• Proceedings of the KIEE Conference
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• 2001.11c
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• pp.187-190
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• 2001

A new ultrasound imaging technique based on simultaneous multiple transmit focusing using orthogonal modified Golay codes is presented. modified Golay codes are used to increase signal-to-noise-ratio(SNR) and maximize the transmit power efficiency(TPE). Conventional Golay codes consist of a pair of complementary codes with same length and can be compressed into a delta-like signal due to their complementary property. In the present work, two modified Golay codes focused at different depths are transmitted at the same time, which are mutually orthogonal. On receive, these orthogonal modified Golay codes are separately compressed into two short pulses and individually focused. These two focused beam are combined to form a frame of image with improved lateral resolution. Computer simulations are performed to verity the proposed method improves the lateral resolution of image compared with the conventional echo system.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2013.11a
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• pp.18-19
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• 2013

본 논문에서는 시간영역에서 Golay 시퀀스를 이용한 주파수 분할 다중화(orthogonal frequency division multiplexing; OFDM) 시스템의 채널 추정 기법을 제안하였다. 두 개의 시퀀스를 하나의 쌍으로 Golay 시퀀스 쌍은 이상적인 비주기 자기상관 특성을 가지며, 다중경로 채널 환경에서 직교성이 유지되는 강인한 특성을 가진다. 이러한 Golay 시퀀스 기반의 시간영역 채널 추정 기법은 시면 채널에서의 시간동기에 용이하며, Golay 시퀀스의 이상적인 자기상관 특성으로 인하여 채널 추정 시 수신단의 복잡도를 낮출 수 있는 장점을 갖는다. 그리고 OFDM 기반 시스템에서의 PAPR(peak to average power ration) 문제를 해결할 수 있다. 그러므로 본 논문에서는 Golay 시퀀스의 특성을 이용한 전송 구조 제안 및 채널 추정 성능을 시뮬레이션을 통하여 분석하였다.

• Journal of the Institute of Convergence Signal Processing
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• v.9 no.4
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• pp.304-312
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• 2008

Orthogonal codes like Walsh and Golay codes may have large correlation value when they are not synchronized, hence they are seldom used in asynchronous CDMA systems. Wysocki[1] showed that by multiplying the original Walsh-Hadamard matrix with an orthogonal transformation matrix the resultant matrix sustains orthogonality between row vectors and their cross-correlation can be reduced. Soberly and Wysocki[2] proposed similar scheme on Golay codes. This implies that using the proper orthogonal transformation cross-correlation of Walsh and Golay codes can be reduced, and the transformed codes can be used for user separation in the CDAM reverse link. In this paper we discuss cross-correlation related parameters which affect the performance of an asynchronous CDMA link, and we investigate the correlation properties of the transformed codes. When we designed orthogonal transformation matrices for Walsh and Golay codes, we minimized the maximum value of aperiodic cross-correlation of the codes ($ACC_{max}$) or the mean square value of the aperiodic cross-correlation($R_{cc}$) with preserving the orthogonality of the modified codes. We also evaluate the asynchronous CDMA system that uses the transformed Walsh and Golay codes.

• Korean Journal of Mathematics
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• v.10 no.1
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• pp.89-95
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• 2002

We present a simple but new way of decoding the binary Golay code.

• Journal of the Korea Society of Computer and Information
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• v.28 no.1
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• pp.17-26
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• 2023

In this paper, we propose a several smoothing techniques are compared and applied to increase the application of the LSTM-based learning model and its effectiveness. The applied smoothing technique is Savitky-Golay, exponential smoothing, and weighted moving average. Through this study, the LSTM algorithm with the Savitky-Golay filter applied in the preprocessing process showed significant best results in prediction performance than the result value shown when applying the LSTM model to Bitcoin data. To confirm the predictive performance results, the learning loss rate and verification loss rate according to the Savitzky-Golay LSTM model were compared with the case of LSTM used to remove complex factors from Bitcoin price prediction, and experimented with an average value of 20 times to increase its reliability. As a result, values of (3.0556, 0.00005) and (1.4659, 0.00002) could be obtained. As a result, since crypto-currencies such as Bitcoin have more volatility than stocks, noise was removed by applying the Savitzky-Golay in the data preprocessing process, and the data after preprocessing were obtained the most-significant to increase the Bitcoin prediction rate through LSTM neural network learning.

• Journal of the Korean Society for Nondestructive Testing
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• v.14 no.3
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• pp.185-193
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• 1994

Conventional ultrasonic flaw detection system uses a large amplitude narrow pulse to excite a transducer. However, these systems are limited in pulse energy. An excessively large amplitude causes a dielectric breakage of the transducer, and an excessively long pulse causes decrease of the resolution. Using the pulse compression, a long pulse of pseudorandom signal can be used without sacrificing resolution by signal correlation. In the present work, the pulse compression technique was implemented into an ultrasonic system. Golay code was used as a pseudorandom signal in this system, since pair sum of autocorrelations has no sidelobe. The equivalent input pulse of the Golay code was derived to analyze the pulse compression system. Throughout the experiment, the pulse compression technique has demonstrated for its improved SNR(signal to noise ratio) by reducing the system's white noise. And the experimental data also indicated that the SNR enhancement was propotional to the square root of the code length used. The technique seems to perform particularly well with highly energy-absorbent materials such as polymers, plastics and rubbers.

• Journal of the Korean Mathematical Society
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• v.39 no.2
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• pp.289-317
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• 2002

We associate binary codes to polynomials over fields of characteristic two and show that the binary Golay codes are associated to the Mathieu group polynomials in characteristics two. We give two more polynomials whose Galois group in $M_{12}$ but different self-orthogonal binary codes are associated. Also, we find a family of $M_{24}$-coverings which includes previous ones.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.6 no.1
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• pp.53-60
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• 1996

오증 요소로부터 오류위치다항식의 계수를 계산함으로서 (23,12) Golay 부호를 복호할 수 있는 대수적 복호법이 최근 증명되었다. GF(2)상에서의 3중 오류정정 BCH부호의 복호법을 이 부호에 완벽하게 적용하여 해석하는 것을 소개한다. 그리고 GF(2)에 대한 최적의 정규기저를 구하여 이를 유한체 연산에 적용하며 단계별로 복호 회로의 구성을 제시한다. 이는 기존의 복호기보다 논리회로적으로 간단하며, 복호된 정보를 얻기까지 35번의 치환이 필요하다.

• Journal of Multimedia Information System
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• v.9 no.1
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• pp.69-72
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• 2022

Extraction of a salient chromagram is utmost important for cover song identification. Cover song refers to a live performance, a remix, or a new recording of a previously recorded track. This paper utilizes the Savitzky-Golay filters in chromagram extraction for suppressing timber-related components of a music signal, which is not preserved while generating cover songs. By removing the timber-related components, the discriminative tonal components, which are conducive for cover song identification, are emphasized in chromagram. Experiments on cover song identification over two datasets show that the Savitzky-Golay filters are more effective in reducing timber effects in chromagram than other types of filters.

• Journal of Biomedical Engineering Research
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• v.24 no.3
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• pp.217-231
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• 2003

Coded excitation with complementary Golay sequences is an effective means to increase the SNR and penetration of ultrasound imaging. in which the two complementary binary codes are transmitted successively along each scan-line, reducing the imaging frame rate by half. This method suffers from low frame rate particularly when multiple transmit focusing is employed, since the frame rate will be further reduced in proportion to the number of focal zones. In this paper. a new ultrasound imaging technique based on simultaneous multiple transmit focusing using modified orthogonal Golay codes is proposed to improve lateral resolution with no accompanying decrease in the imaging frame rate, in which a pair of orthogonal Golay codes focused at two different focal depths are transmitted simultaneously. On receive, these modified orthogonal Golay codes are separately compressed into two short pulses and individually focused. These two focused beams are combined to form a frame of image with improved lateral resolution. The Golay codes were modified to improve the transmit power efficiency (TPE) for practical imaging. Computer simulations and experimental results show that the proposed method improves significantly the lateral resolution and penetration of ultrasound imaging compared with the conventional method.