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.

STFT With Adaptive Window Width Based on the Chirp Rate

Abstract: An adaptive time-frequency representation (TFR) with higher energy concentration usually requires higher complexity. Recently, a low-complexity adaptive short-time Fourier transform (ASTFT) based on the chirp rate has been proposed. To enhance the performance, this method is substantially modified in this paper: i) because the wavelet transform used for instantaneous frequency (IF) estimation is not signal-dependent, a low-complexity ASTFT based on a novel concentration measure is addressed; ii) in order to increase robustness to IF estimation error, the principal component analysis (PCA) replaces the difference operator for calculating the chirp rate; and iii) a more robust Gaussian kernel with time-frequency-varying window width is proposed. Simulation results show that our method has higher energy concentration than the other ASTFTs, especially for multicomponent signals and nonlinear FM signals. Also, for IF estimation, our method is superior to many other adaptive TFRs in low signal-to-noise ratio (SNR) environments.

Signal Decomposition by Using the S-Method With Application to the Analysis of HF Radar Signals in Sea-Clutter

Abstract: This paper presents a new approach to the time-frequency signal analysis and synthesis, using the eigenvalue decomposition method. It is based on the S-method, the time-frequency representation that can produce a distribution equal or close to a sum of the Wigner distributions of individual signal components. The new time-frequency signal decomposition method is evaluated on the simulated and experimental high-frequency surface-wave radar (HFSWR) data. Results demonstrate that it provides an effective way for analyzing and detecting maneuvering air targets with significant velocity changes, including target signal separation from the heavy clutter. The analysis shows that this method can provide additional insight into the interpretation and processing of radar signals, with respect to the traditional Fourier transform based methods currently used by the HFSWRs. The proposed method could also be used in other signal processing applications

Comments on the interpretation of instantaneous frequency

Abstract: Instantaneous frequency, taken as the derivative of the phase of the signal, is interpreted in the time-frequency literature as the average frequency of the signal at each time. We point out some difficulties with this interpretation, and show that for a generic two-component AM-FM signal, the interpretation holds only when the components are of equal strength. We conclude that instantaneous frequency and the average frequency at each time are generally two different quantities. One possible interpretation of the difference between these two quantities is suggested.

Time-Frequency Squeezing and Generalized Demodulation Combined for Variable Speed Bearing Fault Diagnosis

Abstract: High-resolution time-frequency representation (TFR) method is effective for signal analysis and feature detection. However, for variable speed bearing vibration signal, conventional TFR method is prone to blur and affect the accuracy of the instantaneous frequency estimation. Moreover, the traditional order tracking, relying on equi-angular resampling, usually suffers from interpolation error. To solve such problems, we propose a joint time-frequency (TF) squeezing method and generalized demodulation (GD) to realize variable speed bearing fault diagnosis. The method can represent the time-varying fault characteristic frequency precisely and be free from resampling. First, using fast spectral kurtosis to select the optimal-frequency band which is sensitive to rolling bearing fault, and extracting envelope by Hilbert transform within the selected optimal frequency band. Next, a high-quality TF clustering method based on short-time Fourier transform is applied to the TF analysis of the envelope to get a clear TFR, from which the frequency information for GD is obtained. Finally, processing the basic demodulator via the peak search through the TF analysis results in the TFR for GD to gain a resampling-free-order spectrum. Based on the more precise TF information from the clearer TFR, the bearing fault can be diagnosed via GD without tachometer or any resampling involved, avoiding the amplitude error and low computational efficiency of resampling. Simulation study and experimental signal analysis validate that the proposed method has better performance than those methods based on conventional TF analysis and resampling.