Time-varying spectral analysis: theory and applications (original) (raw)

Advanced spectral analysis methods

1997

The purpose of time-series analysis is to detect basic properties of the system that engenders a time series. The hope of predicting the system's future evolution is closely related to the possibility of such detection. The most easily predictable components of a system's evolution are the regular, deterministic ones; hence we look for trends and periodic oscillations. In doing so, it is often convenient to move from the time domain to the frequency domain.

Spectral Analysis for Nonstationary and Nonlinear Systems: A Discrete-Time-Model-Based Approach

IEEE Transactions on Biomedical Engineering, 2000

A new frequency-domain analysis framework for nonlinear time-varying systems is introduced based on parametric time-varying nonlinear autoregressive with exogenous input models. It is shown how the time-varying effects can be mapped to the generalized frequency response functions (FRFs) to track nonlinear features in frequency, such as intermodulation and energy transfer effects. A new mapping to the nonlinear output FRF is also introduced. A simulated example and the application to intracranial electroencephalogram data are used to illustrate the theoretical results.

Estimation and Classification of Non-Stationary Processes : Applications in Time-Frequency Analysis

2019

This thesis deals with estimation and classification problems of non-stationary processes in a few special cases.In paper A and paper D we make strong assumptions about the observed signal, where a specific model is assumed and the parameters of the model are estimated.In Paper B, Paper C, and Paper E more general assumptions about the structure of the observed processes are made, and the methods in these papers may be applied to a wider range of parameter estimation and classification scenarios.All papers handle non-stationary signals where the spectral power distribution may change with respect to time. Here, we are interested in finding time-frequency representations (TFR) of the signal which can depict how the frequencies and corresponding amplitudes change.In Paper A, we consider the estimation of the shape parameter detailing time- and frequency translated Gaussian bell functions.The algorithm is based on the scaled reassigned spectrogram, where the spectrogram is calculated u...

Spectral Analysis for Amplitude-Modulated Time Series

Journal of Time Series Analysis, 1993

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Time-frequency analysis and nonstationary filtering

2005

The primary objective of this workshop was to bring together both theoretical researchers and the more applied practitioners in time-frequency analysis for a constructive exchange of ideas. There are many very advanced concepts in the recent theoretical publications in this field but most of these have had little impact to date upon applications to real world signals. The organizers invited some of the top theoreticians in time-frequency analysis to interact with mathematical physicists and engineers, particularly such as those in geophysics and communications engineering where nonstationary filtering is a fundamental tool. The workshop provided a format with time for formal presentations as well as unstructured time for interaction and collaboration.

Efficient Spectral Analysis of Time Series

2008

This work focuses on efficient, joint time-frequency analysis of time series data. Joint time-frequency analysis is based on the sliding window.There are two major contributions of this thesis. Firstly, we have introduced a notion of “aggregate spectrogram (AS)” which is a unimodal distribution at each time instant.The AS is extremely useful and computationally efficient when we are interested in a few spectral features and not the entire spectrum.Properties/characteristics of the AS have been listed.A parametric method, based on a second order autoregressive model of the signal, for the construction of the AS, has been described. Of all the existing spectral estimation tools, the AS has the least computational complexity.Based on the AS, instantaneous frequency estimation for multicomponent signals with equal amplitudes has been achieved.The AS does not require Goertzel filters in dual tone multi frequency detection applications.The AS finds many potential application.A few example...

Comparative study between four classical spectral analysis methods

2005

This work presents a comparison between four classical spectral analyses: Fourier, multitaper, maximum entropy and iterative regression. Six 256-sample artificial series were generated by superposition of sine functions, long trends (of time scale greater than series length) and noise (generated by pseudo-random function). A spectral analysis of an observational time series (sunspot number) was also performed. Advantages and drawbacks of every method are described in this work.

Time-Local Spectral Analysis for Non-Stationary Time Series: The S-Transform for Noisy Signals

Fluctuation and Noise Letters, 2003

The S-transform is a method of time-local spectral analysis (also known as time-frequency analysis), a modified short-time Fourier Transform, in which the width of the analyzing window scales inversely with frequency, in analogy with continuous wavelet transforms. If the time series is non-stationary and consists of a mix of Gaussian white noise and a deterministic signal, though, this type of scaling leads to larger apparent noise amplitudes at higher frequencies. In this paper, we introduce a modified S-transform window with a different scaling function that addresses this undesirable characteristic.