Home

Sofia C. Olhede

  1. Generalized Morse Wavelets as a Superfamily of Analytic Wavelets.

    Fri, 03/16/2012 - 15:01 — SomNambul
    Authors: Sofia C. Olhede, Jonathan M. Lilly
    Subjects: Methodology
    Abstract

    The generalized Morse wavelets are shown to constitute a superfamily that
    essentially encompasses all other commonly used analytic wavelets. Details of
    the time/frequency concentration, frequency-domain symmetry, and Gaussianity of
    these wavelets are investigated. The generalized Morse wavelets are controlled
    by two parameters, one determining the Fourier-domain bandwidth, and the
    second, called $\gamma$, determining the lowest-order departure of the wavelet
    from a Gaussian form.

  2. Bivariate Instantaneous Frequency and Bandwidth.

    Tue, 10/18/2011 - 15:01 — SomNambul
    Authors: Sofia C. Olhede, Jonathan M. Lilly
    Subjects: Methodology
    Abstract

    The generalizations of instantaneous frequency and instantaneous bandwidth to
    a bivariate signal are derived. These are uniquely defined whether the signal
    is represented as a pair of real-valued signals, or as one analytic and one
    anti-analytic signal. A nonstationary but oscillatory bivariate signal has a
    natural representation as an ellipse whose properties evolve in time, and this
    representation provides a simple geometric interpretation for the bivariate
    instantaneous moments.

  3. Analysis of Modulated Multivariate Oscillations.

    Wed, 04/13/2011 - 15:01 — SomNambul
    Authors: Sofia C. Olhede, Jonathan M. Lilly
    Subjects: Methodology
    Abstract

    The concept of a common modulated oscillation spanning multiple time series
    is formalized, a method for the recovery of such a signal from potentially
    noisy observations is proposed, and the time-varying bias properties of the
    recovery method are derived. The method, an extension of wavelet ridge analysis
    to the multivariate case, identifies the common oscillation by seeking, at each
    point in time, a frequency for which a bandpassed version of the signal obtains
    a local maximum in power.

  4. Non-Parametric Tests of Structure for High Angular Resolution Diffusion Imaging in Q-Space.

    Wed, 11/17/2010 - 16:01 — SomNambul
    Authors: Sofia C. Olhede, Brandon Whitcher
    Subjects: Applications
    Abstract

    High angular resolution diffusion imaging data is the observed characteristic
    function for the local diffusion of water molecules in tissue. This data is
    used to infer structural information in brain imaging. Non-parametric scalar
    measures are proposed to summarize such data, and to locally characterize
    spatial features of the diffusion probability density function (PDF), relying
    on the geometry of the characteristic function. Summary statistics are defined
    so that their distributions are, to first order, both independent of nuisance
    parameters and also analytically tractable.

  5. On the Analytic Wavelet Transform.

    Thu, 10/29/2009 - 16:01 — SomNambul
    Authors: Sofia C. Olhede, Jonathan M. Lilly
    Subjects: Statistics
    Abstract

    An exact and general expression for the analytic wavelet transform of a
    real-valued signal is constructed, resolving the time-dependent effects of
    non-negligible amplitude and frequency modulation. The analytic signal is first
    locally represented as a modulated oscillation, demodulated by its own
    instantaneous frequency, and then Taylor-expanded at each point in time. The
    terms in this expansion, called the instantaneous modulation functions, are
    time-varying functions which quantify, at increasingly higher orders, the local
    departures of the signal from a uniform sinusoidal oscillation.

  6. Estimation of Ambiguity Functions With Limited Spread.

    Mon, 08/24/2009 - 13:10 — SomNambul
    Authors: Heidi Hindberg, Sofia C. Olhede
    Subjects: Methodology
    Abstract

    This paper proposes a new estimation procedure for the ambiguity function of
    a non-stationary time series. The stochastic properties of the empirical
    ambiguity function calculated from a single sample in time are derived.
    Different thresholding procedures are introduced for the estimation of the
    ambiguity function. Such estimation methods are suitable if the ambiguity
    function is only non-negligible in a limited region of the ambiguity plane.

Math-arch

Syndicate content