Reply by robert bristow-johnson●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."
Reply by Billw●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 Jerry Avins●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 Rune Allnor●February 4, 20052005-02-04
Jacob Scarpaci wrote:
> 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
I 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 Jerry Avins●February 4, 20052005-02-04
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.
�����������������������������������������������������������������������
Reply by robert bristow-johnson●February 3, 20052005-02-03
in article 1107470791.086854.147730@g14g2000cwa.googlegroups.com, john at
johns@xetron.com wrote on 02/03/2005 17:46:
> So what about the ideal LPF example I gave? Does it work?
if it's a minimum-phase LPF, then the magnitude response and phase response
are directly related to each other by the Hilbert transform which is, with
the exception of a "DC" component, invertable.
--
r b-j rbj@audioimagination.com
"Imagination is more important than knowledge."
Reply by john●February 3, 20052005-02-03
Jerry Avins wrote:
> robert bristow-johnson wrote:
> > 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)} =3D -Hilbert{ log|H(f)| }
> >>
> >>is actually a relationship between the Magnitude spectrum and the
> >>Minimum Phase. i.e.
> >>
> >>minphase{H(f)} =3D -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.
>
> 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.
>
> Jerry
> --
> Engineering is the art of making what you want from things you can
get.
>
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=
=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF=AF
So what about the ideal LPF example I gave? Does it work?
John
Reply by Jerry Avins●February 3, 20052005-02-03
robert bristow-johnson wrote:
> 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.
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.
Jerry
--
Engineering is the art of making what you want from things you can get.
�����������������������������������������������������������������������
Reply by robert bristow-johnson●February 3, 20052005-02-03
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 Jacob Scarpaci●February 3, 20052005-02-03
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
Jake