Pietruch R., Grzanka A., Konopka W.: Vowels recognition

16 th International Congress on Sound and Vibration, 5–9 July 2009, Kraków, Poland
was made using analysis of acoustical and facial expression parameters.
3. Methods
3.1 Computer system
Presenting system’s platform is Windows XP. Program is based on DirectShow filters technology.
It extracts speech parameters from digital movie files (mostly in MPEG format), visualizes them,
and provides methods for archiving. We implemented automatic face detection algorithm for frontal
view image sequence. The system automatically tracks elements of face in real time, extracts visual
parameters including lips shape, compares them with acoustical descriptors and updates vocal tract
model parameters. Neural network simulation and learning were made on Linux platform Ubuntu
8.04 distribution. We used GNU Octave program version 3.0.0 with nnet-0.1.9 package.
3.2 Acoustical model
In this work we used the model of vocal tract divided into 10 sections of resonance cavities.
We assumed that the palate is closed and the waves don’t pass through the nasal cavity. There is no
energy loss and only reflection effect is taken into consideration. With these assumptions the vocal
tract model is equivalent to lattice filter with PARCOR parameters equal to negative reflection coefficients
[7]. Reversed lattice filter can be then transformed into transversal filter [3], which parameters
can be estimated from speech signal using linear prediction method. Adaptive recursive least squares
algorithm was used to estimate transversal filter LPC coefficients [3]. There is reversed transformation
that from given LPC parameters derives related cross-sectional diameters of vocal tract sections.
Transversal filter coefficients were used to track formant frequencies of six Polish vowels [6]. Two
first formants F1 and F2 were chosen as the acoustical descriptors in audio recognition system.
3.3 Formants tracking
In the system with vowel recognition functionality the formant tracking algorithm was implemented.
There was used Christensen algorithm for finding formants candidates from spectrum [2].
All minimums of spectrum second derivative are chosen. For 4kHz bandwidth that was assumed in
our study we can find up to 5 candidates f K = {f K 1 , f K 2 , · · · , f K nK } and we need to assign 4 formants
numbers F = {F 1, F 2, · · · , F nF }. There can be three situations:
2
1. nK = nF
Then candidates are assigned respectively to formants numbers with a function fK→F according
to equation 1.
fK→F : f K j → F i ⇔ i = j (1)
where : i, j ∈ 1, 2, · · · , nF
2. nK < nF
In this situation nF − nK formants will be rejected. Function 2 will specify which formants
need to be unassigned. The function can be given using BF matrix where each row represents
candidate and each column represents one of formant (equation 3). This transformation is found
using best-fit, minimum cost algorithm 7.
fK→F : f K j → F i (2)
BF (j, i) = 0 ⇔ fK→F (j) = i (3)