• The Journal of Korean Institute of Communications and Information Sciences
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• v.30 no.11C
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• pp.1060-1067
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• 2005

In this paper, we generalize the shift-invariance properties of linear time-frequency distributions to the fractional Fourier domains that interpolate between the time and frequency domains. Magnitude-wise shift invariance in arbitrary fractional Fourier domains distinguishes the short-time Fourier transform (STFT) among all linear time-frequency distributions and simplifies the interpretation of the resultant distribution. We prove that the STFT is the only linear distribution that satisfies the magnitude-wise shift-invariance property in the fractional Fourier domains.

• The Mathematical Education
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• v.48 no.2
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• pp.183-190
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• 2009

This is a following study of the preceding study, Flexibility of mind and divergent thinking in problem solving process that was performed by Choi & Do in 2005. In this paper, we discuss the relationship between ability to shift a viewpoint and insight into invariance, another major consideration in mathematical creativity, in the process of mathematical problem solving.

• Journal of the Korean Institute of Telematics and Electronics A
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• v.33A no.6
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• pp.178-188
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• 1996

In this paper, we propose a new opto-digital object recognition system which has rotation, scale, and shift invariant characteristics. The fourier power spectrum of the object image is modified to get shift invariance. The log-polar transform is used for rotation and scale invariance. And the decision of similarities is performed by nonlinear joint transform correlator (NJTC) that can control the ratio of phase and amplitude signals. Experimental verification of th eproposed optical object recognition system is presented.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.14 no.1
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• pp.77-83
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• 2014

Over-sampled discrete wavelet transformation is one way to overcome the disadvantages of the standard wavelet transform of shift invariance even though it increases the number of subband signals. Non-separable based discrete wavelet transform is efficient that it satisfies shift invariance and directional selectivity. In this paper, since efficient over-sampled wavelet transform is possible in a two-dimensional image processing, we show that the proposed method is well applied with performance improvement of digital image and noise removal.

• The Transactions of the Korea Information Processing Society
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• v.5 no.4
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• pp.959-966
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• 1998

We present fast QR factorization algorithms $m{\times}n\;(m{\geq}n)$ Toeplitz matrix. These QR factorization algortihms are determined from the shift-invariance properties of underlying matrices. The major transformation tool is a stabilized/hyperbolic Householder transformation. The algortihms require O(mn) operations, and can be easily implemented on distributed-memory multiprocessors.

• International Journal of Contents
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• v.5 no.2
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• pp.26-31
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• 2009

This paper describes a new image watermarking scheme invariant to rotation, scaling and translation (RST) attacks. For obtaining the invariance properties we propose to present an image of watermark by wedges and rings to convert its rotation to shift and then utilize the shift invariance property of the Direct Fourier Transform (DFT). But in contrast to conversional schemes based on the Fourier-Mellin transform (FMT), we do not use a log-polar mapping (LPM). As a result, our scheme preserves high quality of original image since it is not underwent to LPM For withstanding against JPEG compression, noise addition and low-pass (LP) filtering attacks a low frequency watermark is embedded into middle frequencies of the original image. Experiments with various attacks show the robustness of the proposed scheme.

• Journal of the Institute of Electronics and Information Engineers
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• v.49 no.9
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• pp.164-171
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• 2012

ESPRIT(Estimation of Signal Parameter via Rotational Invariance Techniques) estimates DOAs(directions of arrival) of the incident signals on a sensor array by exploiting the shift invariance between its two subarrays. This paper suggests an efficient DOA estimation method based on ESPRIT when coherent signals impinge on the sensor array. When applying ESPRIT, it is necessary to find a signal subspace. Though the widely known SS(spatial smoothing) method allows us to obtain a signal subspace in the presence of coherent signals, its computational complexity is very high. Recently a CV(correlation vector) based method has been presented which is computationally simple. However, the number of resolvable signals in the method is smaller than that in the SS based method when multiple coherent signal groups are present. The proposed method in this paper, which obtains a signal subspace by utilizing only part of the correlation matrix, significantly reduces the computational complexity as compared with the SS based one, while the former is resolving the same number of coherent signals as the latter,

• Journal of IKEEE
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• v.27 no.4
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• pp.624-629
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• 2023

Estimation of signal parameters via rotational invariance techniques (ESPRIT) is an algorithm that estimates the angle of a signal arriving at an array antenna using the shift invariance property of an array antenna. ESPRIT offers the good trade-off between performance and complexity. However, the ESPRIT algorithm still requires high-complexity operations such as covariance matrix and eigenvalue decomposition, so implementation with a hardware processor is essential to estimate the angle of arrival in real time. In addition, ESPRIT processors should have high performance. The performance is related to the number of antennas, and the number of antennas required for each application are different. Therefore, we proposed an ESPRIT processor that provides 2 to 8 variable antenna configurations to meet the performance and complexity requirements according to the applied field. The proposed ESPRIT processor was designed using the Verilog-HDL and implemented on a field programmable gate array (FPGA).

• Journal of Korea Society of Digital Industry and Information Management
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• v.8 no.2
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• pp.131-143
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• 2012

This paper introduces the double-density discrete wavelet transform using 3 direction separable processing method, which is a discrete wavelet transform that combines the double-density discrete wavelet transform and quincunx sampling method, each of which has its own characteristics and advantages. The double-density discrete wavelet transform is nearly shift-invariant. But there is room for improvement because not all of the wavelets are directional. That is, although the double-density DWT utilizes more wavelets, some lack a dominant spatial orientation, which prevents them from being able to isolate those directions. The dual-tree discrete wavelet transform has a more computationally efficient approach to shift invariance. Also, the dual-tree discrete wavelet transform gives much better directional selectivity when filtering multidimensional signals. But this transformation has more cost complexity Because it needs eight digital filters. Therefor, we need to hybrid transform which has the more directional selection and the lower cost complexity. A solution to this problem is a the double-density discrete wavelet transform using 3 direction separable processing method. The proposed wavelet transformation services good performance in image and video processing fields.

• Journal of Korea Society of Digital Industry and Information Management
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• v.7 no.4
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• pp.119-131
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• 2011

In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. DDWT main property is a more computationally efficient approach to shift invariance. Also, the DDWT gives much better directional selectivity when filtering multidimensional signals. The dual-tree DWT of a signal is implemented using two critically-sampled DWTs in parallel on the same data. The transform is 2-times expansive because for an N-point signal it gives 2N DWT coefficients. If the filters are designed is a specific way, then the sub-band signals of the upper DWT can be interpreted as the real part of a complex wavelet transform, and sub-band signals of the lower DWT can be interpreted as the imaginary part. The quincunx lattice is a sampling method in image processing. It treats the different directions more homogeneously than the separable two dimensional schemes. Quincunx lattice yields a non separable 2D-wavelet transform, which is also symmetric in both horizontal and vertical direction. And non-separable wavelet transformation can generate sub-images of multiple degrees rotated versions. Therefore, non-separable image processing using DDWT services good performance.