Motivated by the limitation of analyzing oscillatory signals composed of multiple compo-nents with fast-varying instantaneous frequency, we approach the time-frequency analysisproblem by optimization. Based on the proposed adaptive harmonic model, the time-frequency representation of a signal is obtained by directly minimizing a functional, whichinvolves few properties an “ideal...

spectral decomposition is a powerful tool for analysis of seismic data. fourier transform determines the frequency contents of a signal. but for analysis of non-stationary signals, 1-d transform to frequency domain is not sufficient. in early years, transforming of seismic traces into time and frequency domain was done via windowed fourier transform, called a short time fourier transform (stft)...

We present a method for estimating the instantaneous frequency of a signal. This method involves the calculation of a time–frequency energy density of the signal, then obtaining an instantaneous frequency estimate from this joint density. Time–frequency energy density is calculated as a least squares optimal combination of multi–window Gabor based evolutionary spectra. The optimal weights are o...

Connectivity measures are (typically bivariate) statistical measures that may be used to estimate interactions between brain regions from electrophysiological data. We review both formal and informal descriptions of a range of such measures, suitable for the analysis of human brain electrophysiological data, principally electro- and magnetoencephalography. Methods are described in the space-tim...

We study the action on modulation spaces of Fourier multipliers with symbols e, for real-valued functions μ having unbounded second derivatives. We show that if μ satisfies the usual symbol estimates of order α ≥ 2, or if μ is a positively homogeneous function of degree α, the corresponding Fourier multiplier is bounded as an operator between the weighted modulation spaces M δ and M, for every ...

In this paper, we introduce a new adaptive data analysis method to study trend and instantaneous frequency of nonlinear and nonstationary data. This method is inspired by the Empirical Mode Decomposition method (EMD) and the recently developed compressed (compressive) sensing theory. The main idea is to look for the sparsest representation of multiscale data within the largest possible dictiona...

The theory of frames is fundamental to timefrequency (TF or time-scale signal expansions like Gabor ysis of frames via two “TF frame representations” called the Weyl symbol and Wigner distribution of a frame. The T F analysis shows how a frame’s properties depend on the signal’s T F location and on certain frame parameters. 1 I N T R O D U C T I O N Linear time-frequency (TF) or time-scale sign...