On Tuesday, August 19, 2014 6:24:43 AM UTC+12, robert bristow-johnson wrote:
> On 8/18/14 8:15 AM, rsashwinkumar wrote:
> 
> > Thanks all!!
> 
> >
> 
> > I found the mistake. The IIR response I assumed turned out to be
> 
> > non-minimum phase.
> 
> > 	
> 
> 
> 
> i actually have to disagree with Hardy that LMS won't work to match a 
> 
> non-min phase system.  it doesn't really matter.
> 
> 
> 
> for example, LMS are used to do loudspeaker feedback cancellation for 
> 
> speaker phones.  that ain't no minimum-phase system.
> 
> 
> 
> i would suggest modifying it a little and use the Normalized LMS (NLMS) 
> 
> adaptive filter so that the neither the adaptation speed nor the step 
> 
> size are dependent on the loudness of the excitation signal.
> 
> 
> 
> 
> 
> -- 
> 
> 
> 
> r b-j                  rbj@audioimagination.com
> 
> 
> 
> "Imagination is more important than knowledge."

It will only work if you introduce a time-delay in the primary path. What he is doing is inverting a transfer function which is impossible (divergent) if NMP. However, with a delay you are using the uncausal part going backwards in time (hard to explain with out maths) which is convergent. The delay makes it causal.

On 8/18/14 8:15 AM, rsashwinkumar wrote:
> Thanks all!!
>
> I found the mistake. The IIR response I assumed turned out to be
> non-minimum phase.
> 	

i actually have to disagree with Hardy that LMS won't work to match a 
non-min phase system.  it doesn't really matter.

for example, LMS are used to do loudspeaker feedback cancellation for 
speaker phones.  that ain't no minimum-phase system.

i would suggest modifying it a little and use the Normalized LMS (NLMS) 
adaptive filter so that the neither the adaptation speed nor the step 
size are dependent on the loudness of the excitation signal.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

Thanks all!!

I found the mistake. The IIR response I assumed turned out to be
non-minimum phase. 
	 

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On Saturday, August 16, 2014 6:23:18 PM UTC+12, mnentwig wrote:
> Hi,
> 
> 
> 
> it may be a good idea to look into John G. Proakis, "Digital
> 
> communications", chapter 11 "Adaptive equalization". The book is IMHO worth
> 
> buying as paper copy even in the electronic age.
> 
> 
> 
> As a rule of thumb, the equalizer is the inverse of the channel. An IIR
> 
> channel gives an FIR equalizer, because numerator becomes denominator and
> 
> vice versa.
> 
> 
> 
> For a first step, I'd build a non-adaptive equalizer. You can do this
> 
> quickly by putting delayed replicas of the received signal (corresponding
> 
> to the eq's FIR taps) into a matrix M as column vectors:
> 
> 
> 
> Then, solve least-squares against the training sequence b (also column
> 
> vector) for 
> 
> 
> 
> [1]: M*c ~ b:
> 
> 
> 
> [2]: c = pinv(M)*b
> 
> 
> 
> c is then the vector of FIR filter coefficients. Plug it into [1]'s "M*c"
> 
> to apply it to the signal.
> 
> Use this as sanity check for delays and number of taps. It's pure
> 
> zero-forcing so it may misbehave for channel nulls. You can add or
> 
> concatenate a noise term to the signals, also to manage the equalizer's
> 
Easier way is to pick a first order example

1-0.5z^-1

It's inverse is a convergent series

1,0.5,0.25.0.125...etc

Hi,

it may be a good idea to look into John G. Proakis, "Digital
communications", chapter 11 "Adaptive equalization". The book is IMHO worth
buying as paper copy even in the electronic age.

As a rule of thumb, the equalizer is the inverse of the channel. An IIR
channel gives an FIR equalizer, because numerator becomes denominator and
vice versa.

For a first step, I'd build a non-adaptive equalizer. You can do this
quickly by putting delayed replicas of the received signal (corresponding
to the eq's FIR taps) into a matrix M as column vectors:

Then, solve least-squares against the training sequence b (also column
vector) for 

[1]: M*c ~ b:

[2]: c = pinv(M)*b

c is then the vector of FIR filter coefficients. Plug it into [1]'s "M*c"
to apply it to the signal.
Use this as sanity check for delays and number of taps. It's pure
zero-forcing so it may misbehave for channel nulls. You can add or
concatenate a noise term to the signals, also to manage the equalizer's
unwanted out-of-channel gain boost. 	 

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On Saturday, August 16, 2014 11:49:14 AM UTC+12, julius wrote:
> Try a trivial channel, h = [1 0 0 0].';
> 
> Then play around with eq length and target delay. Then change the channel a bit to h = [1 0.2 0 0].';
> 
> 
> 
> So small steps, man.

Oh - sorry, didn't see the decimal point - thats z^2-0.2 ok

On Saturday, August 16, 2014 11:49:14 AM UTC+12, julius wrote:
> Try a trivial channel, h = [1 0 0 0].';
> 
> Then play around with eq length and target delay. Then change the channel a bit to h = [1 0.2 0 0].';
> 
> 
> 
> So small steps, man.

The second example is unstable when inverted since its polynomial is z^2-2=0 or z=+/jsqrt(2).   

Try a trivial channel, h = [1 0 0 0].';
Then play around with eq length and target delay. Then change the channel a bit to h = [1 0.2 0 0].';

So small steps, man.

On Saturday, August 16, 2014 7:55:42 AM UTC+12, rsashwinkumar wrote:
> Hi all,
> 
> 
> 
> I am new to signal processing; In my application, I need to use an adaptive
> 
> LMS equalizer.
> 
> I have some doubts regarding that. 
> 
> 
> 
> I can model my scenario as a signal x[n] passing through a channel with a
> 
> transfer function H(z) and output Y(z)=H(z)X(z)+N(z), where N(z) is an
> 
> additive noise (which can be filtered). Now I need to design an equalizer
> 
> so that the effect of H(z) can be nullified and I expect an output
> 
> Y1(z)=X(z)+N1(z), where N1(z) is a noise which can be filtered. Is it
> 
> possible to design an adaptive equalizer that could do the above said
> 
> function?
> 
> 
> 
> Also, when I tried some basic MATLAB simulations for an LMS filter, if the
> 
> channel response I assume is an IIR response, the filter coefficients seem
> 
> to diverge even with a very small step size 0.0001and a very long training
> 
> period 2^15. So does adaptive equalization work only for FIR channel
> 
> respones?
> 
> 
> 
> 	 
> 
> 
> 
> _____________________________		
> 
> Posted through www.DSPRelated.com

Ok just try it first on a known FIR system ex coefficients 1, -0.5 and see if it converges. Remember if you are equalizing that the inverse of the filter must be stable! So don't pick a non-min phase IIR filter or it won't work. There are way around this by introducing a delay in one of the paths but first things first.

Hi all,

I am new to signal processing; In my application, I need to use an adaptive
LMS equalizer.
I have some doubts regarding that. 

I can model my scenario as a signal x[n] passing through a channel with a
transfer function H(z) and output Y(z)=H(z)X(z)+N(z), where N(z) is an
additive noise (which can be filtered). Now I need to design an equalizer
so that the effect of H(z) can be nullified and I expect an output
Y1(z)=X(z)+N1(z), where N1(z) is a noise which can be filtered. Is it
possible to design an adaptive equalizer that could do the above said
function?

Also, when I tried some basic MATLAB simulations for an LMS filter, if the
channel response I assume is an IIR response, the filter coefficients seem
to diverge even with a very small step size 0.0001and a very long training
period 2^15. So does adaptive equalization work only for FIR channel
respones?

	 

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