Synchrosqueezing-based Recovery of Instantaneous Frequency from Nonuniform Samples

We propose a new approach for studying the notion of the instantaneous frequency of a signal. We build on ideas from the Synchrosqueezing theory of Daubechies, Lu and Wu and consider a variant of Synchrosqueezing, based on the short-time Fourier transform, to precisely define the instantaneous frequencies of a multi-component AM-FM signal. We describe an algorithm to recover these instantaneous frequencies from the uniform or nonuniform samples of the signal and show that our method is robust to noise. We also consider an alternative approach based on the conventional, Hilbert transform-based notion of instantaneous frequency to compare to our new method. We use these methods on several test cases and apply our results to a signal analysis problem in electrocardiography.Comment: 19 pages, 9 figure

Sparse Time-Frequency decomposition for multiple signals with same frequencies

In this paper, we consider multiple signals sharing same instantaneous frequencies. This kind of data is very common in scientific and engineering problems. To take advantage of this special structure, we modify our data-driven time-frequency analysis by updating the instantaneous frequencies simultaneously. Moreover, based on the simultaneously sparsity approximation and fast Fourier transform, some efficient algorithms is developed. Since the information of multiple signals is used, this method is very robust to the perturbation of noise. And it is applicable to the general nonperiodic signals even with missing samples or outliers. Several synthetic and real signals are used to test this method. The performances of this method are very promising

Instantaneous frequencies of a chaotic system

International audienceThe structure and geometry of high-dimensional, complex dynamical systems is usually hidden under a profusion of numerical data. We show that time-frequency analysis allows one to analyze these data regardless of the number of degrees of freedom. Our method takes snapshots of the system in terms of its instantaneous frequencies defined as ridges of the time-frequency landscape. Using the wavelet transform of a single trajectory, it can characterize key dynamical properties like the extent of chaos, resonance transitions and trapping

One-shot 3d surface reconstruction from instantaneous frequencies: solutions to ambiguity problems

Phase-measuring profilometry is a well known technique for 3D surface reconstruction based on a sinusoidal pattern that is projected on a scene. If the surface is partly occluded by, for instance, other objects, then the depth shows abrupt transitions at the edges of these occlusions. This causes ambiguities in the phase and, consequently, also in the reconstruction.\ud This paper introduces a reconstruction method that is based on the instantaneous frequency instead of phase. Using these instantaneous frequencies we present a method to recover from ambiguities caused by occlusion. The recovery works under the condition that some surface patches can be found that are planar. This ability is demonstrated in a simple example. \u

Time-frequency analysis of the restricted three-body problem: transport and resonance transitions

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

The Dynamic Performance of Cavitating Turbopumps

Knowledge of the dynamic performance of turbopumps is essential for the prediction of instabilities in hydraulic systems; the necessary information is in the form of a transfer function relating the instantaneous pressures and mass flow rates at inlet and discharge. Cavitation has a significant effect on this transfer function since dynamical changes in the volume of cavitation contribute to the difference in the instantaneous flow rates. The present paper synthesizes the transfer matrix for cavitating inducers at moderately low frequencies and shows that the numerical results are consistent with observations on rocket engine turbopumps