Ultrasound is inherently band-limited thus limiting the temporal resolution of the system. Spectral extrapolation, coupled with deconvolution can improve the lack of resolution. I'm attempting to compare the Yule-Walker algorithm to Berg's method and the Levinson-Durbin algorithm for stability and accuracy.
The best papers on a comparison between Yule-Walker (which should always be avoided due to very poor condition number of the autocorrelation matrices), Levinson-Durbin (which is the forward-backward least squares) and Burg's modification (which minimizes the forward-backward predication error) are published by Prof. Piet Broersen. If you browse the internet on his name you find plenty of good results.
The Y-W algorithm is based on an autocorrelation estimate; so it is bad when compared with "covariance" based algorithms. If your signal can be considered as stationary you can use the Larry Marple algorithm. Any way you can use the Burg algorithm or the modified Burg algorithm that is better.
You might be able to correlate your band limited spectrum with spectra for sources you know and expect and replace the spectrogram column (or row) with the entire spectra. This might allow you to discriminate between known sources with the band limited match, and transform back to the original signal as it was embeded in the temporal UT signal if you can get the amplitude and phases right.
The best papers on a comparison between Yule-Walker (which should always be avoided due to very poor condition number of the autocorrelation matrices), Levinson-Durbin (which is the forward-backward least squares) and Burg's modification (which minimizes the forward-backward predication error) are published by Prof. Piet Broersen. If you browse the internet on his name you find plenty of good results.
Thank you, that would be much appriciated. my email is [email protected]
Where you say "Berg's method" you mean "Burg's method".
I have implemented YW, Burg, covariance and modified covariance methods and for Ultrasound signals and for Atrial Electrogram spectral estimation they all work and produce spectral estimators that tell basically the same story, with the same dominant frequencies. Of course if one uses fabricated signals in simulations that might not be true. And a final warning, the methods to estimate the order of the model frequently select an AR model with too few coefficients, which will produce a spectral estimate that is too smooth, sometimes modifying the estimation of the dominant frequency.
I recommend using some evolutionary computing techniques too for the comparison. Also as far as ultrasound signals are concerned, its good that you use high resolution time-frequency methods to improve upon their resolution. Please go through a good research paper on the same titled "high resolution time-frequency methods-a review' at EURASIP Journal on Advances in Signal processing
@Imran Shafi - It is not that I didn't like it. Actually I haven't read it, It is just that I think one should not advertise his/her own research this way. Publish it, go to conferences and present it and let readers and listeners decide :-)
Agree with Narayanankutty, from Monsoon Hayess, we have good adaptive filter include Math-lab example.
I suggest the book published by Steven M. Kay: Modern Spectral Estimation Theory and Application, Prentice-Hall, 1988). I prefer it to the book by Marple (but this is a personal preference).
For example, Burg's code is on page 265-266 of Kay's book. The book also has examples of the implementation of Yule-Walker, covariance and modified covariance methods (and other techniques). As I said before, in my experience, for 'real-world' signals the differences when the spectra are compared in linear scale are small. You only see very big differences in the spectral estimators for 'fabricated' signals and when plotting the spectra in log scale.
Happy programming :-)
I agree with Syam K. The Orfanidis text has lots of C algorithms in the back.
One option is "Statistical and Adaptive Signal Processing Spectral Estimation, Signal Modeling, Adaptive Filtering, and Array Processing," by Dimitris G. Manolakis, Massachusetts Institute of Technology Lincoln Laboratory; Vinay K. Ingle, Northeastern University; Stephen M. Kogon, Massachusetts Institute of Technology, Lincoln Laboratory.
This manuscript might be helpful http://www.nt.ntnu.no/users/skoge/prost/proceedings/cdc-ecc-2011/data/papers/1941.pdf
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