version 1.0.4

This python package provides the tools necessary to decompose the voiced part of a speech signal into its modulated components, aka AM-FM decomposition. This designation is used due the fact that, in this method, the signal is modeled as a sum of amplitude- and frequency-modulated components.

The goal is to overcome the drawbacks from Fourier-alike techniques, e.g. SFFT, wavelets, etc, which are limited in the time-frequency analysis by the so-called Heisenberg-Gabor inequality.

The algorithms here implemented are the QHM (Quasi-Harmonic Model), and its upgrades, aQHM (adaptive Quasi-Harmonic Model) and eaQHM (extended adaptive Quasi-Harmonic Model). Their formulation can be found at references [2-4].

Since that the tools mentioned above require a fundamental frequency reference, the package also includes the pitch tracker YAAPT (Yet Another Algorithm for Pitch Tracking) [1], which is extremely robust for both high quality and telephone speech.

The study of AM-FM decomposition algorithms was the theme from my Master Thesis. The original YAAPT program in MATLAB is provided for free by its authors, while the QHM algorithms I implemented by myself also in MATLAB. I'm porting them now to python because:

• the python language is easier to share, read and understand, making it a better way to distribute the codes;
• is more resourceful than MATLAB (has different data structures, scripting options, etc), which will be useful for me in future studies;
• the computational performance from its numeric and scientific packages (numpy and scipy) is equivalent to MATLAB;
• python is free-to-use, while MATLAB is a proprietary software;

As for the algorithms computational performance, I optimized the YAAPT code, so my pyhton version runs now about twice as fast as the original MATLAB one. However, the QHM algorithms still run as fast as their counterparts in MATLAB. That's because the main bottleneck of both versions are the matrix dot and least-squares operations. Since numpy and MATLAB are already optimized to perform these tasks using internal Fortran functions, as far as I investigated there's no way to speed them up (like using Cython, for example). Nevertheless, I still looking for ways to make my code faster.

In [1] the YAAPT is compared with well-known pitch trackers like the YIN and the RAPT, and presents the best results. In fact, so far I've been using it, the algorithm has been proved to be indeed very robust. It must be emphasized that I merely translated the code, so I only have an average knowledge about its theoretical formulation. For deep questions concerning it, I would advise to contact the original authors.

The QHM-like algorithms present some stability problems concerning small magnitude modulated components, which are already documented at [2,3]. In my python code I implemented a workaround to this problem, but it is still a sub-optimal solution.

Actually, I dedicated a chapter in my Master Thesis to a deeper study about this problem and came up with a better solution. Unfortunately, due stupid bureaucratic issues, I don't know if and when my work will be defended and published (to be short, the deadline was expired because me and my advisor needed more time to correct and improve the thesis text. Then we required a prorrogation, but the lecturers board declined it. So, basically, I was expelled from the post-gradute program with a finished and working thesis). Anyway, I'm still trying to figure out do now with my work and as soon as find a solution, I'll add my own contributions to this package.

In my thesis I also ran performance tests comparing the QHM family with other two AM-FM decomposition algorithms. Therefore, my next goal is to add these methods to the package. Since they are third-part free MATLAB codes, probably it will take a couple of months to fully translate them.

The pypi page https://pypi.python.org/pypi/AMFM_decompy/1.0.4 is recommended for a quick installation. But you can also copy all directories here and then run

python setup.py install

in command line. After that, run the test script by typing

AMFM_test.py

to check if everything is ok (it can take couple of minutes to calculate the results). This script is a example about how to use the package.

I've tested the installation script and the package itself in Linux and Windows systems (but not in iOS) and everything went fine. So, if a problem comes up, it must be probably something about python not finding the files paths.

Check the AMFM_decompy pdf documentation included in the docs folder or the online documentation at http://bjbschmitt.github.io/AMFM_decompy. The amfm_decompy folder contains the sample.wav file that is used to ilustrate the package's code examples.

The original MATLAB YAAPT program was written by Hongbing Hu and Stephen A.Zahorian from the Speech Communication Laboratory of the State University of New York at Binghamton.

It is available at http://www.ws.binghamton.edu/zahorian as free software. Further information about the program can be found at

[1] Stephen A. Zahorian, and Hongbing Hu, "A spectral/temporal method for robust
    fundamental frequency tracking," J. Acosut. Soc. Am. 123(6), June 2008.

The QHM algorithm and its upgrades are formulated and presented in the following publications:

[2] Y. Pantazis, “Decomposition of AM-FM signals with applications in speech 
    processing”, PhD Thesis, University of Creta, 2010.

[3] Y. Pantazis, O. Rosec and Y. Stylianou, “Adaptive AM-FM signal decomposition 
    with application to speech analysis”, IEEE Transactions on Audio, Speech and 
    Language Processing, vol. 19, n 2, 2011.

[4] G. P. Kafentzis, Y. Pantazis, O. Rosec and Y. Stylianou, “An extension of the 
    adaptive quasi-harmonic model”, in IEEE International Conference on Acoustics, 
    Speech and Signal Processing (ICASSP), 2012.

The AMFM_decompy is free to use, share and modify under the terms of the MIT license.

Questions, comments, suggestions, and contributions are welcome. Please contact me at bernardo.jb.schmitt@gmail.com.