4 mixture MAR speech phone classification experiment with Tidigits database.

with orders 0 (=GMM), and order 1.

While the MAR training is much improved compared to that for speaker recognition, several MARs have unstable LP filters. 

For example,

MAR for phone 'eh':

    -0.538622,-7.40511,0.511876,-1.00976,-0.0363068,1.72345,0.0344415,3.63107,0.166895,0.401951,0.197388,0.233765,3.82232,0.919171,2.42735,2.76272;

    lp values for the 4 mixtures: -0.538622; 0.511876; -0.0363068; 0.0344415.

    All these have magnitudes well below 1. So all lp filters are stable.


MAR for phone 'v':

    0.859516,-1.81306,0.140502,1.27415,1.22606,0.882606,0.931222,0.6465,0.142945,0.19393,0.203027,0.460098,3.40355,3.54933,0.901838,0.950244 

    lp values for the 4 mixtures: 0.859516; 0.140502; 1.22606; 0.931222.

    Here there is one lp filter that is clearly unstable.


The effect of having unstable lp filters in MAR is documented in the two plots:

hist_eh_mfcc_1.jpg: We know the lp filters are stable for this MAR from above. Histograms from both MAR order 0 and 1 are quite similar to actual histogram. Therefore, we expect that MAR order 1 not only captures the static pdf information, but also the evolution of the pdf with time accurately.

hist_v_mfcc_1.jpg: We know the lp filters are UNstable for this MAR from above. While histogram for MAR order 0 closely follows the actual histogram, that for order 1 has a much wider range - the effect of the unstable lp filter. In fact, if the unstable filter is forced to a stable one (by simply transforming 1.2206 to 0.9, for example), the resemblance of the synthesized signal histogram's shape is quite close to the actual histogram and so is the range.

Thus the next obvious step is to try constraining the poles of the unstable lp filters to lie within the unit circle.