Gain of an IIR Filter

On Sep 5, 12:22 am, Jerry Avins <j...@ieee.org> wrote:
>
> I think that phase due to pure delay is irrelevant. Consider my playing
> the CD you made for me tonight and again tomorrow night using the same
> equipment. 'Nuff said?

yup.  that's all i was trying to say.  in this extreme case (pure
delay) the effect of change of phase is decidedly inaudible.  that
erects a boundary on one side (linear phase APF, a.k.a. "delay line"
is inaudible).

> >   H(z) = (z^(-N) - p)/(1 - p*z^(-N))
>
> > certainly if p=0, you are left with a pure delay that we are not
> > counting as an audible difference since the listener has no reference
> > to hear it against (no direct path, no echoes).  the listener cannot
> > be expected to know if some particular sound got delayed 25 ms or
> > not.  but a non-trivial psycho-acoustic perceptual question arizes
> > when p <> 0 and N > 0.  what values of delay N, and feedback
> > coefficient, p, cause the listener to know that the APF was placed in
> > the signal path as opposed to not?  i can safely say that if p = 0.95
> > and N = 20000 (assuming approx 44 kHz sampling rate), that any
> > listener who is not deaf will hear the difference for sounds that have
> > a beginning and an end.  but it's an APF, no frequency components are
> > changed in amplitude.
>
> > now whether or not a listener can hear the difference when the common
> > source is a solid periodic tone, that's a different story.  certainly
> > if the tone is a single sinusoid, the listener cannot know the
> > difference, for the same reason as the pure delay, we are phase
> > insensitive to that.  but if the tone has harmonics and some harmonics
> > are delayed differently than other harmonics, it is a useful and non-
> > trivial question to ask "under what circustances can we hear a
> > difference?"
>
> Yes. I, guru that I am can tell you. :-) Try this with a percussive
> sound, wood block showing the effect better than most drum skins. But
> the effect is subtle, and I for one don't ordinarily care.

it won't be so subtle if p = 0.98 and N = 20000 (assuming 44.1 kHz
sampling rate).  you would care.  but it's still an all-pass filter.

> > this is the only well-defined context i can think of where this
> > "audibility of phase" question really is meaningful.
>
> Agreed.

we're one big happy agreeing family. :-)

r b-j

Hello,

>> only well-defined context i can think of where this
> > "audibility of phase" 

I've got a related example:
In a piano, there are several strings tuned "almost" to the same
frequency.
But they are slightly off-tune - it may be one Hz or even less - and it's
heard as a beat note.

Or: Time-varying phase difference meets the ear's nonlinearity.

Cheers

Markus

"robert bristow-johnson" <rbj@audioimagination.com> wrote in 
message 
news:1188954726.414162.141250@50g2000hsm.googlegroups.com...

> i am envisioning listening to two, possibly different and 
> possibly
> identical, sounds, one after the other.  this is what i 
> would call "AB
> Testing" as opposed to "ABX Testing" where in the latter 
> you hear two
> sounds (A&B) that are nominally different, and then a 
> third sound (X)
> that you assign to A or B.  in AB Testing, you hear two 
> sounds and you
> have to say if they are the same or if they are not. 
> there will be an

If you're open to looking at this from another angle, choose 
a low frequency sinusoid, say 110 Hz.  Apply it to Left Ear 
through good headphones.  Phase modulate the Left Ear signal 
+/- Pi with a very low frequency sinusoid, say 2 Hz.  Apply 
phase modulated signal to Right Ear.  I'd expect the 
combination to be perceived as the sensation of a large 
insect circling one's head.  Removing the phase modulation 
should dead-center the "bug" directly in front of or behind 
you.

It's easy to verify by experiment...

My guess about the outcome:
- Phase shift alone will not give any spacial sensation, because the ear
cannot resolve phase, as discussed.

- It should work fine with a more complicated waveform - guitar strums for
example - if it's delayed on one ear (linear phase change over frequency).


I've once seen a demo, where the direction-dependent frequency response
was also modeled. The result was impressive, a really realistic illusion.

Cheers

Markus

mnentwig wrote:

> It's easy to verify by experiment...

> My guess about the outcome:
> - Phase shift alone will not give any spacial sensation, because the ear
> cannot resolve phase, as discussed.

> - It should work fine with a more complicated waveform - guitar strums for
> example - if it's delayed on one ear (linear phase change over frequency).

As I understand it, the ear can resolve phase.

Direction sense involves the time difference between the arrival at
the two ears, and so needs some way to sense phase.  I believe, though,
that it is processed separately from the frequency (musical) sense.
I suppose that many natural sounds are phase insensitive so there is no
advantage and some disadvantage to including phase in the frequency sense.

-- glen

"glen herrmannsfeldt" <gah@ugcs.caltech.edu> wrote in message 
news:JIqdnVSzPZr2CkPbnZ2dnUVZ_qiinZ2d@comcast.com...

>
> As I understand it, the ear can resolve phase.
>
> Direction sense involves the time difference between the arrival at
> the two ears, and so needs some way to sense phase.  I believe, though,
> that it is processed separately from the frequency (musical) sense.
> I suppose that many natural sounds are phase insensitive so there is no
> advantage and some disadvantage to including phase in the frequency sense.
>

Clearly, something resolves phase differences, but it probably doesn't 
happen in the inner ear.  It would be interesting to know whether the 
auditory system does position estimation based on TDOA (phase) or amplitude 
differences (or both).  Surely someone has done some research that answers 
this question?

On Sep 5, 5:39 am, "John E. Hadstate" <jh113...@hotmail.com> wrote:
> "robert bristow-johnson" <r...@audioimagination.com> wrote in
> messagenews:1188954726.414162.141250@50g2000hsm.googlegroups.com...
>
> > i am envisioning listening to two, possibly different and
> > possibly
> > identical, sounds, one after the other.  this is what i
> > would call "AB
> > Testing" as opposed to "ABX Testing" where in the latter
> > you hear two
> > sounds (A&B) that are nominally different, and then a
> > third sound (X)
> > that you assign to A or B.  in AB Testing, you hear two
> > sounds and you
> > have to say if they are the same or if they are not.
> > there will be an
>
> If you're open to looking at this from another angle, choose
> a low frequency sinusoid, say 110 Hz.  Apply it to Left Ear
> through good headphones.  Phase modulate the Left Ear signal
> +/- Pi with a very low frequency sinusoid, say 2 Hz.  Apply
> phase modulated signal to Right Ear.  I'd expect the
> combination to be perceived as the sensation of a large
> insect circling one's head.  Removing the phase modulation
> should dead-center the "bug" directly in front of or behind
> you.

i don't think that there is much controversy regarding the audibility
of Inter-Aural Phase Difference (or time difference).  this is what
the Blumlein stereo patent was about, i think.

http://mixonline.com/TECnology-Hall-of-Fame/alan-dower-blumlein-090106/
http://www.eqmag.com/article/blumlein-pair-stereo/Jul-07/29600
(i can't seem to find a good one with a diagram showing the time
arrival difference as a function of azimuth angle.)

if you applied the phase shift equally to both ears, would it make a
difference?

what the dispute (regarding audibility of phase) was about is if one
applies different amounts of time delays to different frequencies,
what happens if you pass through some hypothetical filter that changes
no amplitudes and is *not* phase linear.  apply the same filter to
both ears.

r b-j

On Sep 5, 7:23 am, "mnentwig" <mnent...@elisanet.fi> wrote:
> It's easy to verify by experiment...
>
> My guess about the outcome:
> - Phase shift alone will not give any spacial sensation,

i think John was saying something about different phase shifts applied
to the different ears simultaneously.  that's gotta do something to
one's sense of localization.

> because the ear
> cannot resolve phase, as discussed.

the gross example i cited (all-pass filter with very long delay
element inside) is such that there is *only* phase shift.  are you
saying that such is inaudible?

r b-j

On Sep 5, 9:51 am, robert bristow-johnson <r...@audioimagination.com>
wrote:
> On Sep 5, 5:39 am, "John E. Hadstate" <jh113...@hotmail.com> wrote:
>
>
>
> > "robert bristow-johnson" <r...@audioimagination.com> wrote in
> > messagenews:1188954726.414162.141250@50g2000hsm.googlegroups.com...
>
> > > i am envisioning listening to two, possibly different and
> > > possibly
> > > identical, sounds, one after the other.  this is what i
> > > would call "AB
> > > Testing" as opposed to "ABX Testing" where in the latter
> > > you hear two
> > > sounds (A&B) that are nominally different, and then a
> > > third sound (X)
> > > that you assign to A or B.  in AB Testing, you hear two
> > > sounds and you
> > > have to say if they are the same or if they are not.
> > > there will be an
>
> > If you're open to looking at this from another angle, choose
> > a low frequency sinusoid, say 110 Hz.  Apply it to Left Ear
> > through good headphones.  Phase modulate the Left Ear signal
> > +/- Pi with a very low frequency sinusoid, say 2 Hz.  Apply
> > phase modulated signal to Right Ear.  I'd expect the
> > combination to be perceived as the sensation of a large
> > insect circling one's head.  Removing the phase modulation
> > should dead-center the "bug" directly in front of or behind
> > you.
>
> i don't think that there is much controversy regarding the audibility
> of Inter-Aural Phase Difference (or time difference).  this is what
> the Blumlein stereo patent was about, i think.
>
> http://mixonline.com/TECnology-Hall-of-Fame/alan-dower-blumlein-090106/http://www.eqmag.com/article/blumlein-pair-stereo/Jul-07/29600
> (i can't seem to find a good one with a diagram showing the time
> arrival difference as a function of azimuth angle.)
>
> if you applied the phase shift equally to both ears, would it make a
> difference?
>
> what the dispute (regarding audibility of phase) was about is if one
> applies different amounts of time delays to different frequencies,
> what happens if you pass through some hypothetical filter that changes
> no amplitudes and is *not* phase linear.  apply the same filter to
> both ears.

LInear-phase filtering is already known to introduce some pre-ringing
artifacts at low frequencies.  Wouldn't any sharp phase discontinuity
centered at a bass frequency energy peak cause a similar effect?


IMHO. YMMV.
--
rhn A.T nicholson d.0.t C-o-M

glen herrmannsfeldt <gah@ugcs.caltech.edu> wrote in news:y8udnf47-d-
94UHbnZ2dnUVZ_u6rnZ2d@comcast.com:

> Not that phase isn't important, but the human auditory system is
> somewhat (not completely) insensitive to phase, and it isn't easy
> to control.   For a loudspeaker it usually depends on position in
> the room which makes it hard to give a specific value.

Actually, for lower frequency hearing (about 2K and below) the human 
auditory system is exquisitely sensitive to phase (specifically time delays 
between the two ears), and clearly uses the information for localizing 
sound sources.  

-- 
Scott
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