(continued from previous post)
One option would be to somehow modify the LPC inverse filtering process to be amenable to a parameter configuration instead. However, I am not sure how to do this, or whether it is even possible (perhaps a good place to start would be to frame the problem as a matrix equation?).
On the other hand, another option would be to create a cascade filter from the estimated parallel filter. This could be done by first starting with just the first resonance. This is the same in both cases. Then we go on to add the second one. Before adding it, we calculate the current value in the cascade filter at the next resonance's center frequency, we then scale its amplitude by the reciprocal of this value. This new filter will not be exactly the same, but it should be reasonably close. Actually, it may be a better model of the vocal tract. Perhaps also the FRIR algorithm could be used to refine it, even in the cascade case, since it should have a very low error?
The final procedure then, would be to run one iteration of the WBHSM algorithm, to estimate the EpR parameters. Then, for each instant an EpR model has been estimated, only the poles are extracted and are then converted to a cascade filter. Next, the inverse filtering is performed. For each inverse filtering frame (which can be as small as a single frame), the closest vocal tract filter estimates are interpolated using, for example, linear or spline interpolation. Next, the z-transfer function denominator of the resultant filter is expanded using the standard procedure to obtain the LPC coefficient, which are finally used to do the inverse filtering itself. The final step is the second pass of WBHSM, over the inversecfiltered signal. Since it has been inverse filtered, there should be no interference between voice pulses. An additional potential benefit is the harmonic envelope no longer contains resonances, which may improve the estimation of the source curve and zeros, although the same effect could also be achieved in the traditional EpR estimation by using two passes. Finally, a combined EpR model is created from the resonance plus the source and residual model obtained in the last step.
This procedure makes one significant presumption, which is that most of the error of WBHSM is concentrated in the non-resonance part of the EpR model. This would seem to be a reasonable assumption to make, given that EpR is fitted using multiple harmonics, and that it could furthermore be filtered across multiple frame using techniques such as lowpass filtering, moving averages, or exponential moving averages. However, I do not yet have empirical evidence for this. One possible case wherein the presumption would not hold would be if the error changes slowly over frequency, for example. Actually, a type of error with precisely this fingerprint does exist; it results from the fundamental frequency changing. However, I have already proposed a solution to it, within the RVPM framework: https://listserv.cuit.columbia.edu/scripts/wa.exe?A2=MUSIC-DSP;31999a11.2608A&S=