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Establishing a precise electromagnetic scattering model of surfaces is of great significance for comprehending the underlying mechanics of synthetic aperture radar (SAR) imaging. To describe surface electromagnetic scattering more comprehensively, this paper established a nonlinear integral equation model with the Creamer model and bispectrum (IEM-C). Based on the IEM-C model, the effect of parameters, such as radar wave incidence angle, wind speed and direction of sea surfaces, and different polarization modes on the backscattering coefficients of C-band radar waves, was systematically evaluated. The results show that the IEM-C model can characterize both the vertical nonlinear features due to wave interactions and the horizontal nonlinear features due to the wind direction. The sensitivity of the sea surface backscattering coefficient in the IEM-C model to nonlinear effects varies with different incident angles. At the incident angle of 30°, the IEM-C model exhibits the most significant nonlinear effects. The nonlinear effects of the IEM-C model vary under different wind speeds. By comparing with the measured data, it is proved that the IEM-C model is closer to the real sea surface scattering situation than the IEM model.
In this chapter we present an introduction to the vast subject of non-Gaussian perturbations. We mainly concentrate on the bispectrum and the trispectrum. We define some standard shapes of the bispectrum in Fourier space and translate them to angular space. For a description of arbitrary N-point function in the sky we introduce a basis of rotation-invariant functions on the sphere in Appendix 4. This chapter has been added in the second edition.
Higher-Order Spectra (HOS) are used to characterise the nonlinear aeroelastic behaviour of a plunging and pitching 2-degree-of-freedom aerofoil system by diagnosing structural and/or aerodynamic nonlinearities via the nonlinear spectral content of the computed displacement signals. The nonlinear aeroelastic predictions are obtained from high-fidelity viscous fluid-structure interaction simulations. The power spectral, bi-spectral and tri-spectral densities are used to provide insight into the functional form of both freeplay and inviscid/viscous aerodynamic nonlinearities with the system displaying both low- and high-amplitude Limit Cycle Oscillation (LCO). It is shown that in the absence of aerodynamic nonlinearity (low-amplitude LCO) the system is characterised by cubic phase coupling only. Furthermore, when the amplitude of the oscillations becomes large, aerodynamic nonlinearities become prevalent and are characterised by quadratic phase coupling. Physical insights into the nonlinearities are provided in the form of phase-plane diagrams, pressure coefficient distributions and Mach number flowfield contours.
In this paper a new multifractal stochastic process called Limit of the
Integrated Superposition of Diffusion processes with Linear differencial
Generator (LISDLG) is presented which realistically characterizes the network
traffic multifractality. Several properties of the LISDLG model are presented
including long range dependence, cumulants, logarithm of the characteristic
function, dilative stability, spectrum and bispectrum. The model captures
higher-order statistics by the cumulants. The relevance and validation of the
proposed model are demonstrated by real data of Internet traffic.
We introduce a frequency-domain test of time reversibility, the
REVERSE test. It is based on the bispectrum. We analytically
establish the asymptotic distribution of the test and also explore
its finite-sample properties through Monte-Carlo simulation.
Following other researchers who demonstrated that the problem of
business-cycle asymmetry can be stated as whether macroeconomic
fluctuations are time irreversible, we use the REVERSE test as a
frequency-domain test of business-cycle asymmetry. Our empirical
results show that time irreversibility is the rule rather than the
exception for a representative set of macroeconomic time series for
five OECD countries.
A technique for reconstructing diffraction-limited image of an object from speckle images without reference star is applied to both simulated and real data. The object spectrum is estimated by blind deconvolution using the power spectrum of the speckle images and the phase is restored from the bispectrum.
This paper deals with the stationary bilinear model with Hermite degree 2 in discrete time which is built up by the first- and second-order Hermite polynomial of a Gaussian white noise process. The exact spectrum and bispectrum is constructed in terms of the transfer functions of the model.
A linear process is generated by applying a linear filter to independent, identically distributed random variables. Only the modulus of the frequency response function can be estimated if only the linear process is observed and if the independent identically distributed random variables are Gaussian. In this case a number of distinct but related problems coalesce and the usual discussion of these problems assumes, for example, in the case of a moving average that the zeros of the polynomial given by the filter have modulus greater than one. However, if the independent identically distributed random variables are non-Gaussian, these problems become distinct and one can estimate the transfer function under appropriate conditions except for a possible linear phase shift by using higher-order spectral estimates.
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