AR parameter estimation

Hi all

i am working on reverberation rejection algorithm based on AR prewhitening.


According to my understanding i can model a time-domain signal (say A)
using AR method and if i pass a unit variance white noise through the
filter based on AR parameters, i should get a signal approximate to
original signal(A).

I have tried to implement same theory in MATLAB using ar, armcov etc for AR
parameter estimation* and 'filter' command to filter wgn noise using ar
parameters but could not approximate the original signal anyway. 

*I created the original signal using random noise inserted with some peak
signals in it

Kindly help me 

Best Regards

abraham007 wrote:

> i am working on reverberation rejection algorithm based on AR prewhitening.
> 
> According to my understanding i can model a time-domain signal (say A)
> using AR method and if i pass a unit variance white noise through the
> filter based on AR parameters, i should get a signal approximate to
> original signal(A).

So far so good.

> I have tried to implement same theory in MATLAB using ar, armcov etc for AR
> parameter estimation* and 'filter' command to filter wgn noise using ar
> parameters but could not approximate the original signal anyway. 

"MATLAB: dumb methods for dumb people" (tm)

> *I created the original signal using random noise inserted with some peak
> signals in it
> 
> Kindly help me 

Help you what? What is the problem?

>
>
>abraham007 wrote:
>
>> i am working on reverberation rejection algorithm based on AR
prewhitening.
>> 
>> According to my understanding i can model a time-domain signal (say A)
>> using AR method and if i pass a unit variance white noise through the
>> filter based on AR parameters, i should get a signal approximate to
>> original signal(A).
>
>So far so good.
>
>> I have tried to implement same theory in MATLAB using ar, armcov etc for
AR
>> parameter estimation* and 'filter' command to filter wgn noise using ar
>> parameters but could not approximate the original signal anyway. 
>
>"MATLAB: dumb methods for dumb people" (tm)
>
>> *I created the original signal using random noise inserted with some
peak
>> signals in it
>> 
>> Kindly help me 
>
>Help you what? What is the problem?
>
Thanks for reply dear.Problem is that i am not being able to recover the
original signal as theory says.I have tried different orders of AR models
but result is always incorrect.

On Oct 5, 12:08&#4294967295;am, "abraham007" <abrahamnick73@n_o_s_p_a_m.yahoo.com>
wrote:
> >abraham007 wrote:
>
> >> i am working on reverberation rejection algorithm based on AR
> prewhitening.
>
> >> According to my understanding i can model a time-domain signal (say A)
> >> using AR method and if i pass a unit variance white noise through the
> >> filter based on AR parameters, i should get a signal approximate to
> >> original signal(A).
>
> >So far so good.
>
> >> I have tried to implement same theory in MATLAB using ar, armcov etc for
> AR
> >> parameter estimation* and 'filter' command to filter wgn noise using ar
> >> parameters but could not approximate the original signal anyway.
>
> >"MATLAB: dumb methods for dumb people" (tm)
>
> >> *I created the original signal using random noise inserted with some
> peak
> >> signals in it
>
> >> Kindly help me
>
> >Help you what? What is the problem?
>
> Thanks for reply dear.Problem is that i am not being able to recover the
> original signal as theory says.I have tried different orders of AR models
> but result is always incorrect.

You need to review the theory. The signal you construct with your
white noise input will have (approximately) the same spectral density
- it will not give you an exact reconstruction of some deterministic
signal.

If you use linear prediction (of sufficient order) the output is
decorrelated an should therefore be white. Note that it is not
necessarily gaussian, just white.

Therefore, running the filter in the reverse direction i.e. switching
inputs and outputs, feeding in a white input signal will generate a
signal which has the same spectral density as your input signal.

Cheers,
Dave

>You need to review the theory. The signal you construct with your
>white noise input will have (approximately) the same spectral density
>- it will not give you an exact reconstruction of some deterministic
>signal.
>
>If you use linear prediction (of sufficient order) the output is
>decorrelated an should therefore be white. Note that it is not
>necessarily gaussian, just white.
>
>Therefore, running the filter in the reverse direction i.e. switching
>inputs and outputs, feeding in a white input signal will generate a
>signal which has the same spectral density as your input signal.
>
>Cheers,
>Dave
>
Thanks much Dave. Yes, you are right, it is the spectral density that will
be reconstructed not the original signal.

 Now i come to the original problem. I want to cancel out reverberations
using AR Prewhitening before match filter operation. AR prewhitening
actually design an inverse filter using AR parameters estimated from data
set A and apply this inverse filter to immediate adjacent data set B.


If there is a time domain signal A in which only reverberations are present
and there is a time domain signal B in which reverberations plus some
target is present, does signals A and B have different spectral densities
(although reflections from surface and bottom(reverberation) and from
target are of same frequency pulse )?

Can you kindly put some light on how this prewhitener works?