The main objective of this dissertation is to develop a pole-zero modeling algorithm which can accurately represent the spectral envelopes of speech signals. So far, most of the block processed pole-zero modeling algorithms yield a suboptimal estimation when input excitation is not known. And they cannot track the instantaneous variations of the signal parameters due to the nature of the algorithms which are developed for a block data processing. To alleviate these problems, we suggest several recursive pole-zero modeling algorithms, which can estimate the precise input excitation sequences and track the time-varying parameters of speech signals only from the observed time sequences.
First, we propose a modified transversal Kalman filter (MTKF) algorithm which simultaneously estimates the unknown input excitation and the unknown parameters of a time-varying autoregressive moving average (ARMA) model based on the nonstationary transversal Kalman filter algorithm. The time variation of parameters is modeled as a random noise process whose statistics is assumed to be smoothly changing. And the second-order statistical information of the time variation is extracted from the Prediction errors. Accordingly, the input pitch pulses which induce on abrupt change in the prediction error are discriminated against the time variation of parameters. Therefore, the proposed algorithm can exactly detect pitch pulse instants and track time-varying parameters undisturbed by pitch pulses. In addition, we suggest a simplified version of the algorithm that can drastically reduce the computational complexity and has comparable performance to the original algorithm in the analysis of natural speech.
Second, utilizing the well-known prewindowed least squares lattice (LSL) algorithm which is stable and has fast convergence speed, we propose a dual recursive least squares lattice(DRLSL) algorithm. In this algorithm, the autoregressive (AR) estimator and the moving average (MA) estimator are developed by two independent AR-LSL joint process estimators, respectively. The unknown input excitation is estimated by a bootstrapping frequently used in recursive ARMA modeling algorithms. Consequently, somewhat complicate ARMA modeling problems can easily be solved by duplicating the relatively simple AR lattice joint estimator. Although the two estimators are independently implemented, they are closely correlated by their joint estimator inputs. Since the pole and zero coefficients are interactively updated, this algorithm can be treated as a simultaneous pole-zero coefficient estimation algorithm.
Finally, we propose two recursive least squares lattice algorithms which are named the expanded least squares lattice (ELSL) algorithms for an ARMA signal modeling. The two ELSL algorithms are developed by a geometric projection approach in a Hilbert space depending on input excitation information. One is the ELSL-UN algorithm which is dedicated to the unknown input excitation case accompanying a bootstrap input estimation, and the other is the ELSL-KN algorithm which is dedicated to the known input excitation case. Since each algorithm is specialized depending on the input information, the ELSL algorithms can utilize all available information of the input excitation and the observed output signal efficiently. The algorithm development can be classified into two parts, that is, the development of ARMA lattice filter, and the development of LS adaptation algorithm for the ARMA models. The developed ARMA lattice filter is a canonical expansion of the conventional all-pole lattice filter, and the LS adaptation algorithm is developed as an exact LS technique. Thus the two ELSL algorithms can be treated as the ARMA model counterparts of the conventional LSL algorithm which is known as one of the best adaptive all-pole modeling algorithms. Moreover, we develop transversal prediction filter coefficient (i.e., the pole-zero coefficients) update algorithms, which can obtain pole-zero coefficients at any time when one requires them, with a time-sampled manner without time-recursive updating of the explicit pole-zero coefficients.
According to experimentations for each of the proposed algorithms, all of the algorithms yield a good performance in spectral envelope estimation of speech signals. Also, the proposed algorithms can be used in noisy signal processing, linear system identification, and parametric speech coding.
본 논문의 주된 목적은 음성신호의 spectral envelope을 정확히 표현할 수 있는 pole-zero 모델링 알고리즘의 개발에 있다.
이제까지 제안된 block 처리 pole-zero 모델링 알고리즘은 음성의 입력여기(input excitation) 신호를 알 수 없는 관계로 spectral envelope의 예측이 suboptimal 하였으며, 한 block의 음성이 stationary 하다고 가정되었기 때문에 주어진 block 내에서 spectral envelope이 변하게 되는 경우 적절한 예측이 이루어 질 수가 없다. 이러한 문제들을 완화시키고 더욱좋은 성능을 얻을 수 있는 알고리즘으로서, 입력신호를 매 sample 마다 예측하고 spectral envelope의 변화를 추적할 수 있는 세가지의 연속적응 pole-zero 모델링 알고리즘을 제안하였다.
먼저, nonstationary transversal Kalman 알고리즘에 근거한 modified transversal Kalman filter(MTKF) 알고리즘을 제시하였다. MTKF 알고리즘은 음성신호의 계수들이 천천히 변한다는 가정하에서, 그계수의 변화량을 백색 잡음으로 모델링하고 백색잡음의 variance 및 입력여기 신호를 음성신호의 예측 오차로 부터 구함으로써 시변하는 음성신호의 spectral envelope을 정확하게 추적하였다.
다음으로, 안정되고 빠른 수렴 속도를 갖고 있는 least squares lattice(LSL) 알고리즘을 이용하여 dual recursive least squares lattic(DRLSL) 알고리즘을 제안하였다. 이 알고리즘은 pole 계수와 zero 계수를 각각 독립된 LSL joint estimation 알고리즘에 의하여 구함으로써 복잡하다고 알려진 pole-zero 모델링을 간단하게 구현하였으며 입력여기 신호를 bootstrapping에 의하여 쉽게 구할 수 있었다. 비록 pole과 zero가 독립된 예측기에 의해서 얻어지지만 각 예측기는 그들의 joint estimation 입력에 의해서 상호연결되기 때문에 pole과 zero의 예측은 긴밀하게 이루어진다.
마지막으로, expanded least squares lattice(ELSL) 알고리즘을 제안하였는데, ELSL 알고리즘을 음성신호와 같이 입력여기 신호를 알 수 없는 경우에 적용되는 ELSL-UN 알고리즘과 입력여기 신호를 알수 있는 경우에 적용되는 ELSL-KN 알고리즘 두가지로 구분하였다. ELSL-UN 알고리즘의 입력여기 신호는 bootstrapping에 의해서 얻어졌다. 제안된 ELSL 알고리즘의 filter 구조는 all-pole lattic filter 구조가 pole-zero 모델로 확장된것이며, 적응 알고리즘은 all-pole LSL 알고리즘의 적응 알고리즘처럼 정확한 것이기 때문에 본 ELSL 알고리즘은 all-pole 모델에 있어서의 LSL 알고리즘에 대응하는 pole-zero 모델에 있어서의 LSL 알고리즘이라고 할만하다.
이상에서 제안된 세가지 알고리즘을 객관적인 성능평가 방법에 의해 실험한 결과 음성신호의 spectral envelope을 아주 정확히 예측하는 것을 보였으며 시변하는 자연음성신호의 spectral envelope을 잘추적하고 있음을 보였다. 또한 이들 알고리즘들이 잡음신호처리, 선형시스템 예측 그리고 음성의 vocoding에 적용될 수 있음을 논하였다.
