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The technique works as follows:
a) First, for each voice pulse, and then for each harmonic of its spectra, we compute a spline based on the values of the amplitude of that harmonic in the voice pulse as well as a fixed number of surrounding voice pulses.
b) Since the time delta between voice pulses can vary, we then resample each local harmonic spline with fixed steps in time.
c) We compute the fourier transform of these resampled local harmonic trajectories
d) We apply a low-pass and high-pass filter to separate it into low-frequency and high-frequency components.
e) We then apply the inverse fourier transform to each of these. We can then sample the low pass trajectory at the time of the voice pulse to get the amplitude value of the denoised harmonic for that voice pulse. The same can be done for the high pass trajectory to obtain a pseudo-pulse representing the residual. These residual voice pulses can then be synthesized using the WBVPM synthesis method to obtain a time-domain residual signal which can be processed separately from the main harmonic signal.

A significant source of error in this process presumably would come from the resampling step. This can be decreased by using a smaller time step, at an increased computational cost. However, the error could probably be greatly reduced by first calculating the difference between the original amplitudes and the amplitudes at the same times in a spline computed from the resampled harmonic spline before applying the band filters, this difference can later be added back to the low-pass amplitude trajectory.

The denoised harmonic phase can also be computed via the same method, using Bonada's method for unwrapping phase across both frequency and time. The residual phase can be calculated by taking difference of the original phase from the denoised phase and dividing it by the residual amplitude.

RESULTS:

I have tested these improvements and obtained the following results for the aforementioned audio sample:

Original WBVPM: -36.355dB
Warp-correction improvement only: -36.74595dB
Warp-correction & Resilient border interpolation in synthesis: -37.41177dB

More research is needed to properly evaluate these improvements across more samples with more variety, and to see if these techniques still result in improvements with more accurate pitch and MFPA estimation and with proper handling of unvoiced/voiced frames.
Post number No.180303
Board Off-Topic@Heyuri
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