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.

Time-Frequency Analysis of Systems with Changing Dynamic Properties

Abstract: Time-frequency analysis methods transform a time series into a two-dimensional representation of frequency content with respect to time. The Fourier Transform identifies the frequency content of a signal (as a sum of weighted sinusoidal functions) but does not give useful information regarding changes in the character of the signal, as all temporal information is encoded in the phase of the transform. A time-frequency representation, by expressing frequency content at different sections of a record, allows for analysis of evolving signals. The time-frequency transformation most commonly encountered in seismology and civil engineering is a windowed Fourier Transform, or spectrogram; by comparing the frequency content of the first portion of a record with the last portion of the record, it is straightforward to identify the changes between the two segments. Extending this concept to a sliding window gives the spectrogram, where the Fourier transforms of successive portions of the record are assembled into a time-frequency representation of the signal. The spectrogram is subject to an inherent resolution limitation, in accordance with the uncertainty principle, that precludes a perfect representation of instantaneous frequency content. The wavelet transform was introduced to overcome some of the shortcomings of Fourier analysis, though wavelet methods are themselves unsuitable for many commonly encountered signals. The Wigner-Ville Distribution, and related refinements, represent a class of advanced time-frequency analysis tools that are distinguished from Fourier and wavelet methods by an increase in resolution in the time-frequency plane. I introduce several time-frequency representations and apply them to various synthetic signals as well as signals from instrumented buildings. vi For systems of interest to engineers, investigating the changing properties of a system is typically performed by analyzing vibration data from the system, rather than direct inspection of each component. Nonlinear elastic behavior in the forcedisplacement relationship can decrease the apparent natural frequencies of the system - these changes typically occur over fractions of a second in moderate to strong excitation and the system gradually recovers to pre-event levels. Structures can also suffer permanent damage (e.g., plastic deformation or fracture), permanently decreasing the observed natural frequencies as the system loses stiffness. Advanced time-frequency representations provide a set of exploratory tools for analyzing changing frequency content in a signal, which can then be correlated with damage patterns in a structure. Modern building instrumentation allows for an unprecedented investigation into the changing dynamic properties of structures: a framework for using time-frequency analysis methods for instantaneous system identification is discussed.

High-Order Synchroextracting Time–Frequency Analysis and Its Application in Seismic Hydrocarbon Reservoir Identification

Abstract: Time–frequency (TF) analysis (TFA) plays an important role in seismic hydrocarbon reservoir identification, which is attributed to its ability to effectively identify the oil and gas seismic response characteristics of geological bodies in different frequency bands. In this letter, we introduce a novel TFA method termed high-order synchroextracting transform (SET) and apply it to the high-precision identification of gas-bearing reservoirs. Under the premise of short-time Fourier transform (STFT), this method defines a new synchroextracting operator (SEO) based on high-order approximations of signal amplitude and phase. Furthermore, only the TF information highly correlated with the TF characteristics of the signal is extracted from the STFT spectrum by using the SEO. Therefore, for a wider variety of the nonstationary signal, a highly energy-concentrated TF representation can be effectively obtained. The application of STFT and different-order SET on 1-D synthetic signal and field seismic data verifies the effectiveness of the proposed method.

Time-frequency analysis in power measurement using complex wavelets

Abstract: The problem of a useful electrical power quantification in environments with power quality problems is discussed. As it is difficult to correctly apply a Fourier-based approach, alternative power quantifications in the time-frequency domain, based on a complex wavelet transform, are presented. Using the property that instantaneous amplitudes of voltages and currents as well as instantaneous phase differences can be obtained, power definitions with time and frequency localization properties are derived. The physical interpretation is given and a comparison with traditional formulae is made. Examples, with typical power quality problems, illustrating this methodology are given.

The Detection of Frequency Hopping Signal Using Compressive Sensing

Abstract: 1 hyajia@126.com; 2 tpw0802@163.com Abstract: Compressive sensing (CS) creates a new framework of signal reconstruction or approximation from a smaller set of incoherent projection compared with the traditional Nyquist-rate sampling theory. Re- cently, it has been shown that CS can solve some signal processing problems given incoherent measurements without ever reconstructing the signals. Moreover, the number of measurements necessary for most compres- sive signal processing application such as detection, estimation and classification is lower than that necessary for signal reconstruction. Based on CS, this paper presents a novel identification algorithm of frequency hop- ping (FH) signals. Given the hop interval, the FH signals can be identified and the hopping frequencies can be estimated with a tiny number of measurements. Simulation results demonstrate that the method is effective and efficient.

Stationarization via surrogates

Abstract: The surrogate data method, classically used for non-linearity tests, amounts to the use of some constrained noise providing a reference for statistical testing. It is revisited here as a method for stationarization and this feature is put forward in the context of non-stationarity testing. The stationarization property of surrogates is first explored in a time–frequency perspective and used for devising a test of stationarity relative to an observation time. Then, more general forms of surrogates are developed, directly in time–frequency or mixed domains of representation (ambiguity and time-lag domains included), and it is shown how they allow for other tests of non-stationary features: detection of the existence of a transient in some noise; assessment of non-stationary cross-correlations.