1,594 research outputs found
Identifying nonlinear wave interactions in plasmas using two-point measurements: a case study of Short Large Amplitude Magnetic Structures (SLAMS)
A framework is described for estimating Linear growth rates and spectral
energy transfers in turbulent wave-fields using two-point measurements. This
approach, which is based on Volterra series, is applied to dual satellite data
gathered in the vicinity of the Earth's bow shock, where Short Large Amplitude
Magnetic Structures (SLAMS) supposedly play a leading role. The analysis
attests the dynamic evolution of the SLAMS and reveals an energy cascade toward
high-frequency waves.Comment: 26 pages, 13 figure
Filter Bank Fusion Frames
In this paper we characterize and construct novel oversampled filter banks
implementing fusion frames. A fusion frame is a sequence of orthogonal
projection operators whose sum can be inverted in a numerically stable way.
When properly designed, fusion frames can provide redundant encodings of
signals which are optimally robust against certain types of noise and erasures.
However, up to this point, few implementable constructions of such frames were
known; we show how to construct them using oversampled filter banks. In this
work, we first provide polyphase domain characterizations of filter bank fusion
frames. We then use these characterizations to construct filter bank fusion
frame versions of discrete wavelet and Gabor transforms, emphasizing those
specific finite impulse response filters whose frequency responses are
well-behaved.Comment: keywords: filter banks, frames, tight, fusion, erasures, polyphas
Modulated Oscillations in Three Dimensions
The analysis of the fully three-dimensional and time-varying polarization
characteristics of a modulated trivariate, or three-component, oscillation is
addressed. The use of the analytic operator enables the instantaneous
three-dimensional polarization state of any square-integrable trivariate signal
to be uniquely defined. Straightforward expressions are given which permit the
ellipse parameters to be recovered from data. The notions of instantaneous
frequency and instantaneous bandwidth, generalized to the trivariate case, are
related to variations in the ellipse properties. Rates of change of the ellipse
parameters are found to be intimately linked to the first few moments of the
signal's spectrum, averaged over the three signal components. In particular,
the trivariate instantaneous bandwidth---a measure of the instantaneous
departure of the signal from a single pure sinusoidal oscillation---is found to
contain five contributions: three essentially two-dimensional effects due to
the motion of the ellipse within a fixed plane, and two effects due to the
motion of the plane containing the ellipse. The resulting analysis method is an
informative means of describing nonstationary trivariate signals, as is
illustrated with an application to a seismic record.Comment: IEEE Transactions on Signal Processing, 201
- …