Time–frequency analysis

About: Time–frequency analysis is a research topic. Over the lifetime, 5407 publications have been published within this topic receiving 104346 citations.

Bayesian variable selection and regularization for time-frequency surface estimation

Abstract: Summary. We describe novel Bayesian models for time–frequency inverse modelling of non-stationary signals. These models are based on the idea of a Gabor regression, in which a time series is represented as a superposition of translated, modulated versions of a window function exhibiting good time–frequency concentration. As a necessary consequence, the resultant set of potential predictors is in general overcomplete—constituting a frame rather than a basis—and hence the resultant models require careful regularization through appropriate choices of variable selection schemes and prior distributions. We introduce prior specifications that are tailored to representative time series, and we develop effective Markov chain Monte Carlo methods for inference. To highlight the potential applications of such methods, we provide examples using two of the most distinctive time–frequency surfaces—speech and music signals—as well as standard test functions from the wavelet regression literature.

Micro-Doppler Effect Analysis and Feature Extraction in ISAR Imaging With Stepped-Frequency Chirp Signals

Abstract: The micro-Doppler (m-D) effect induced by the rotating parts or vibrations of the target provides a new approach for target recognition. To obtain high range resolution for the extraction of the fine m-D signatures of an inverse synthetic aperture radar target, the stepped-frequency chirp signal (SFCS) is used to synthesize the ultrabroad bandwidth and reduce the requirement of sample rates. In this paper, the m-D effect in SFCS is analyzed. The analytical expressions of the m-D signatures, which are extracted by an improved Hough transform method associated with time-frequency analysis, are deduced on the range-slow-time plane. The implementation of the algorithm is presented, particularly in those extreme cases of rotating (vibrating) frequencies and radii. The simulations validate the theoretical formulation and robustness of the proposed m-D extraction method.

A better way to define and describe Morlet wavelets for time-frequency analysis

Abstract: Morlet wavelets are frequently used for time-frequency analysis of non-stationary time series data, such as neuroelectrical signals recorded from the brain. The crucial parameter of Morlet wavelets is the width of the Gaussian that tapers the sine wave. This width parameter controls the trade-off between temporal precision and frequency precision. It is typically defined as the "number of cycles," but this parameter is opaque, and often leads to uncertainty and suboptimal analysis choices, as well as being difficult to interpret and evaluate. The purpose of this paper is to present alternative formulations of Morlet wavelets in time and in frequency that allow parameterizing the wavelets directly in terms of the desired temporal and spectral smoothing (as full-width at half-maximum). This formulation provides clarity on an important data analysis parameter, and should facilitate proper analyses, reporting, and interpretation of results. MATLAB code is provided.

A Combined Polynomial Chirplet Transform and Synchroextracting Technique for Analyzing Nonstationary Signals of Rotating Machinery

Abstract: Time–frequency analysis (TFA) technique is an effective approach to capture the changing dynamic in a nonstationary signal. However, the commonly adopted TFA techniques are inadequate in dealing with signals having a strong nonstationary characteristic or multicomponent signals having close frequency components. To overcome this shortcoming, a new TFA technique applying a polynomial chirplet transform (PCT) in association with a synchroextracting transform (SET) is proposed in this paper. It is shown that the energy concentration of the time–frequency representation (TFR) of a strong frequency-modulated signal from a PCT transform can be further enhanced by an SET transform. The technique can also be employed to accurately extract the signal components of a multicomponent nonstationary signal with close frequency components by adopting an iterative process. It is found that the TFR calculated from the proposed technique matches well with the ideal TFR, which demonstrates the superiority of the current technique in dealing with nonstationary signals having rapidly changing dynamics. Results from the analysis of the experimental data under varying speed conditions confirm the validity of the proposed technique in dealing with nonstationary signals from practical sources.

Assess Sleep Stage by Modern Signal Processing Techniques

Abstract: In this paper, two modern adaptive signal processing techniques, empirical intrinsic geometry and synchrosqueezing transform, are applied to quantify different dynamical features of the respiratory and electroencephalographic signals. We show that the proposed features are theoretically rigorously supported, as well as capture the sleep information hidden inside the signals. The features are used as input to multiclass support vector machines with the radial basis function to automatically classify sleep stages. The effectiveness of the classification based on the proposed features is shown to be comparable to human expert classification—the proposed classification of awake, REM, N1, N2, and N3 sleeping stages based on the respiratory signal (resp. respiratory and EEG signals) has the overall accuracy $81.7\%$ (resp. $89.3\%$ ) in the relatively normal subject group. In addition, by examining the combination of the respiratory signal with the electroencephalographic signal, we conclude that the respiratory signal consists of ample sleep information, which supplements to the information stored in the electroencephalographic signal.