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.

Fractional Gabor transform.

Abstract: A fractional Gabor transform (FRGT) is proposed. This new transform is a generalization of the conventional Gabor transform (GT) based on the Fourier transform to the windowed fractional Fourier transform (FRFT). The FRGT provides analyses of signals in both the real space and the FRFT frequency domain simultaneously. The space-FRFT frequency pattern can be rotated as the fractional order changes. The FRGT has an additional freedom, compared with the conventional GT, i.e., the transform order. The FRGT may offer a useful tool for guiding optimal filter design in the FRFT domain in signal processing.

Analysis of seismocardiographic signals using polynomial chirplet transform and smoothed pseudo Wigner-Ville distribution

Abstract: Seismocardiographic (SCG) signals are chest surface vibrations induced by cardiac activity. These signals may offer a method for diagnosing and monitoring heart function. Successful classification of SCG signals in health and disease depends on accurate signal characterization and feature extraction. One approach of determining signal features is to estimate its time-frequency characteristics. In this regard, four different time-frequency distribution (TFD) approaches were used including short-time Fourier transform (STFT), polynomial chirplet transform (PCT), Wigner-Ville distribution (WVD), and smoothed pseudo Wigner-Ville distribution (SPWVD). Synthetic SCG signals with known time-frequency properties were generated and used to evaluate the accuracy of the different TFDs in extracting SCG spectral characteristics. Using different TFDs, the instantaneous frequency (IF) of each synthetic signal was determined and the error (NRMSE) in estimating IF was calculated. STFT had lower NRMSE than WVD for synthetic signals considered. PCT and SPWVD were, however, more accurate IF estimators especially for the signal with time-varying frequencies. PCT and SPWVD also provided better discrimination between signal frequency components. Therefore, the results of this study suggest that PCT and SPWVD would be more reliable methods for estimating IF of SCG signals. Analysis of actual SCG signals showed that these signals had multiple spectral components with slightly time-varying frequencies. More studies are needed to investigate SCG spectral properties for healthy subjects as well as patients with different cardiac conditions.

The ambiguity function associated with the linear canonical transform

Abstract: A new kind of ambiguity function (AF) associated with the linearcanonical transform (LCT) is proposed in this article, this new AF is defined based on the LCT and the classical AF. Firstly, the main properties and physical meanings of the newly defined AF are investigated, the results show that this kind of AF can be seen as one generalization of the classical AF. Then, the newly defined AF is applied to detect the parameters of the linear frequency modulated signals by combining with the classical Radon transform. The simulations are performed to verify the correctness of the derived results, and the comparison of the derived results with the common time-frequency analysis tools are also discussed.

A Study of Joint Time-Frequency Analysis-Based Modal Analysis

Abstract: Traditional modal-analysis methods use either time-domain or frequency-domain approaches. Because vibration signals are generally nonstationary, time and frequency information is needed simultaneously in many cases. This paper presents an overview of the applications of joint time-frequency methods for modal analysis. Since a joint time-frequency analysis can decouple vibration modes, it has an advantage, especially when information about the excitation is not available. In this paper, wavelet and Gabor analyses for the modal parameter identification are compared. Two reconstruction approaches - the FFT method and the Gabor expansion method$are also compared. Numerical simulations and experiments have been carried out