Time-varying modelling of arbitrary non-stationary signals

2003 ◽  
Author(s):  
J.R. Bellegarda ◽  
D.C. Farden
Keyword(s):  
Time Varying ◽  
Stationary Signals

scholarly journals A Time–Frequency Correlation Analysis Method of Time Series Decomposition Derived from Synchrosqueezed S Transform

2019 ◽  
Vol 9 (4) ◽  
pp. 777 ◽  
Author(s):  
Gaoyuan Pan ◽  
Shunming Li ◽  
Yanqi Zhu
Keyword(s):  
Time Series ◽  
Correlation Analysis ◽  
Time Varying ◽  
Analysis Method ◽  
Frequency Correlation ◽  
Time Frequency ◽  
Time Series Decomposition ◽  
S Transform ◽  
Stationary Signals ◽  
Correlation Analysis Method

Traditional correlation analysis is analyzed separately in the time domain or the frequency domain, which cannot reflect the time-varying and frequency-varying characteristics of non-stationary signals. Therefore, a time–frequency (TF) correlation analysis method of time series decomposition (TD) derived from synchrosqueezed S transform (SSST) is proposed in this paper. First, the two-dimensional time–frequency matrices of the signals is obtained by synchrosqueezed S transform. Second, time series decomposition is used to transform the matrices into the two-dimensional time–time matrices. Third, a correlation analysis of the local time characteristics is carried out, thus attaining the time–frequency correlation between the signals. Finally, the proposed method is validated by stationary and non-stationary signals simulation and is compared with the traditional correlation analysis method. The simulation results show that the traditional method can obtain the overall correlation between the signals but cannot reflect the local time and frequency correlations. In particular, the correlations of non-stationary signals cannot be accurately identified. The proposed method not only obtains the overall correlations between the signals, but can also accurately identifies the correlations between non-stationary signals, thus showing the time-varying and frequency-varying correlation characteristics. The proposed method is applied to the acoustic signal processing of an engine–gearbox test bench. The results show that the proposed method can effectively identify the time–frequency correlation between the signals.

scholarly journals Message Passing-Based Inference for Time-Varying Autoregressive Models

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 683
Author(s):  
Albert Podusenko ◽  
Wouter M. Kouw ◽  
Bert de Vries
Keyword(s):  
Message Passing ◽  
Synthetic Data ◽  
Model Performance ◽  
Ar Model ◽  
Factor Graph ◽  
Time Varying ◽  
Real World Data ◽  
Data Set ◽  
Inference Problem ◽  
Stationary Signals

Time-varying autoregressive (TVAR) models are widely used for modeling of non-stationary signals. Unfortunately, online joint adaptation of both states and parameters in these models remains a challenge. In this paper, we represent the TVAR model by a factor graph and solve the inference problem by automated message passing-based inference for states and parameters. We derive structured variational update rules for a composite “AR node” with probabilistic observations that can be used as a plug-in module in hierarchical models, for example, to model the time-varying behavior of the hyper-parameters of a time-varying AR model. Our method includes tracking of variational free energy (FE) as a Bayesian measure of TVAR model performance. The proposed methods are verified on a synthetic data set and validated on real-world data from temperature modeling and speech enhancement tasks.

scholarly journals Instantaneous Frequency Estimation of Multi-Component Non- Stationary Signals using Fourier Bessel series and Time-Varying Auto Regressive Model

2015 ◽  
Vol 61 (4) ◽  
pp. 365-376
Author(s):  
G. Ravi Shankar Reddy ◽  
Rameshwar Rao
Keyword(s):  
Instantaneous Frequency ◽  
Estimation Error ◽  
Basis Functions ◽  
Time Varying ◽  
Instantaneous Frequency Estimation ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Stationary Signals ◽  
Auto Regressive ◽  
Non Stationary Signal

Abstract In this paper, we propose a novel technique for Instantaneous Frequency (IF) estimation of multi component non stationary signals using Fourier Bessel Series and Time- Varying Auto Regressive (FB-TVAR) model. In the proposed technique, the Fourier-Bessel (FB) expansion decomposes the multi-component non stationary signal into a number of monocomponent signals and TVAR model is used to model each mono-component signal. In TVAR modeling approach the time varying parameters are expanded as a linear combination of basis functions. In this paper, the TVAR parameters are expanded by a discrete cosine basis functions. The maximum likelihood estimation algorithm for model order selection in TVAR models is also discussed. The Instantaneous Frequency (IF) is extracted from the time-varying parameters by calculating the angles of the estimation error filter polynomial roots. The estimation of the TVAR parameters of a multicomponent signal requires the inversion of a large covariance matrix, while the projected technique (FB-TVAR) requires the inversion of a number of comparatively small covariance matrices with better numerical stability properties. Simulation results are presented for Multi component discrete Amplitude and Frequency modulated (AM-FM) signal

FEATURE EXTRACTION OF RADAR MULTIPLE-TARGET ECHOES USING WAVELET PACKET TRANSFORM WITH THE BEST BASES

2003 ◽  
Vol 17 (01) ◽  
pp. 127-150 ◽  
Author(s):  
SHOUYONG WANG ◽  
GUANGXI ZHU ◽  
YUAN Y. TANG
Keyword(s):  
Wavelet Packet ◽  
Wavelet Packet Transform ◽  
Time Varying ◽  
Multiple Target ◽  
Time Frequency ◽  
Frequency Decomposition ◽  
Frequency Domains ◽  
Stationary Signals ◽  
Entropy Criterion ◽  
Positive Results

Extraction of effective features plays a key role in pattern recognition. A large number of patterns, such as speech, radar signals, earthquake signals, handwriting, etc. are of non-stationary signals or exhibit time-varying behavior. The features of these patterns are often located in both the time and frequency domains. The traditional methods fail to extract such kind of features. Fortunately, wavelet packet transform (WPT) can provide an arbitrary time-frequency decomposition for the signals, because a wavelet packet (WP) library contains many WP bases, which can handle the different components of a signal. Therefore, by selecting a suitable basis, which is called "best basis", the effective features can be extracted. In this paper, three criteria are used to select the best WPT basis, namely: (1) distance criterion, (2) divergence criterion and (3) entropy criterion. Three algorithms to implement the above criteria are also provided. Experiments are conducted and the positive results are obtained.

Sign in / Sign up

Export Citation Format

Share Document