A NOTE ON ANALYTIC SIGNALS WITH NONLINEAR PHASE

2009 ◽  
Vol 07 (05) ◽  
pp. 711-720 ◽  
Author(s):  
SHOUYIN CHEN
Keyword(s):  
Information Processing ◽  
Instantaneous Frequency ◽  
Basic Concept ◽  
Analytic Signal ◽  
Analytic Representation ◽  
Nonlinear Phase ◽  
Band Limited ◽  
Instantaneous Frequencies ◽  
Analytic Signals

Instantaneous frequency, defined as the derivative of the phase of a complex analytic representation of the signal, is a basic concept and plays an important role in communication and information processing. It is not unusual to expect that the instantaneous frequency of an analytic signal is nonnegative. In this note, we exhibit new families of analytic signals with band-limited amplitudes and positive nonlinear instantaneous frequencies. The structures of analytic signals with band-limited amplitude and rational as well as linear plus periodic instantaneous frequencies have been analyzed.

Quasi-analytic multidimensional signals

2013 ◽  
Vol 61 (4) ◽  
pp. 1017-1024
Author(s):  
S.L. Hahn ◽  
K.M. Snopek
Keyword(s):  
Carrier Frequency ◽  
Analytic Signal ◽  
Specific Form ◽  
Unified Theory ◽  
Frequency Space ◽  
Fourier Frequency ◽  
Multidimensional Signals ◽  
Low Pass ◽  
Base Band ◽  
Analytic Signals

Abstract In a recent paper, the authors have presented the unified theory of n-dimensional (n-D) complex and hypercomplex analytic signals with single-orthant spectra. This paper describes a specific form of these signals called quasi-analytic. A quasi-analytic signal is a product of a n-D low-pass (base-band) real (in general non-separable) signal and a n-D complex or hypercomplex carrier. By a suitable choice of the carrier frequency, the spectrum of a low-pass signal is shifted into a single orthant of the Fourier frequency space with a negligible leakage into other orthants. A measure of this leakage is defined. Properties of quasi-analytic signals are studied. Problems of polar representation of quasi-analytic signals and of its lower rank representation are discussed.

scholarly journals A generalized demodulation approach to time-frequency projections for multicomponent signals

2005 ◽  
Vol 461 (2059) ◽  
pp. 2159-2179 ◽  
Author(s):  
S Olhede ◽  
A.T Walden
Keyword(s):  
Instantaneous Frequency ◽  
Additive Noise ◽  
Simulation Experiment ◽  
Wavelet Packet ◽  
Covariance Structure ◽  
Time Instant ◽  
Analytic Signal ◽  
Flexible Approach ◽  
Time Frequency ◽  
Multicomponent Signals

In this paper, we introduce a flexible approach for the time-frequency analysis of multicomponent signals involving the use of analytic vectors and demodulation. The demodulated analytic signal is projected onto the time-frequency plane so that, as closely as possible, each component contributes exclusively to a different ‘tile’ in a wavelet packet tiling of the time-frequency plane, and at each time instant, the contribution to each tile definitely comes from no more than one component. A single reverse demodulation is then applied to all projected components. The resulting instantaneous frequency of each component in each tile is not constrained to a set polynomial form in time, and is readily calculated, as is the corresponding Hilbert energy spectrum. Two examples illustrate the method. In order better to understand the effect of additive noise, the approximate variance of the estimated instantaneous frequency in any tile has been formulated by starting with pure noise and studying its evolving covariance structure through each step of the algorithm. The validity and practical utility of the resulting expression for the variance of the estimated instantaneous frequency is demonstrated via a simulation experiment.

Time-frequency analysis of deep crustal reflection seismic data using Wigner-Ville distributions

2001 ◽  
Vol 38 (7) ◽  
pp. 1027-1035 ◽  
Author(s):  
Kris Vasudevan ◽  
Frederick A Cook
Keyword(s):  
Frequency Analysis ◽  
Instantaneous Frequency ◽  
Seismic Data ◽  
Drill Hole ◽  
Lateral Variation ◽  
Time Frequency Analysis ◽  
Time Frequency ◽  
Reflection Seismic ◽  
Instantaneous Frequencies ◽  
Crustal Reflection

One important component of deep crustal reflection seismic data in the absence of drill-hole data and surface-outcrop constraints is classifying and quantifying reflectivity patterns. One approach to this component uses a recently developed data-decomposition technique, seismic skeletonization. Skeletonized coherent events and their attributes are identified and stored in a relational database, allowing easy visualization and parameterization of the reflected wavefield. Because one useful attribute, the instantaneous frequency, is difficult to derive within the current framework of skeletonization, time–frequency analysis and a new method, empirical mode skeletonization, are used to derive it. Other attributes related to time–frequency analysis that can be derived from the methods can be used for shallow and deep reflection seismic interpretation and can supplement the seismic attributes accrued from seismic skeletonization. Bright reflections observed from below the sedimentary basin in the Southern Alberta Lithosphere Transect have recently been interpreted to be caused by highly reflective sills. Time–frequency analysis of one of these reflections shows the lateral variation of energy with instantaneous frequency for any given time and the lateral variation of energy with time for any instantaneous frequency. Results from empirical mode skeletonization for the same segment of data illustrate the differences in the instantaneous frequencies among the intrinsic modes of the data. Thus, time–frequency distribution of amplitude or energy for any signal may be a good indicator of compositional differences that can vary from one location to another.

On: “3-D instantaneous frequency used as a coherency/continuity parameter to interpret reservoir compartment boundaries across an area of complex turbidite deposition,” (B. A. Hardage et al., GEOPHYSICS, Vol. 63, 1520–1531)

Geophysics ◽  
2000 ◽  
Vol 65 (2) ◽  
pp. 683-686 ◽  
Author(s):  
Arthur E. Barnes
Keyword(s):  
Instantaneous Frequency ◽  
Reservoir Characterization ◽  
Valuable Study ◽  
Instantaneous Frequencies

Hardage et al. are to be commended for a thoughtful and valuable study on instantaneous frequency applied to reservoir characterization. Of particular note is the observation that anomalous instantaneous frequencies often correspond to lower seismic coherency and form interpretable patterns. This observation has an interesting background.

FAST NONLINEAR FOURIER EXPANSIONS

2009 ◽  
Vol 01 (03) ◽  
pp. 373-405 ◽  
Author(s):  
RUI WANG ◽  
YUESHENG XU ◽  
HAIZHANG ZHANG
Keyword(s):  
Fourier Expansion ◽  
Approximation Error ◽  
Analytic Signal ◽  
Optimal Selection ◽  
Approximation Properties ◽  
Orthonormal Bases ◽  
Construction Methods ◽  
Signal Approach ◽  
Instantaneous Frequencies ◽  
Selection Of

Motivated by the analytic signal approach and general construction methods by Qian et al. (accepted by Adv. Comput. Math.), we construct a class of orthonormal bases for the real signal space [Formula: see text], which have nonconstant physically meaningful instantaneous frequencies. We develop a fast algorithm for computing the Hilbert–Fourier expansion of a given function in terms of the orthonormal bases. Moreover, we study the approximation properties of the Hilbert–Fourier expansion. A numerical example is presented to demonstrate an adaptive Fourier expansion based on an optimal selection of the parameter a in the orthonormal bases according to the approximation error.

Ambiguity Intolerance Considerations when Designing Health and Risk Messages

2017 ◽  
Author(s):  
Adrian Furnham
Keyword(s):  
Information Processing ◽  
Basic Concept ◽  
Religious Beliefs ◽  
Experimental Studies ◽  
Uncertainty Avoidance ◽  
Theoretical Development ◽  
Ambiguity Tolerance ◽  
Different Types ◽  
And Behaviors ◽  
Novel Products

The concept of ambiguity tolerance (TA), variously called Uncertainty Avoidance, Ambiguity Avoidance, or Intolerance, can be traced back nearly 70 years. It has been investigated by many different types of researchers from clinical and differential, to neuro- and work psychologists. Each sub-discipline has tended to focus on how their variable relates to beliefs and behaviors in their area of expertise, from religious beliefs to reactions to novel products and situations. The basic concept is that people may be understood on a dimension that refers to their discomfort with, and hence attempts to avoid, ambiguity or uncertainty in many aspects of their lives. There have been many attempts to devise robust and valid measures of this dimension, most of which are highly inter-correlated and require self-reporting. There remains a debate as to whether it is useful having just one or more dimensions/facets of the concept. Using these tests, there have been many correlational studies that have sought to validate the measure by looking at how those high and low on this dimension react to different situations. There have also been some, but many fewer, experimental studies, which have tested very specific hypotheses about how TA is related to information processing and reactions to specific stimuli. There is now a welcomed interest by neuroscientists to explore the concept from their perspective and using their methodologies. These studies have been piecemeal, though most have supported the tested hypotheses. There has been less theoretical development, however, of the concept attempting to explain how these beliefs arise, what sustains them, and how, why, and when they may change. However, the concept has continued to interest researchers from many backgrounds, which attests to its applicability, fecundity, and novelty.

Two families of unit analytic signals with nonlinear phase

2006 ◽  
Vol 221 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Qiuhui Chen ◽  
Luoqing Li ◽  
Tao Qian
Keyword(s):  
Nonlinear Phase ◽  
Analytic Signals
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