>On Apr 10, 5:15 pm, "sopapo" <sop...@sopapo.com> wrote:
>> Hi everyone,
>>
>> I'm working on my phd thesis in a field related with the active noise
>> control and i'm looking for an algorithm with good tracking capability,
to
>> work with a time-varying input signal (non stastionary).
>>
>> I have made several test with FXLMS, N-FXLMS, Leaky-FXLMS without much
>> succes, I'm going in wrong direction with this algorithms?
>> Variable-step-size-LMS could improve that tracking capability?
>>
>> Any advice is welcomed.
>> Thx.
>
>Submit for a Masters.
>
>K.
>

Try googling for a Wiener-Hopf adaptive algorithm? From the description,
I'm not sure exactly what you're trying to do. D

On Apr 11, 7:16 am, "Manolis C. Tsakiris" <el01...@mail.ntua.gr>
wrote:
> >>> *.LMS are inherently bad algorithms. They are not optimal and can't be
> >> made optimal by the black magic manipulations. The only justification
> >> for the *.LMS is the simplicity.
>
> >> Vladimir Vassilevsky
> >> DSP and Mixed Signal Design Consultanthttp://www.abvolt.com
>
> >Actually a few years back there was a paper that proved that LMS is
> >optimal in the sense of H infinity.
>
> >K.
>
> Hi K.,
>
> do you remember who wrote the paper?
>
> Manolis

 H({infinity} ) optimality of the LMS algorithm
Hassibi, B | Sayed, A H | Kailath, T
IEEE Transactions on Signal Processing. Vol. 44, no. 2, pp. 267-280.
Feb. 1996

We show that the celebrated least-mean squares (LMS) adaptive
algorithm is H({infinity}) optimal. The LMS algorithm has been long
regarded as an approximate solution to either a stochastic or a
deterministic least-squares problem, and it essentially amounts to
updating the weight vector estimates along the direction of the
instantaneous gradient of a quadratic cost function. We show that the
LMS can be regarded as the exact solution to a minimization problem in
its own right. Namely, we establish that it is a minimax filter: it
minimizes the maximum energy gain from the disturbances to the
predicted errors, whereas the closely related so-called normalized LMS
algorithm minimizes the maximum energy gain from the disturbances to
the filtered errors. Moreover, since these algorithms are central
H({infinity}) filters, they minimize a certain exponential cost
function and are thus also risk-sensitive optimal. We discuss the
various implications of these results and show how they provide
theoretical justification for the widely observed excellent robustness
properties of the LMS filter

K.

>>> *.LMS are inherently bad algorithms. They are not optimal and can't be
>> made optimal by the black magic manipulations. The only justification
>> for the *.LMS is the simplicity.
>>
>> Vladimir Vassilevsky
>> DSP and Mixed Signal Design Consultanthttp://www.abvolt.com
>
>Actually a few years back there was a paper that proved that LMS is
>optimal in the sense of H infinity.
>
>K.
>

Hi K.,

do you remember who wrote the paper?

Manolis

On Apr 11, 1:32 am, Vladimir Vassilevsky <antispam_bo...@hotmail.com>
wrote:
> sopapo wrote:
> > Hi everyone,
>
> > I'm working on my phd thesis in a field related with the active noise
> > control and i'm looking for an algorithm with good tracking capability, to
> > work with a time-varying input signal (non stastionary).
>
> Excuse me, but what is exactly new in your thesis ?
>
> By definition, there is no way to track the non-stationary signal. In
> order to track the signal, you have to assume that it obeys some
> stationarity. Then it is down to the classic problem of Wiener/Kalman
> filter.
>
> > I have made several test with FXLMS, N-FXLMS, Leaky-FXLMS without much
> > succes, I'm going in wrong direction with this algorithms?
> > Variable-step-size-LMS could improve that tracking capability?
>
> *.LMS are inherently bad algorithms. They are not optimal and can't be
> made optimal by the black magic manipulations. The only justification
> for the *.LMS is the simplicity.
>
> Vladimir Vassilevsky
> DSP and Mixed Signal Design Consultanthttp://www.abvolt.com

Actually a few years back there was a paper that proved that LMS is
optimal in the sense of H infinity.

K.

>Running the software of your own, WDM mode.
>With Windows XP, it is possible to have the audio in-out processing 
>delay at the order of tens of milliseconds.

Two questions:

1)is kernel mode achievable with Windows XP?

2)when i process let's say classic music at 44.1kHz, then the distance
between two successive samples is 1/44100, approximately 0.02 msec. If the
delay of the hardware is say 10 msec then the predictor will operate with a
delay of 10/0.02 = 500 samples. I don't think that this can still be
considered as real-time processing. 

thanx,

Manolis

Manolis C. Tsakiris wrote:

>>>A piece of classic music is a broadband signal and consequently highly
>>>unpredictable.
>>
>>I have to disagree. A piece of classic music is quasi stationary and 
>>somewhat 90% predictable in the short term.
> 
> 
> You mean that by having let's say M samples of the piece 
> {u(i), u(i-1), ..., u(i-M+1)} i can predict with 90% accuracy the sample
> at time instant u(i+1)?

Pretty much so. The prediction gain is about 20dB on the average. That 
is part of the reason why the lossy audio compression schemes do so well.

> Is this predictability high because of the absence
> of impulses(for example drums)? What about a rock piece of music?

Boom-Boom is not too bad. What knocks the predictor down is the high 
frequency tchk-tchk, cymbals and such.

>
>>>i did not have time even to invert a matrix. For heavy stuff consider
>>>TMS320).
>>
>>Yes, largely it is a computing issue. BTW, a common PC with P-4 beats up
>>the single DSPs easily.
> 
> yes but can you do the processing in real time with a common PC? If yes
> how?

Running the software of your own, WDM mode.
With Windows XP, it is possible to have the audio in-out processing 
delay at the order of tens of milliseconds.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

>
>
>Manolis C. Tsakiris wrote:
>
>> A piece of classic music is a broadband signal and consequently highly
>> unpredictable.
>
>I have to disagree. A piece of classic music is quasi stationary and 
>somewhat 90% predictable in the short term.


You mean that by having let's say M samples of the piece 
{u(i), u(i-1), ..., u(i-M+1)} i can predict with 90% accuracy the sample
at time instant u(i+1)? Is this predictability high because of the absence
of impulses(for example drums)? What about a rock piece of music?


>> 1)Choose a representative signal to be tracked (i.e. of a given degree
of
>> non-stationarity).
>> 2)experiment in MATLAB with different adaptive filters. Choose the
filter
>> that serves you better.
>> 3)implement it in real time (i have used ADSP 21065L of Analog Devices
and
>> i did not have time even to invert a matrix. For heavy stuff consider
>> TMS320).
>
>Yes, largely it is a computing issue. BTW, a common PC with P-4 beats up

>the single DSPs easily.

yes but can you do the processing in real time with a common PC? If yes
how?

thanx,

Manolis

Manolis C. Tsakiris wrote:

> A piece of classic music is a broadband signal and consequently highly
> unpredictable.

I have to disagree. A piece of classic music is quasi stationary and 
somewhat 90% predictable in the short term.

> 1)Choose a representative signal to be tracked (i.e. of a given degree of
> non-stationarity).
> 2)experiment in MATLAB with different adaptive filters. Choose the filter
> that serves you better.
> 3)implement it in real time (i have used ADSP 21065L of Analog Devices and
> i did not have time even to invert a matrix. For heavy stuff consider
> TMS320).

Yes, largely it is a computing issue. BTW, a common PC with P-4 beats up 
the single DSPs easily.


Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

sopapo wrote:

> Hi everyone,
> 
> I'm working on my phd thesis in a field related with the active noise 
> control and i'm looking for an algorithm with good tracking capability, to 
> work with a time-varying input signal (non stastionary).

Excuse me, but what is exactly new in your thesis ?

By definition, there is no way to track the non-stationary signal. In 
order to track the signal, you have to assume that it obeys some 
stationarity. Then it is down to the classic problem of Wiener/Kalman 
filter.


> I have made several test with FXLMS, N-FXLMS, Leaky-FXLMS without much 
> succes, I'm going in wrong direction with this algorithms?
> Variable-step-size-LMS could improve that tracking capability?

*.LMS are inherently bad algorithms. They are not optimal and can't be 
made optimal by the black magic manipulations. The only justification 
for the *.LMS is the simplicity.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

A piece of classic music is a broadband signal and consequently highly
unpredictable. If your ANC configuration is feedback, then the performance
of the LMS type algorithms is expected to be poor. The reason is that in
the feedback ANC configuration, where the reference signal is synthesized
from the error signal, the adaptive filter operates as a predictor of the
noise to be cancelled. If the noise to be cancelled is highly random, then
the ability of the adaptive filter to predict it will be small. 

For this reason, i suggest that you consider the feedforward configuration
(if it can be applied at your problem), which can work pretty good for
highly non-stationary signals. If it cannot be applied, do not expect many
things from feedback ANC.

At any case, you can experiment in the feedback ANC with more advanced
adaptive filters. For example the Affine Projection Algorithm (APA) has
better tracking capabilities than the LMS (RLS is often worse than LMS in
tracking but not always). APA is something between LMS and RLS. The
adaptive Kalman filter, used in highly non-stationary environments, is
another possiblity, though very advanced. 

Finally, the correct order is:
1)Choose a representative signal to be tracked (i.e. of a given degree of
non-stationarity).
2)experiment in MATLAB with different adaptive filters. Choose the filter
that serves you better.
3)implement it in real time (i have used ADSP 21065L of Analog Devices and
i did not have time even to invert a matrix. For heavy stuff consider
TMS320).

Manolis