Hilbert transform to calculate Magnitude from Phase?
Started by ●February 2, 2005
Reply by ●February 4, 20052005-02-04
Reply by ●February 4, 20052005-02-04
Jacob Scarpaci wrote:> I believe the one issue that is left out here is that thecalculation> referred to > > phase{H(f)} = -Hilbert{ log|H(f)| } > > is actually a relationship between the Magnitude spectrum and the > Minimum Phase. i.e. > > minphase{H(f)} = -Hilbert{ log|H(f)| } > > This is a one to one relationship, if you know the Mag you know theMin> Phase. It does not work for other phase spectrums. > > So I believe that Robert is correct that you can reverse thealgorithm> if you have the signals minphase spectrumI have seen this argument before, regarding phase and magnitude spectra. The 1975 Oppenheim / Schafer book investigates the real and imaginary parts of the spectrum in terms of Hilbert transform pairs, and the whole derivation is shown there in all its gory detail. O&S mentions the mag/phase being a Hilbert transform pair in the context of cepstra, and only as a nice design *choise* for ensuring the *cepstrum* to be real-valued. Could somebody please come up with a reference to where it is shown that magnityude and phase being a Hilbert transform pair also ensures that the time signal, not the cepstrum, is minimum phase? Rune
Reply by ●February 4, 20052005-02-04
Rune Allnor wrote: ...> Could somebody please come up with a reference to where it is > shown that magnityude and phase being a Hilbert transform pair > also ensures that the time signal, not the cepstrum, is > minimum phase?Google gives me http://sepwww.stanford.edu/sep/prof/pvi/spec/paper_html/node13.html. In a db-amplitude/log(frequency) plot, the amplitude part of a Bode plot, sketch in the asymptotes. From the intersections, read off the poles and zeros. (Single ones where the slope changes 6 dB/8ve.) The phase derived from them, either by rules of thumb or by math, give the minimum-phase response. I have the derivation you want in Guilleman somewhere, but there are several Guilleman's on my shelf, and you'll have to bribe me to hunt through them. Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●February 4, 20052005-02-04
Yes, I guess I left out the "minimum phase" stipulation in the question. Is was meant to be there. "robert bristow-johnson" <rbj@audioimagination.com> wrote in message news:BE27BFC9.43E6%rbj@audioimagination.com...> in article 1107448616.648053.229600@f14g2000cwb.googlegroups.com, Jacob > Scarpaci at scarpaci@gmail.com wrote on 02/03/2005 11:36: > > > I believe the one issue that is left out here is that the calculation > > referred to > > > > phase{H(f)} = -Hilbert{ log|H(f)| } > > > > is actually a relationship between the Magnitude spectrum and the > > Minimum Phase. i.e. > > > > minphase{H(f)} = -Hilbert{ log|H(f)| } > > > > This is a one to one relationship, if you know the Mag you know the Min > > Phase. It does not work for other phase spectrums. > > > > So I believe that Robert is correct that you can reverse the algorithm > > if you have the signals minphase spectrum > > it was my assumption from the beginning. you know what that word ass_u_me > can do to a person. i guess, whenever i see the words "Hilbert Transform" > associated with the words "Magnitude" and "Phase", that's what comes to > mind. > > > -- > > r b-j rbj@audioimagination.com > > "Imagination is more important than knowledge." > >
Reply by ●February 4, 20052005-02-04
in article 4203bebb$1@news.xetron.com, Billw at notarealemail@nowhere.com wrote on 02/04/2005 13:28:> Yes, I guess I left out the "minimum phase" stipulation in the question. Is > was meant to be there.well, i guess that would leave out all-pass filter. -- r b-j rbj@audioimagination.com "Imagination is more important than knowledge."
