Topic
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.
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TL;DR: A new instantaneous frequency estimation method is proposed for signals with heavy noise, which is based on a polynomial chirplet transform and a ridge curve extraction scheme and an iterative stepwise refinement algorithm is developed to generate a time-frequency distribution with satisfactory energy concentration.
Abstract: Time-frequency analysis (TFA) is an effective tool to identify the signal frequency components and to reveal their time variant features. In this paper, a new instantaneous frequency (IF) estimation method is proposed for signals with heavy noise, which is based on a polynomial chirplet transform and a ridge curve extraction scheme. Based on this method, an iterative stepwise refinement algorithm is developed to generate a time-frequency distribution (TFD) with satisfactory energy concentration. Both simulated signals and experimental vibration signals are used to validate the performance of the proposed methods. The results demonstrate that the proposed TFA method is more effective in processing the nonstationary signals with heavy noise. Further, it can perform an accurate evaluation of the IF and obtain a clear TFD.
27 citations
TL;DR: The efficacy of the proposed time–frequency distribution for solving real-life problems is illustrated by employing it to estimate direction of arrival of sparsely sampled sources in under-determined scenario.
Abstract: Multi-component characteristics and missing data samples introduce artifacts and cross-terms in quadratic time–frequency distributions, thus affecting their readability. In this study, we propose a new time–frequency method that employs directional smoothing and compressive sensing to reduce cross-terms and mitigate artifacts associated with missing samples. The efficacy of the proposed time–frequency distribution for solving real-life problems is illustrated by employing it to estimate direction of arrival of sparsely sampled sources in under-determined scenario. Numerical results show that the proposed method is superior to other state-of-the-art methods both in terms of obtaining clear time–frequency representation and accurately estimating direction of arrival.
27 citations
TL;DR: In this article, a method of time-frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body problem in both the planar and the spatial versions of the problem.
Abstract: A method of time–frequency analysis based on wavelets is applied to the problem of transport between different regions of the solar system, using the model of the circular restricted three-body problem in both the planar and the spatial versions of the problem. The method is based on the extraction of instantaneous frequencies from the wavelet transform of numerical solutions. Time-varying frequencies provide a good diagnostic tool to discern chaotic trajectories from regular ones, and we can identify resonance islands that greatly affect the dynamics. Good accuracy in the calculation of time-varying frequencies allows us to determine resonance trappings of chaotic trajectories and resonance transitions. We show the relation between resonance transitions and transport in different regions of the phase space.
27 citations
TL;DR: In this paper, it was shown that cochlear models of the Bekesy-type perform a time/frequency analysis in the sense of Gabor's Gabor analysis, i.e., the resolution depends upon spectral as well as temporal features of the applied signal.
Abstract: With respect to the present inquiry, cochlear analysis of an applied signal is considered to be given by the distribution of amplitudes along the partition. Since Ohm and Helmholtz, this form of resolution has been thought to correspond to the result of a straightforward Fourier analysis. The present paper intends to show that cochlear models of the Bekesy‐type perform a time/frequency analysis in the sense of Gabor. Along the existing time/frequency continuum, the response to sinusoidal signals represents one extreme, approaching a pure Fourier (frequency) analysis, and the response to transients the other extreme, approaching a pure time (waveform) analysis. Responses to all other signals arrange themselves between those two extremes; i.e., the resolution depends upon spectral as well as temporal features of the applied signal.With modulated signals, a process of demodulation occurs. Its origin was finally traced to hydrodynamic events which take place in the region of rapid phase changes of the traveli...
27 citations
15 Mar 1999
TL;DR: A new uncertainty measure, H/sub p/, is used that predicts the compactness of digital signal representations to determine a good (non-orthogonal) set of basis vectors and indicates that a mixture of sinusoidal and impulsive or "blocky" basis functions may be best for compactly representing signals.
Abstract: We use a new uncertainty measure, H/sub p/, that predicts the compactness of digital signal representations to determine a good (non-orthogonal) set of basis vectors. The measure uses the entropy of the signal and its Fourier transform in a manner that is similar to the use of the signal and its Fourier transform in the Heisenberg uncertainty principle. The measure explains why the level of discretization of continuous basis signals can be very important to the compactness of representation. Our use of the measure indicates that a mixture of (non-orthogonal) sinusoidal and impulsive or "blocky" basis functions may be best for compactly representing signals.
27 citations