Block-Skew-Circulant Matrices in Complex-Valued Signal Processing

We consider the skew circulant and skew left circulant matrices with any continuous Lucas numbers. Firstly, we discuss the invertibility of the skew circulant matrices and present the determinant and the inverse matrices by constructing the transformation matrices. Furthermore, the invertibility of the skew left circulant matrices is also discussed. We obtain the determinants and the inverse matrices of the skew left circulant matrices by utilizing the relationship between skew left circulant matrices and skew circulant matrix, respectively. Finally, the four kinds of norms and bounds for the spread of these matrices are given, respectively.

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Statistical View on Phase and Magnitude Information in Signal Processing

Artificial Satellites ◽

10.2478/v10018-012-0018-6 ◽

2012 ◽

Vol 47 (3) ◽

pp. 127-136

Author(s):

Waldemar Popiński

Keyword(s):

Signal Processing ◽

Time Domain ◽

Signal Reconstruction ◽

Time Domain Signal ◽

Reconstructed Signal ◽

Band Pass ◽

Expected Values ◽

Random Fluctuations ◽

Phase Distortions ◽

Complex Valued

Statistical View on Phase and Magnitude Information in Signal ProcessingIn this work the problem of reconstruction of an original complex-valued signalot,t= 0, 1, …,n- 1, from its Discrete Fourier Transform (DFT) spectrum corrupted by random fluctuations of magnitude and/or phase is investigated. It is assumed that the magnitude and/or phase of discrete spectrum values are distorted by realizations of uncorrelated random variables. The obtained results of analysis of signal reconstruction from such distorted DFT spectra concern derivation of the expected values and bounds on variances of the reconstructed signal at the observation moments. It is shown that the considered random distortions in general entail change in magnitude and/or phase of the reconstructed signal expected values, which together with imposed random deviations with finite variances can blur the similarity to the original signal. The effect of analogous random amplitude and/or phase distortions of a complex valued time domain signal on band pass filtration of distorted signal is also investigated.

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COMPLEX-VALUED MINIMAL RESOURCE ALLOCATION NETWORK FOR NONLINEAR SIGNAL PROCESSING

International Journal of Neural Systems ◽

10.1142/s0129065700000090 ◽

2000 ◽

Vol 10 (02) ◽

pp. 95-106 ◽

Cited By ~ 24

Author(s):

JIANPING DENG ◽

N. SUNDARARAJAN ◽

P. SARATCHANDRAN

Keyword(s):

Resource Allocation ◽

Signal Processing ◽

Communication Systems ◽

Learning Algorithm ◽

Nonlinear Signal Processing ◽

Hidden Neurons ◽

Nonlinear Signal ◽

Complex Valued ◽

Complex Channel ◽

Minimal Resource

This paper presents a sequential learning algorithm and evaluates its performance on complex valued signal processing problems. The algorithm is referred to as Complex Minimal Resource Allocation Network (CMRAN) algorithm and it is an extension of the MRAN algorithm originally developed for online learning in real valued RBF networks. CMRAN has the ability to grow and prune the (complex) RBF network's hidden neurons to ensure a parsimonious network structure. The performance of the learning algorithm is illustrated using two applications from signal processing of communication systems. The first application considers identification of a nonlinear complex channel. The second application considers the use of CMRAN to QAM digital channel equalization problems. Simulation results presented clearly show that CMRAN is very effective in modeling and equalization with performance achieved often being superior to that of some of the well known methods.

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Four-Dimensional Almost Einstein Manifolds with Skew-Circulant Structres

10.20944/preprints201906.0109.v1 ◽

2019 ◽

Author(s):

Iva Dokuzova ◽

Dimitar Razpopov

Keyword(s):

Tangent Space ◽

Local Coordinate System ◽

Complex Structure ◽

Hermitian Manifold ◽

Circulant Matrices ◽

Fourth Power ◽

Einstein Manifolds ◽

Almost Hermitian Manifold ◽

Riemannian Connection ◽

Skew Circulant

We consider a four-dimensional Riemannian manifold M equipped with an additional tensor structure S, whose fourth power is minus identity and the second power is an almost complex structure. In a local coordinate system the components of the metric g and the structure S form skew-circulant matrices. Both structures S and g are compatible, such that an isometry is induced in every tangent space of M. By a special identity for the curvature tensor, generated by the Riemannian connection of g, we determine classes of an Einstein manifolds and an almost Einstein manifolds. For such manifolds we obtain propositions for the sectional curvatures of some special 2-planes in a tangent space of M. We consider an almost Hermitian manifold associated with the studied manifold and find conditions for g, under which it is a Kähler manifold. We construct some examples of the considered manifolds on Lie groups.

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