scholarly journals Cross-Correlation Properties of Costas Arrays and Their Images under Horizontal and Vertical Flips

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Konstantinos Drakakis ◽  
Rod Gow ◽  
John Healy ◽  
Scott Rickard
Keyword(s):  
Cross Correlation ◽  
The Cross ◽  
Correlation Properties

We consider the cross-correlation of a Costas array with its image under a horizontal and/or a vertical flip. We propose and prove several bounds on the maximal cross-correlation and on its value at the origin, for both general Costas arrays and for algebraically constructed ones.

EFFECT OF LINEAR AND NONLINEAR FILTERS ON MULTIFRACTAL DETRENDED CROSS-CORRELATION ANALYSIS

Fractals ◽  
2011 ◽  
Vol 19 (04) ◽  
pp. 443-453 ◽  
Author(s):  
JIE SONG ◽  
PENGJIAN SHANG
Keyword(s):  
Correlation Analysis ◽  
Power Law ◽  
Cross Correlation ◽  
Influence Factors ◽  
Nonlinear Filters ◽  
Cross Correlation Analysis ◽  
Cross Correlations ◽  
Linear And Nonlinear ◽  
The Cross ◽  
Correlation Properties

When probing the dynamical properties of complex systems, such as physical and physiological systems, the output signal may be not the expected one. It is often a linear or nonlinear filter (or a transformation) of the right one represented the properties we want to investigate. Besides, for a multiple-component system, it is necessary to consider the relations between different influence factors. Here, we investigate what effect kinds of linear and nonlinear filters have on the cross-correlation properties of monofractal series and binomial multifractal series relatively. We use the multifractal detrended cross-correlation analysis (MFDCCA) that has been known well for its accurate quantization of cross-correlations between two time series. We study the effect of five filters: (i) linear (yi = axi + b); (ii) polynomial [Formula: see text]; (iii) logarithmic (yi = log (xi + δ)); (iv) exponential (yi = exp (axi + b)); and (v) power-law (yi = (xi + a)b). We find that for both monofractal and multifractal signals, linear filters have no effect on the cross-correlation properties while the influence of polynomial, logarithmic and power-law filters mainly depends on (a) the strength of cross-correlations in the original series; (b) the parameter b of the polynomial filter; (c) the offset δ in the logarithmic filter; and (d) both the parameter a and b of the power-law filter. In addition, the parameter a and b of the exponential filter change the cross-correlation properties of monofractal signal, yet they have little influence on that of multifractal signal.

scholarly journals PERIODICITY SEARCH ALGORITHMS IN DIGITAL SEQUENCES WITH BLOCK CODING BY THEIR CORRELATION PROPERTIES

2021 ◽  
pp. 7-18
Author(s):  
О. М. Romanov ◽  
V. Yu. Kotiubin
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
A Priori ◽  
Error Correcting Code ◽  
Search Algorithms ◽  
Cross Correlation Function ◽  
Block Coding ◽  
The Cross ◽  
A Priori Uncertainty ◽  
Correlation Properties

Context. To improve the noise immunity of communication and data transmission systems, error-correcting coding is widely used. The most common because of their effectiveness are block coding methods. Under conditions of partial a priori uncertainty of the type and parameters of encoding, before decoding the digital sequence, a preliminary analysis is carried out to determine them. In block coding, to determine the period of a digital sequence caused by the addition of a sync sequence to it, and which can determine the type and parameters of coding, a common approach is to use their correlation properties. Objective. The object of the research is the presentation of periodicity search algorithms in digital sequences with block errorcorrecting coding under conditions of partial a priori uncertainty of the type and parameters of the error-correcting code. Method. The article presents two periodicity search algorithms in digital sequences with block coding and describes the principle of their operation. The basis of one algorithm is the calculation of the autocorrelation function, the basis of the other is calculation of the cross-correlation function. It is shown that the length of the digital sequence should be twice as long as the maximum possible period. The operation of both algorithms is illustrated by examples. Results. Based on the proposed algorithms, special software has been developed. The results of determining the period of digital sequences with block error-correcting coding at different values of the period confirmed the efficiency of the proposed algorithms. Both proposed algorithms give approximately the same result. Experimental dependences of the calculation time of auto- and crosscorrelation functions from the length of the digital sequence and the maximum possible period are established. The period search algorithm in a digital sequence, that use the cross-correlation function of its components, is more efficient due to fewer calculations. Conclusions. For the first time, two periodicity search algorithms in digital sequences with block error-correcting based on the determination of their correlation functions are obtained. The application of the developed algorithms in practice allows, under partial a priori uncertainty of the type and parameters of the error-correcting code, to determine the period of digital sequences in real time even at large values of the period, and based on it, to identify the type and parameters of block error-correcting codes.

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