Method for testing the stability of an autoregressive model of the vocal tract and adjusting its parameters

Within the framework of the traditional direction of research in the field of acoustic measurements, an autoregressive model of the vocal tract as a key link in the human speech apparatus is considered. The acute problem of ensuring the stability of the autoregressive model in systems with adaptation of its parameters to the observed speech signal of short duration is pointed out. To overcome this problem, the task was set of testing the stability of the autoregressive model and adjusting its parameters based on the results of this testing. The study is based on the author’s method of formant analysis of vowel sounds of speech through the synthesis of a recursive shaping filter in the free oscillation mode. To solve sated task, a method is proposed for testing the stability and adjusting the parameters of the autoregressive model of the vocal tract based on a two-stage algorithm for its transformation. At the first stage of transformation, the stability of the autoregressive model is tested using the impulse response of the shaping filter. At the second stage, if the stability of the autoregressive model is violated, its impulse response is modified by element-by-element multiplication by a variable exponential value that asymptotically converges to zero. A regular algorithm has been developed for recalculating the modified impulse response into an adjusted vector of autoregressive parameters at the second stage of transformation. Based on the results of experimental testing of the proposed method, it was concluded that guaranteed stability of the autoregressive model of the vocal tract has been achieved with minimal distortion in the frequency domain. The results obtained are useful in the development and modernization of automatic speech recognition systems, digital speech communications, artificial intelligence and other information systems that use data compression and speech coding based on an autoregressive model of the vocal tract in automatic speech signal processing.

1. Ternström S. Special Issue on Current Trends and Future Directions in Voice Acoustics Measurement. Applied Sciences, 13(6), 3514, (2023). https://doi.org/10.3390/app13063514

2. O’Shaughnessy D. Review of methods for coding of speech signals. Journal on Audio, Speech, and Music Processing, (8), (2023). https://doi.org/10.1186/s13636-023-00274-x

3. Savchenko V. V. A measure of differences in speech signals by the voice timbre. Measurement Techniques, 66(3), 803–812 (2024). https://doi.org/10.1007/s11018-024-02294-1

4. Rabiner L. R., Shafer R. W. Theory and Applications of Digital Speech Processing, Pearson, Boston (2010).

5. Gibson J. Mutual Information, the Linear Prediction Model and CELP Voice Codecs. Information, 10(5), 179 (2019). https://doi.org/10.3390/info10050179

6. Savchenko V. V., Savchenko L. V. Method for asynchronous analysis of a glottal source based on a two-level autoregressive model of the speech signal. Izmeritel’naya Tekhnika, 73(2), 55–62 (2024). https://doi.org/10.32446/0368-1025it. 2024-2-55-62 (In Russ.)

7. Kim H. S. Linear predictive coding is all-pole resonance modeling, Center for Computer Research in Music and Acoustics, Stanford University (2023).

8. Savchenko V. V. Method for comparison testing of parametric power spectrum estimates: spectral analysis via time series synthesis. Measurement Techniques, 66(6), 430–438 (2023). https://doi.org/10.1007/s11018-023-02244-3

9. Savchenko V. V. Method for reduction of speech signal autoregression model for speech transmission systems on lowspeed communication channels. Radioelectronics and Communications Systems, 64, 592–603 (2021). https://doi.org/10.3103/S0735272721110030

10. Kathiresan Th., Maurer D., Suter H., Dellwo V. Formant pattern and spectral shape ambiguity in vowel synthesis: The role of fundamental frequency and formant amplitude. The Journal of Acoustical Society of America, 143(3), 1919–1920 (2018). https://doi.org/10.1121/1.5036258

11. Palaparthi A., Titze I. R. Analysis of glottal inverse filtering in the presence of source-filter interaction. Speech Communication, 123, 98–108 (2020). https://doi.org/10.1016/j.specom.2020.07.003

12. Venkatraman A. Algorithms and Software for Predictive and Perceptual Modeling of Speech. Springer Cham. (2011). https://doi.org/10.1007/978-3-031-01516-8

13. Alku P., Kadiri S. R., Gowda D. Refining a deep learning-based formant tracker using linear prediction methods. Computer Speech & Language, 81, 101515 (2023). https://doi.org/10.1016/j.csl.2023.101515

14. Fu M., Wang X., Wang J. Polynomial-Decomposition-Based LPC for Formant Estimation. IEEE Signal Processing Letters, 29, 1392–1396 (2022). https://doi.org/10.1109/LSP.2022.3181523

15. Candan С. Making Linear Prediction Perform Like Maximum Likelihood in Gaussian Autoregressive Model Parameter Estimation. Signal Processing, 166, 107256 (2020). https://doi.org/10.1016/j.sigpro.2019.107256

16. Wei B., Gibson J. D. A new discrete spectral modeling method and an application to CELP coding, In: IEEE Signal Processing Letters, 10(4), 101–103 (2003). https://doi.org/10.1109/LSP.2003.808550

17. Sadhu S., Hermansky H. Radically Old Way of Computing Spectra: Applications in End-to-End ASR. Audio and Speech Processing (eess.AS); Sound (cs.SD). arXiv:2103.14129 [eess.AS] (2021). https://doi.org/10.48550/arXiv.2103.14129

18. Oh H. Recursively Adaptive Randomized Multi-Tree Coding (RAR MTC) of Speech with VAD/CNG. University of California, Santa Barbara, Theses and Dissertations (2023).

19. Marple S. L. Digital Spectral Analysis with Applications. 2nd ed., Dover Publications, Mineola, New York (2019).

20. Cui S., Li E., Kang X. Autoregressive model based smoothing forensics of very short speech clips. In: 2020 IEEE International Conference on Multimedia and Expo (ICME), London, UK, 1–6 (2020). https://doi.org/10.1109/ICME46284.2020.9102765

21. Esfandiari M., Vorobyov S. A., Karimi M., New estimation methods for autoregressive process in the presence of white observation noise. Signal Processing, 171, 107480 (2020). https://doi.org/10.1016/j.sigpro.2020.107480

22. Savchenko V. V., Savchenko L. V. Suboptimal algorithm for measuring pitch frequency using discrete fourier transform of a speech signal. Journal of Communications Technology and Electronics, 68(7), 757–764 (2023). https://doi.org/10.1134/S1064226923060128

23. O’Shaughnessy D. Review of analysis methods for speech applications. Speech Communication, 151, 64–75 (2023). https://doi.org/10.1016/j.specom.2023.05.008

24. Ternström S., Pabon P. Voice Maps as a Tool for Understanding and Dealing with Variability in the Voice. Applied Sciences, 12, 11353 (2022). https://doi.org/10.3390/app122211353

25. Sun P., Mahdi A., Xu J., Qin J. Speech enhancement in spectral envelope and details subspaces. Speech Communication, 101, 57–69 (2018). https://doi.org/10.1016/j.specom.2018.05.006

26. Tohyama M. Spectral envelope and source signature analysis. In: Acoustic signals and hearing. Academic Press, 89– 110 (2020). https://doi.org/10.1016/B978-0-12-816391-7.00013-9

27. Savchenko V. V. A Method for autoregression modeling of a speech signal using the envelope of the schuster periodogram as a reference spectral sample. Journal of Communications Technology and Electronics, 68(2), 121–127 (2023). https://doi.org/10.1134/S1064226923020122

28. El-Jaroudi A., Makhoul J. Discrete all-pole modeling. IEEE Transactions on Signal Processing, 39(2), 411–423 (1991). https://doi.org/10.1109/78.80824

29. Mustiere F., Bouchard M., Bolic M. All-Pole modeling of discrete spectral powers: a unified approach. IEEE Transactions on Audio Speech and Language Processing, 20(2), 705–708 (2012). https://doi.org/10.1109/TASL.2011.2163511

30. Savchenko V. V., Savchenko L. V. Speech signal autoregression modeling based on the discrete fourier transform and scale-invariant measure of information discrimination. Journal of Communications Technology and Electronics, 66(11), 1266–1273 (2021). https://doi.org/10.1134/s1064226921110085

31. Vinay H., Lavanya P., Hippargi A. A., Purohith A., Lohith D. A comparative analysis on speech enhancement and coding techniques. In: 2021 International Conference on Recent Trends on Electronics, Information, Communication & Technology (RTEICT), Bangalore, India, 543–549 (2021). https://doi.org/10.1109/RTEICT52294.2021.9573847

32. Savchenko V. V. Words phonetic decoding method with the suppression of background noise. Journal of Communications Technology and Electronics, 62(7), 788–793 (2017). https://doi.org/10.1134/S1064226917070099

33. Palani S. Principles of digital signal processing. 2nd Edition. Springer Cham. (2022). https://doi.org/10.1007/978-3-030-96322-4

34. Nam S. H. Stabilizing discrete spectral modeling of audio signals. IEEE Signal Processing Letters, 9(9), 292–294 (2002). https://doi.org/10.1109/LSP.2002.803406

35. Magi C., Pohjalainen J., Backstrom T., Alku P. Stabilised weighted linear prediction. Speech Communication, 51(5), 401–411 (2009). https://doi.org/10.1016/j.specom.2008.12.005

36. Miran K. S., Pal P., Babadi B., Wu M. Sampling requirements for stable autoregressive estimation. IEEE Transactions on Signal Processing, 65(9), 2333–2347 (2017). https://doi.org/10.1109/TSP.2017.2656848

37. Kumar S., Singh S. K., Bhattacharya S. Performance evaluation of a ACF-AMDF based pitch detection scheme in realtime. International Journal of Speech Technology, 18, 521–527 (2015). https://doi.org/10.1007/s10772-015-9296-2