Hello; I have just one simple question.Assuming that Y= latcfilt(k,x) is the output of a lattice filter, i search to find the k coefficients using Y. is it possible ? thank you for your answers
Hello Meziane,
if the filter output Y is obtained through Y= latcfilt(k,x), it is possible to recover the value of the k coefficient at the condition that the input signal x is a white noise. If not, you could not get these coefficients.
To get these coefficients, you should implement a decorrelating filter in a lattice form. This could be done using adaptive filtering techniques (LMS algo...) if the k coefficients are time-varying.
I hope this will help.
Hello Meziane,
if the filter output Y is obtained through Y= latcfilt(k,x), it is possible to recover the value of the k coefficient at the condition that the input signal x is a white noise. If not, you could not get these coefficients.
To get these coefficients, you should implement a decorrelating filter in a lattice form. This could be done using adaptive filtering techniques (LMS algo...) if the k coefficients are time-varying.
I hope this will help.
hello Pascal Scalart
thank you for your answer,
to get these coefficients with LMS i shoud use a signal x, but me i search to get these coefficients using only Y signal.
Hello Meziane,
I understand your problem : you want to get back the coefficients k by applying a filter on the signal Y= latcfilt(k,x). You can do that by filtering the signal Y with a decorrelating (or whitening) filter. This is the same kind of problem that you have for example when you have an AR (autoregressive) signal Y(n) that is avalaible :
x = randn(N,1); Y = filter(k,1,x)
and you want to estimate the AR coefficients k : this can be done by the instruction [a,g] = lpc(Y,p) that implements a decorrelating filter and the estimate of the coefficients k are given by vector a.
In your problem, estimating the coefficients k from Y is possible by implementing an inverse Lattice FIR Filter where the filter coefficients are computed in order to minimize the mean square error Jm = E(fm (n) 2) + E(bm(n) 2) where fm(n) and bm(n) stand for the m-stage forward and backward prediction errors at time n.
If coefficients k are time-varying, you need to implement an adaptive inverse Lattice FIR Filter. See for example on page 12 of http://www.cs.tut.fi/~tabus/course/ASP/LectureNew8.pdf
It seems that you can use some Matlab functions to implement the adaptive lattice FIR filter: see https://fr.mathworks.com/help/dsp/ref/dsp.adaptivelatticefilter-class.html
Pascal Scalart
thank you dear Pascal
I applied durbin's methode, it works with white noise :
v = 0.4;
w = sqrt(v)*randn(1500000,1);
k= [1 0.00766 0.008000 0.009 ];
x = filter(k,1,w);
a = durbin(x,q,p);
but when i try to do this with a stereo signal, that's does not work.
NB: lpc uses to estimate AR parameters, but in my case i search to get MA parameters.
Thank you again for all this expalantion
You are rigth, but as stated in an earlier response, if the filtered signal w is white then the AR an MA model are related to each other and it is possible to identify the AR parameters from the analysis of signal Y available at the output of the MA model.
Attached, please find such an implemention of the estimate of the AR parameters with an LMS algorithm.
hello dear Pascal
thank you for your answer,
You were right from the beginning, you can apply these methods only with a white noise, and I tried to apply them for a signal of the song stereo, for now I work on the lattice filter, Try to program it in C with its inverse.
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