• Geophysics and Geophysical Exploration
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• v.7 no.1
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• pp.7-13
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• 2004

In this paper, we demonstrate that Common Mid-Point (CMP) cross-correlation gathers of multi-channel and multi-shot surface waves give accurate phase-velocity curves, and enable us to reconstruct two-dimensional (2D) velocity structures with high resolution. Data acquisition for CMP cross-correlation analysis is similar to acquisition for a 2D seismic reflection survey. Data processing seems similar to Common Depth-Point (CDP) analysis of 2D seismic reflection survey data, but differs in that the cross-correlation of the original waveform is calculated before making CMP gathers. Data processing in CMP cross-correlation analysis consists of the following four steps: First, cross-correlations are calculated for every pair of traces in each shot gather. Second, correlation traces having a common mid-point are gathered, and those traces that have equal spacing are stacked in the time domain. The resultant cross-correlation gathers resemble shot gathers and are referred to as CMP cross-correlation gathers. Third, a multi-channel analysis is applied to the CMP cross-correlation gathers for calculating phase velocities of surface waves. Finally, a 2D S-wave velocity profile is reconstructed through non-linear least squares inversion. Analyses of waveform data from numerical modelling and field observations indicate that the new method could greatly improve the accuracy and resolution of subsurface S-velocity structure, compared with conventional surface-wave methods.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.6
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• pp.891-897
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• 2013

The spectrum and the number of the values of the cross-correlation function between the maximal period binary sequences have been extensively studied because of their importance in communications applications. In this paper, we propose the new family of the sequences using the decimation $d=2^{m-1}(3{\cdot}2^{m}-1)$. And we find the spectrum of the cross-correlation function of the sequences and analyze the number of times each value occurs for $0{\leq}{\tau}{\leq}2^{n}-2$.

• The Journal of the Acoustical Society of Korea
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• v.37 no.5
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• pp.271-275
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• 2018

There are several methods for estimating the time delay between incoming signals to two sensors. Among them, the GCC-PHAT (Generalized Cross Correlation-Phase Transform) method, which estimates the relative delay from the signal whitening and the cross-correlation between the different signal inputs to the two sensors, is a traditionally well known method for achieving stable performance. In this paper, we have identified a part of GCC-PHAT that can improve the periodicity. Also, we apply the auto-correlation method that is widely used as a method to improve the periodicity. Comparing the proposed method with the GCC-PHAT method, we show that the proposed method improves the mean square error performance by 5 dB ~ 15 dB at the SNR above 0 dB for white Gaussian signal source and also show that the method improves the mean square error performance up to 15 dB at the SNR above 2 dB for the color signal source.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.17 no.5
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• pp.1138-1144
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• 2013

Cross-correlation functions of maximal period sequences have been studied for decades. In this paper, we find the cross-correlation values of non-linear sequences $S_a^r(t)=Tr_1^m\{[Tr_m^n(a{\alpha}^t+{\alpha}^{dt})]^r\}$ having the maximal period $2^n-1$ for Niho type decimation $d=2^{m-2}(2^m+3)$, where n=2m. In particular, we call d Niho type decimation in case $d{\equiv}1(mod\;2^m-1)$. And we analyze the cross-correlation distributions of $S_a^r(t)$ when the phase shift ${\tau}=(2^m+1)k(0{\leq}k{\leq}2^m-2)$ and provide experiment results.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.9C
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• pp.669-675
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• 2008

For an odd prime p, n=4k and $d=((p^2k+1)/2)^2$, there are $(p^{2k}+1)/2$ distinct decimated sequences, s(dt+1), $0{\leq}l<(p^{2k}+1)/2$, of a p-ary m-sequence, s(t) of period $p^n-1$. In this paper, it is shown that the cross-correlation function between s(t) and s(dt+l) takes the values in $\{-1,-1{\pm}\sqrt{p^n},-1+2\sqrt{p^n}\}$ and their, cross-correlation distribution is also derived.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.869-876
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• 2013

The design of large family size with the optimal cross-correlation property is important in spread spectrum and code division multiple access communication systems. In this paper we present the sequences with the decimation $d=2{\cdot}2^m-1$, calculate the cross-correlation spectrum for $0{\leq}t{\leq}2^n-2$ and count the number of the value $2^m-1$ occurring for $0{\leq}{\tau}2^n-2$. The sequences have the optimal cross-correlation property. The work on this paper can make it easier to count the number of the whole value occurring for $0{\leq}{\tau}2^n-2$.

• The Journal of the Korea institute of electronic communication sciences
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• v.8 no.2
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• pp.263-269
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• 2013

In this paper we give a proof for finding the values of the cross-correlation function $C_d({\tau})$, when $d=3{\cdot}2^m-2$ where n=2m, m=4k ($k{\geq}2$). And the linear span of the sequences in the proposed sequence family are derived in the some cases.

• Journal of applied mathematics & informatics
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• v.30 no.5_6
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• pp.903-911
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• 2012

Let $\{u(t)\}$ and $\{u(dt)\}$ be two maximal length sequences of period $2^n-1$. The cross-correlation is defined by $C_d({\tau})=\sum{_{t=0}^{2^n-2}}(-1)^{u(t+{\tau})+v(t)$ for ${\tau}=0,1,{\cdots},2^n-2$. In this paper, we propose a new proof for finding the values and the number of occurrences of each value of $C_d({\tau})$ when $d=2^{k-2}(2^k+3)$, where $n=2k$, $k$ is a positive integer.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.6
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• pp.1369-1375
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• 2012

One of important problems in the theory of sequences is to determine the values and number of occurrences of each value taken on by the cross-correlation. In this paper, we find the values and the number of occurrences of each value of cross-correlation between an m-sequence u(t) of period $2^n-1$ and its decimation $u(dt)(0{\leq}t{\leq}2^n-2)$ where n=2m, 2s|m and $d=(2^{2m}+2^{2s+1}-2^{m+s+1}-1)/(2^s-1)$. Also we show that a family of decimations leads to a four-valued cross-correlation.

• East Asian mathematical journal
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• v.29 no.5
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• pp.529-536
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• 2013

In this paper, we find the values and the number of occurrences of each value of the cross-correlation function $C_d({\tau})$ when $d=\frac{2^{k-1}}{2^s-1}(2^{k(i+1)}-2^{ki}+2^{s+1}-2^k-1)$, where n = 2k, s is an integer such that 2s divides k, and i is odd.