Time-varying autoregressive modelling for nonstationary acoustic signal and its frequency analysis

A time-varying autoregressive (TVAR) approach is used for modeling nonstationary signals, and frequency information is then extracted from the TVAR parameters. Two methods may be used for estimating the TVAR parameters: the adaptive algorithm approach and the basis function approach. Adaptive algorithms, such as the least mean square (LMS) and the recursive least square (RLS), use a dynamic model for adapting the TVAR parameters and are capable of tracking time-varying frequency, provided that the variation is slow. It is observed that, if the signals have a single time-frequency component, the RLS with a fixed pole on the unit circle yields the fastest convergence. The basis function method employs an explicit model for the TVAR parameter variation, and model parameters are estimated via a block calculation. We proposed a modification to the basis function method by utilizing both forward and backward predictors for estimating the time-varying spectral density of nonstationary signals. It is shown that our approach yields better accuracy than the existing basis function approach, which uses only the forward predictor. The selection of the basis functions and limitations are also discussed in this thesis. Finally, the proposed approach is applied to analyze violin vibrato. Our results showed superior frequency resolution and spectral line smoothness using the proposed approach, compared to conventional analysis with the short time Fourier transform (STFT) whose frequency resolution is very limited. It was also found that frequency modulation of vibrato occurs at the rate of 6 Hz, and the frequency variations for each partial are different and increase nonlinearly with the partial number.