Results 1  10
of
19
System Reconstruction Based on Selected Regions of the Discretized HOS
 IEEE Trans. Sig. Proc
, 1997
"... Abstract — We consider the problem of system reconstruction from arbitrarily selected slices of the nthorder output spectrum. We establish that unique identification of the impulse response of a system can be performed, up to a scalar and a circular shift, based on any two onedimensional (1D) sli ..."
Abstract

Cited by 9 (4 self)
 Add to MetaCart
(Show Context)
Abstract — We consider the problem of system reconstruction from arbitrarily selected slices of the nthorder output spectrum. We establish that unique identification of the impulse response of a system can be performed, up to a scalar and a circular shift, based on any two onedimensional (1D) slices of the discretized nthorder output spectrum, (n 3), as long as the distance between the slices and the grid size satisfy a simple condition. For the special case of real systems, one slice suffices for system reconstruction. The ability to choose the slices to be used for reconstruction enables us to avoid regions of the nthorder spectrum, where the estimation variance is high, or where the ideal polyspectrum is expected to be zero, as is the case for bandlimited systems. We show that the obtained system estimates are asymptotically unbiased and consistent. We propose a mechanism for selecting slices that result in improved system estimates. We also demonstrate via simulations the superiority, in terms of estimation bias and variance, of the proposed method over existing approaches in the case of bandlimited systems. Index Terms—Bandlimited system, higher order spectra, system reconstruction, variance reduction.
Phase Reconstruction from Bispectrum Slices
"... We propose a new method for the reconstruction of the Fourier phase of a complex LTI system based on the principal arguments of any pair of horizontal consecutive bispectrum slices of the system output. Since principal bispectrum arguments only are required, there is no need for twodimensional phase ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
(Show Context)
We propose a new method for the reconstruction of the Fourier phase of a complex LTI system based on the principal arguments of any pair of horizontal consecutive bispectrum slices of the system output. Since principal bispectrum arguments only are required, there is no need for twodimensional phase unwrapping. The reconstructed phase differs from the true one by a constant, integer multiples of 2ß, and a linear phase component corresponding to an integer time delay. The ability to choose the location of the two slices enables us to avoid low signaltonoise ratio bispectral regions, which usually occur in the case of bandlimited systems. Manuscript submitted to the IEEE Transactions on Signal Processing in September 1996. Major part of support for this work came from NSF under grant MIP955 3227. 1 Introduction A linear stationary nonGaussian process can be modeled as the response of a LTI system excited by white nonGaussian input. While the power spectrum can be used for the e...
Characteristic eddy decomposition of turbulence in a channel
 J. Fluid Mech
, 1989
"... The proper orthogonal decomposition technique (Lumley's decomposition) is applied to the turbulent flow in a channel to extract coherent structures by decomposing the velocity field into characteristic eddies with random coefficients. In the homogeneous spatial directions, a generalization of t ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
The proper orthogonal decomposition technique (Lumley's decomposition) is applied to the turbulent flow in a channel to extract coherent structures by decomposing the velocity field into characteristic eddies with random coefficients. In the homogeneous spatial directions, a generalization of the shotnoise expansion is used to determine the characteristic eddies. In this expansion, the Fourier coefficients of the characteristic eddy cannot be obtained from secondorder statistics. Three different techniques are used to determine the phases of these coefficients. They axe based on (1) the bispectrum, (2) a spatial compactness requirement, and (3) a functional continuity argument. Results from these three techniques are found to be similar in most respects. The implications of these techniques and the shotnoise expansion are discussed in the appendix. The dominant eddy is found to contribute as much as 76 % to the turbulent kinetic energy. In both two and three dimensions, the characteristic eddies consist of an ejection region straddled by streamwise vortices that leave the wail in the very short streamwise distance of about 100 wall units. 1
Algorithms for image reconstruction from photonlimited data using the triple correlation
, 1987
"... The triplecorrelation technique of speckle imaging has been investigated in the lowlightlevel regime. Three practical methods for digital triplecorrelation processing have been developed. Each of these methods has successfully reconstructed images from computersimulated speckle interferograms. ..."
Abstract

Cited by 5 (1 self)
 Add to MetaCart
(Show Context)
The triplecorrelation technique of speckle imaging has been investigated in the lowlightlevel regime. Three practical methods for digital triplecorrelation processing have been developed. Each of these methods has successfully reconstructed images from computersimulated speckle interferograms. In this paper we describe and compare the three algorithms.
System Reconstruction From Selected HOS Regions
 IEEE Sig. Proc. Workshop on HOS
, 1997
"... System reconstruction from arbitrarily selected slices of the nth order output spectrum is considered. We establish that unique identification of the impulse response of a system can be performed, up to a scalar and a circular shift, based on any two horizontal slices of the discretized nth order ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
System reconstruction from arbitrarily selected slices of the nth order output spectrum is considered. We establish that unique identification of the impulse response of a system can be performed, up to a scalar and a circular shift, based on any two horizontal slices of the discretized nth order output spectrum, (n 2 3), as long as the distance between the slices and the grid size satisfy a simple condition. For the special case of real systems, one slice sufices for reconstruction. The ability to select the slices to be used for reconstruction enables one to avoid regions of the nth order spectrum where the estimation variance is high, or where the ideal bispectrum is expected to be zero, as in the case of bandlimited systems. We propose a mechanism for selecting slices that result in improved system estimates. We also demonstrate via simulations the superiority, in terms of estimation bias and variance, of the PTOposed method over existing approaches in the case of bandlimited systems. 1.
IMPROVED PHASE ESTIMATION BASED ON COMPLETE BISPECTRUM AND MODIFIED GROUP DELAY
 SIGNAL, IMAGE AND VIDEO PROCESSING, ONLINE AVAILABLE: FEBRUARY 2008
, 2008
"... In this paper, a new method for extracting the system phase from the bispectrum of the system output has been proposed. This is based on the complete bispectral data computed in the frequency domain and modified group delay. The frequency domain bispectrum computation improves the frequency resoluti ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
In this paper, a new method for extracting the system phase from the bispectrum of the system output has been proposed. This is based on the complete bispectral data computed in the frequency domain and modified group delay. The frequency domain bispectrum computation improves the frequency resolution and the modified group delay reduces the variance preserving the frequency resolution. The use of full bispectral data also reduces the variance as it is used for averaging. For the proposed method at a signal to noise ratio of 5dB, the reduction in root mean square error is in the range of 1.5 to 7 times over the other methods considered.
Uniqueness properties of higherorder
, 1990
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
Abstract
 Add to MetaCart
(Show Context)
All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
SpeckleDegraded Images BY
, 1992
"... Bispectral reconstruction of speckledegraded images ..."
(Show Context)
Cepstrum of Bispectrum A New Approach to Blind System Reconstruction
"... In this paper, an improved approach to blind deconvolution of LTI systems incorporating phase unwrapping is presented. The method can recover a noisefree estimate of the logarithm of the system transfer function which enables reconstruction of the system. The algorithm is fast due to simple computa ..."
Abstract
 Add to MetaCart
(Show Context)
In this paper, an improved approach to blind deconvolution of LTI systems incorporating phase unwrapping is presented. The method can recover a noisefree estimate of the logarithm of the system transfer function which enables reconstruction of the system. The algorithm is fast due to simple computation and accurate as it includes phase unwrapping. The proposed method is compared via simulation with other methods, selected as representative of both bispectrum and bicepstrum based techniques. In general, it performs as well as or much better than the other methods considered. The proposed method is also shown to perform well under low signaltonoise ratios.