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.

A high resolution data-adaptive time-frequency representation

Abstract: We present a data-adaptive time-frequency representation that obtains high resolution of signal components in time-frequency. This representation overcomes the often poor resolution of the traditional short-time Fourier transform, while avoiding the nonlinearities that make the Wigner distribution and other bilinear representations difficult to interpret and use. The new method uses adaptive Gaussian windows, with the window parameters varying at different time-frequency locations to maximize the local signal concentration in time-frequency. Two methods for selecting the Gaussian parameters are presented: a parameter estimation approach, and a method that maximizes a measure of local signal concentration.

Second-Order Synchroextracting Transform With Application to Fault Diagnosis

Abstract: Synchrosqueezing transform (SST) is a currently proposed novel postprocessing time–frequency (TF) analysis tool. It has been widely shown that SST is able to improve TF representation. However, so far, how to improve the TF resolution while ensuring the accuracy of signal reconstruction is still an open question, particularly for the vibration signal with time-varying instantaneous frequency (IF) characteristics, due to the fact that the vibration signals of mechanical equipment usually contain many types of noise generated by harsh operating conditions, and the SST will mix these noise into the real signal. Our first contribution is using the Gaussian modulated linear chirp (GMLC) signal model to represent the general nonstationary signals. The GMLC signal model can more accurately represent the time-varying nonstationary signal, compared with the SST signal model composed of linear phase function and constant amplitude. Our second contribution in this work is proposing a method to improve the TF resolution and reconstruction accuracy for nonstationary signals with time-varying IF, which we coined the second-order synchroextracting transform (SET2). In SET2, we apply the GMLC to deduce the nonstationary signal model and then only use the energy at the IF to characterize the TF distribution, which improves the TF while reducing the impact of noise on the real signal.

Time-frequency analysis of band-limited EEG with BMFLC and Kalman filter for BCI applications.

Abstract: Time-Frequency analysis of electroencephalogram (EEG) during different mental tasks received significant attention. As EEG is non-stationary, time-frequency analysis is essential to analyze brain states during different mental tasks. Further, the time-frequency information of EEG signal can be used as a feature for classification in brain-computer interface (BCI) applications. To accurately model the EEG, band-limited multiple Fourier linear combiner (BMFLC), a linear combination of truncated multiple Fourier series models is employed. A state-space model for BMFLC in combination with Kalman filter/smoother is developed to obtain accurate adaptive estimation. By virtue of construction, BMFLC with Kalman filter/smoother provides accurate time-frequency decomposition of the bandlimited signal. The proposed method is computationally fast and is suitable for real-time BCI applications. To evaluate the proposed algorithm, a comparison with short-time Fourier transform (STFT) and continuous wavelet transform (CWT) for both synthesized and real EEG data is performed in this paper. The proposed method is applied to BCI Competition data IV for ERD detection in comparison with existing methods. Results show that the proposed algorithm can provide optimal time-frequency resolution as compared to STFT and CWT. For ERD detection, BMFLC-KF outperforms STFT and BMFLC-KS in real-time applicability with low computational requirement.