Learn More
– Current methods for power spectrum estimation by wavelet thresholding use the empirical wavelet coefficients derived from the log periodogram. Unfortunately, the periodogram is a very poor estimate when the true spectrum has a high dynamic range and/or is rapidly varying. Also, because the distribution of the log periodogram is markedly non-Gaussian,(More)
Spectral and coherence methodologies are ubiquitous for the analysis of multiple time series. Partial coherence analysis may be used to try to determine graphical models for brain functional connectivity. The outcome of such an analysis may be considerably influenced by factors such as the degree of spectral smoothing, line and interference removal, matrix(More)
If, as is widely believed, schizophrenia is characterized by abnormalities of brain functional connectivity, then it seems reasonable to expect that different subtypes of schizophrenia could be discriminated in the same way. However, evidence for differences in functional connectivity between the subtypes of schizophrenia is largely lacking and, where it(More)
—This paper examines the class of generalized Morse wavelets, which are eigenfunction wavelets suitable for use in time-varying spectrum estimation via averaging of timescale eigenscalograms. Generalized Morse wavelets of order (the corresponding eigenvalue order) depend on a doublet of parameters (,); we extend results derived for the special case = = 1(More)
We consider the problem of testing whether a complex-valued random vector is proper, i.e., is uncorrelated with its complex conjugate. We formulate the testing problem in terms of real-valued Gaussian random vectors, so we can make use of some useful existing results which enable us to study the null distributions of two test statistics. The tests depend(More)
The use of the wavelet coherence of two series in hypothesis testing relies on some sort of smoothing being carried out in order that the coherence estimator is not simply unity. A previous study considered averaging via the use of multiple Morse wavelets. Here we consider time-domain smoothing and use of a single Morlet wavelet. Since the Morlet wavelet is(More)
The contribution to a stationary complex-valued time series at a single frequency magnitude takes the form of a random ellipse, and its properties such as aspect ratio (which includes rotational direction) and orientation are of great interest in science. A case when both the aspect ratio and orientation are fixed is found, and their variability, in(More)
Scaling characteristics of stochastic processes can be examined using wavelet cross-covariances. For jointly stationary but generally non-Gaussian linear processes, the asymptotic properties of the resulting wavelet cross-covariance estimator are derived. The linear processes are assumed to have only a square-summable weight sequence, so that the class of(More)
  • A T Walden
  • 2013
Rotary analysis decomposes vector motions on the plane into counter-rotating components, which have proved particularly useful in the study of geophysical flows influenced by the rotation of the Earth. For stationary random signals, the motion at any frequency takes the form of a random ellipse. Although there are numerous applications of rotary analysis,(More)