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— 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)

– 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)

—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)

In many branches of science, particularly astronomy and geophysics, power spectra of the form f ; where is a negative power-law exponent, are common. This form of spectrum is characterized by a sharp increase in the spectral density as the frequency f decreases towards zero. A power spectrum analysis method which has proven very powerful wherever the… (More)

The use of multiple complex-valued Morse wavelets for the scalogram study of signals which are unidirectional at any time, but are bidirectional overall is considered. These wavelets are well-suited to identifying the forward and reverse components. Scalogram averaging which is possible due to the multiplicity of the complex-valued wavelets leads to a… (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 rota-tional 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)

—Recently, it was suggested that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate. The particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator, applying an orthonormal transform derived from a… (More)