Parametric spectral estimation has received much attention. Its main advantages are an improved accuracy at high signal-to-noise ratios, especially for short data samples, and the flexibility of analysis and synthesis. The models may be used to analyze the signal, leading to an estimation of the power spectral density of the signal, and subsequently a signal having the same spectral characteristics as the original one may be synthesized. This is what makes the parametric approach so attractive for various fields. However, a strong limitation of these methods lies in the necessary assumption of a stationary signal. One way to overcome this difficulty in speech analysis is to perform the identification of the model over short segments, but this requires a compromise between the accuracy that can be achieved with a short data segment and the faithfulness with which the spectrum must be followed. This is one reason why we need parametric methods valid for nonstationary signals. Modeling of nonstationary signals can be achieved through time-dependent autoregressive moving-average (ARMA) models, by the use of a limited series expansion of the time-varying coefficients in the models. This method leads to an extension of several well-known techniques of stationary spectral estimation to the nonstationary case. Nevertheless, their applications are very limited, which are applied upon very simple nonstationary signals. In this paper, a new method for analyzing nonstationary signals by time-dependent ARMA modeling is presented. It includes two procedures. First, using some signal decomposition method, any complicated nonstationary signal can be decomposed into a finite and often small number of basic components. This decomposition method is adaptive, and therefore, highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it is applicable to nonlinear and nonstationary processes. Second, a specially processed time-dependent ARMA model which has time-varying parameters assumed to be linear combinations of a set of basis time-varying functions in the left and constant parameters in the right is established in any of these basic components. The feedback linear estimation is used to estimate the parameters of ARMA model, and gets their time-frequency spectrum. The method is simple, and can save computation time and storage space. An example from simulation experiment is given to demonstrate the power of this new method. This presented method can analyze complicated nonlinear and nonstationary signal. Finally, the related problems that need further study in this field are pointed out, too.
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