Minimum phase vice versa minimum phase

Hello,

I'm actually confused with minimum phase.
I know actually two applications for minimum phase:

1. A FIR filter is designed and the result typically is a time domain
signal (or taps) with a symmetric structure = linear phase
This filter can be converted to a minimum phase filter e.g. by methods
described at dspguru. So for example Hilbert transforms are often
used.
If I do a FFT to the minimum phase filter I can calculate the
magnitude and the minimum phase response.

2. If I measure the response of a loudspeaker in a room I get a time
domain signal too. This signal contains minimum phase (because of the
causal behaviour of the speaker) and excessive phase. I read that the
minimum phase extraction can also be done by some kind of Hilbert
transform. After applying a FFT to the result I expect to be able to
calculate again magnitude and minimum phase response.

Because I'm new to DSP (not too much knowledge about unit circles
etc.) I have used a given example of an algorithm for point 1
successfully. Can I use it also for point 2 ?

I recognized that point 1 and 2 are always treated indepandantly but
to me the given tasks seem to be very similar.
Is there an algorithm existing that solves both points or do I need
two different algorithms?

Uli Brueggemann

Hi Uli,

I'm sorry but I don't understand your question. You say you get a 
minimum phase (impulse?) response from your speaker and are asking how 
to calculate a minimum phase impulse response from the DFT of that 
response...? Why would you need the DFT in the first place if your 
response is already minimum phase. Can you be more specific what you 
are trying to do?
-- 
Stephan M. Bernsee
http://www.dspdimension.com

uli.brueggemann@freenet.de (Uli Brueggemann) wrote in message news:<c77c52c1.0411021137.196600bf@posting.google.com>...
> Hello,
> 
> I'm actually confused with minimum phase.
> I know actually two applications for minimum phase:
> 
> 1. A FIR filter is designed and the result typically is a time domain
> signal (or taps) with a symmetric structure = linear phase
> This filter can be converted to a minimum phase filter e.g. by methods
> described at dspguru. So for example Hilbert transforms are often
> used.
> If I do a FFT to the minimum phase filter I can calculate the
> magnitude and the minimum phase response.

...just the same way a DFT will reveal the mixed-phase response of a 
mixed-phase filter or a maximum-phase response of a maximum-phase filter.

> 2. If I measure the response of a loudspeaker in a room I get a time
> domain signal too. This signal contains minimum phase (because of the
> causal behaviour of the speaker) and excessive phase.

I am not completely sure what you mean here, I think you mean what I 
would term "mixed phase". Minimum phase has nothing to do with causality, 
since this aspect of the phase response is giverned by zeros in the 
transfer function. Causality is caused by the poles of the transfer 
function being located inside the unit circle. A completely different 
thing.

> I read that the
> minimum phase extraction can also be done by some kind of Hilbert
> transform. After applying a FFT to the result I expect to be able to
> calculate again magnitude and minimum phase response.

Where did you read that? The "easy" way of finding a minimum phase 
response to your system, is to use an AR method to model your system.
This will produce a system filter that is minimum pase. The problem 
is that many physical systems are mixed phase, so that these naive 
ideas don't always work. There was a couple of guys who investigated 
mixed/phase parameters a few years ago, try to search for authors
Milton and Ursin in the seismics literature. 

> Because I'm new to DSP (not too much knowledge about unit circles
> etc.) I have used a given example of an algorithm for point 1
> successfully. Can I use it also for point 2 ?
> 
> I recognized that point 1 and 2 are always treated indepandantly but
> to me the given tasks seem to be very similar.
> Is there an algorithm existing that solves both points or do I need
> two different algorithms?
> 
> Uli Brueggemann

Rune

"Rune Allnor" <allnor@tele.ntnu.no> wrote in message 
news:f56893ae.0411022344.68e32dfb@posting.google.com...
> uli.brueggemann@freenet.de (Uli Brueggemann) wrote in message 
> news:<c77c52c1.0411021137.196600bf@posting.google.com>...

Snipped

>
> I am not completely sure what you mean here, I think you mean what I
> would term "mixed phase". Minimum phase has nothing to do with causality,
> since this aspect of the phase response is giverned by zeros in the
> transfer function. Causality is caused by the poles of the transfer
> function being located inside the unit circle. A completely different
> thing.

One minor clarification, the causality is determined by the Region of 
Convergence (ROC) that you want for the Z transform. The DFT automatically 
assumes the ROC mag(z) <= 1 (I believe the equality holds). By choosing 
different ROCs you trade off causality with stability.

For most purposes in DSP the convenient ROC (shown above) is taken, and what 
Rune says is correct.

Cheers,
David 

Stephan M. Bernsee <spam@dspdimension.com> wrote in message news:<2ur9j6F2daq9uU1@uni-berlin.de>...
> Hi Uli,
> 
> I'm sorry but I don't understand your question. You say you get a 
> minimum phase (impulse?) response from your speaker and are asking how 
> to calculate a minimum phase impulse response from the DFT of that 
> response...? Why would you need the DFT in the first place if your 
> response is already minimum phase. Can you be more specific what you 
> are trying to do?

Hi Stephan,

in my understanding a loudspeaker driver behaves like a minimum phase
system. This means that after a short time the driver reacts to an
impulse with a big amplitude and then the amplitude decays.
In a room this reaction is overlaid by the sound transfer to the
listening position. So the different wavelengths together with the
transfer distance plus room reflections result in a lot of phase
changes. The impulse response arriving is thus a much more complex mix
of the original minimum phase and the so-called excessive phase.
The goal is to extract the minimum phase included in the impulse
response and to get a time domain signal without the excessive phase.

Uli

Hello Rune,

> I am not completely sure what you mean here, I think you mean what I 
> would term "mixed phase". Minimum phase has nothing to do with causality, 
> since this aspect of the phase response is giverned by zeros in the 
> transfer function. Causality is caused by the poles of the transfer 
> function being located inside the unit circle. A completely different 
> thing.

Linear phase filters with the symmetric structure are described e.g.
in dspguide as non-causal. If you consider the center as zero then the
left sided taps are negative. This cannot happen in nature of course.

> 
> > I read that the
> > minimum phase extraction can also be done by some kind of Hilbert
> > transform. After applying a FFT to the result I expect to be able to
> > calculate again magnitude and minimum phase response.
> 
> Where did you read that? The "easy" way of finding a minimum phase 
> response to your system, is to use an AR method to model your system.
> This will produce a system filter that is minimum pase. The problem 
> is that many physical systems are mixed phase, so that these naive 
> ideas don't always work. There was a couple of guys who investigated 
> mixed/phase parameters a few years ago, try to search for authors
> Milton and Ursin in the seismics literature. 
> 

in a book about loudspeaker measurements of d'Appolito.
In comparison to the filter design here we get the impulse response
from a measurement. The room response contains now a minimum phase and
an excessive phase, maybe we can say in total a mixed phase. I want to
extract the minimum phase. Several audio measurement software packages
can do it, but I don't know how.

What is an AR method?


Uli

On 2004-11-03 15:08:19 +0100, uli.brueggemann@freenet.de (Uli 
Brueggemann) said:

>  The impulse response arriving is thus a much more complex mix
> of the original minimum phase and the so-called excessive phase.

That would be early and late reflections from the room together with 
the IR of the loudspeaker, correct?

> The goal is to extract the minimum phase included in the impulse
> response and to get a time domain signal without the excessive phase.

I would either measure the IR of the loudspeaker in an anechoic chamber 
(this would be the easiest way), or use a separate step to measure the 
room impulse response without the loudspeaker in question (for example, 
by using a different loudspeaker with a known IR). You can then 
deconvolve the two IRs from your combined (measured) IR. Look for the 
keyword "deconvolution" I'm sure you'll find some references.

If the room is large enough and you can capture the sound directly from 
the source you might be lucky and can probably just cut off the 
combined IR after several samples to get rid of the room response. That 
won't work if you use a sine sweep for the measurement, but it will 
work with an impulse.

Btw. if you don't mind a personal question - are you in any way related 
to a Mrs. Br�ggemann who does vinyl cutting the the Frankfurt area?
-- 
Stephan M. Bernsee
http://www.dspdimension.com

Uli Brueggemann wrote:


> in my understanding a loudspeaker driver behaves like a minimum phase
> system. This means that after a short time the driver reacts to an
> impulse with a big amplitude and then the amplitude decays.
> In a room this reaction is overlaid by the sound transfer to the
> listening position. So the different wavelengths together with the
> transfer distance plus room reflections result in a lot of phase
> changes. The impulse response arriving is thus a much more complex mix
> of the original minimum phase and the so-called excessive phase.
> The goal is to extract the minimum phase included in the impulse
> response and to get a time domain signal without the excessive phase.

You can definitely convert what you measure to minimum phase 
but it will only be what the speaker generated, which I'm 
not sure is truly minimum phase anyway, if the room 
preserves the magnitude response.  That is very unlikely.


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

Stephan M. Bernsee <spam@dspdimension.com> wrote in message news:<2usblrF2dq62tU3@uni-berlin.de>...
> On 2004-11-03 15:08:19 +0100, uli.brueggemann@freenet.de (Uli 
> Brueggemann) said:
> 
> >  The impulse response arriving is thus a much more complex mix
> > of the original minimum phase and the so-called excessive phase.
> 
> That would be early and late reflections from the room together with 
> the IR of the loudspeaker, correct?
> 
> > The goal is to extract the minimum phase included in the impulse
> > response and to get a time domain signal without the excessive phase.
> 
> I would either measure the IR of the loudspeaker in an anechoic chamber 
> (this would be the easiest way), or use a separate step to measure the 
> room impulse response without the loudspeaker in question (for example, 
> by using a different loudspeaker with a known IR). You can then 
> deconvolve the two IRs from your combined (measured) IR. Look for the 
> keyword "deconvolution" I'm sure you'll find some references.
> 
> If the room is large enough and you can capture the sound directly from 
> the source you might be lucky and can probably just cut off the 
> combined IR after several samples to get rid of the room response. That 
> won't work if you use a sine sweep for the measurement, but it will 
> work with an impulse.
> 
> Btw. if you don't mind a personal question - are you in any way related 
> to a Mrs. Br&#4294967295;ggemann who does vinyl cutting the the Frankfurt area?

Hello Stephan,

I need the algorithm exactly for room correction purposes, the
possibility of an anechoic chamber is not given. So I have to measure
the speaker in a room and to do the extraction job. I have
possibiltites to measure with an impulse or with a log sine sweep
(that convolved with the right inverse sweep delivers the right
impulse response, much better: nonlinearities are detected, see Angelo
Farina article about LogSweep measurements).

I'm sorry, no relationship to Mrs. Br&#4294967295;ggemann.

Uli

Uli Brueggemann wrote:

  ...

> I need the algorithm exactly for room correction purposes, the
> possibility of an anechoic chamber is not given. So I have to measure
> the speaker in a room and to do the extraction job. I have
> possibiltites to measure with an impulse or with a log sine sweep
> (that convolved with the right inverse sweep delivers the right
> impulse response, much better: nonlinearities are detected, see Angelo
> Farina article about LogSweep measurements).

Convolving with a pseudo-random bit sequence has a higher average- to
peak-power ratio than any other method. You can't be sure that a
loudspeaker has a minimum-phase free-field response. Placing microphone
and loudspeaker on tall step ladders outdoors in a field of tall grass
makes a rather good anechoic setup, according To George Briggs of Wharfdale.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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