• The Transactions of The Korean Institute of Electrical Engineers
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• v.56 no.4
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• pp.790-794
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• 2007

This paper presents a new index mapping method for DFT (Discrete Fourier Transform) and its application to multidimensional DFT. Unlike conventional index mapping methods such as DIT (Decimation in Time) or DIF (Decimation in Frequency) algorithms, the proposed method is based on two levels of decomposition and it can be very efficiently used for implementing multidimensional DFT as well as 1-dimensional DFT. The proposed pipelined architecture for multidimensional DFT is very flexible so that it can lead to the best tradeoff between performance and hardware requirements. Also, it can be easily extended to higher dimensional DFTs since the number of CEs (Computational Elements) and DCs (Delay Commutators) increase only linearly with the dimension. Various implementation options based on different radices and different pipelining depths will be presented.

• Journal of Korea Multimedia Society
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• v.7 no.11
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• pp.1505-1514
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• 2004

Sequence matching in time-series databases is an operation that finds the data sequences whose changing patterns are similar to that of a query sequence. Typically, sequence matching hires a multi-dimensional index for its efficient processing. In order to alleviate the dimensionality curse problem of the multi-dimensional index in high-dimensional cases, the previous methods for sequence matching apply the Discrete Fourier Transform(DFT) to data sequences, and take only the first two or three DFT coefficients as organizing attributes of the multi-dimensional index. This paper first points out the problems in such simple methods taking the firs two or three coefficients, and proposes a novel solution to construct the optimal multi -dimensional index. The proposed method analyzes the characteristics of a target database, and identifies the organizing attributes having the best discrimination power based on the analysis. It also determines the optimal number of organizing attributes for efficient sequence matching by using a cost model. To show the effectiveness of the proposed method, we perform a series of experiments. The results show that the Proposed method outperforms the previous ones significantly.

• Journal of KIISE:Databases
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• v.33 no.7
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• pp.693-707
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• 2006

To improve performance using a multidimensional index in similar sequence matching, we transform a high-dimensional sequence to a low-dimensional sequence, and then construct a low-dimensional MBR that contains multiple transformed sequences. In this paper we propose a formal method that transforms a high-dimensional MBR itself to a low-dimensional MBR, and show that this method significantly reduces the number of lower-dimensional transformations. To achieve this goal, we first formally define the new notion of MBR-safe. We say that a transform is MBR-safe if a low-dimensional MBR to which a high-dimensional MBR is transformed by the transform contains every individual low-dimensional sequence to which a high-dimensional sequence is transformed. We then propose two MBR-safe transforms based on DFT and DCT, the most representative lower-dimensional transformations. For this, we prove the traditional DFT and DCT are not MBR-safe, and define new transforms, called mbrDFT and mbrDCT, by extending DFT and DCT, respectively. We also formally prove these mbrDFT and mbrDCT are MBR-safe. Moreover, we show that mbrDFT(or mbrDCT) is optimal among the DFT-based(or DCT-based) MBR-safe transforms that directly convert a high-dimensional MBR itself into a low-dimensional MBR. Analytical and experimental results show that the proposed mbrDFT and mbrDCT reduce the number of lower-dimensional transformations drastically, and improve performance significantly compared with the $na\"{\i}ve$ transforms. These results indicate that our MBR- safe transforms provides a useful framework for a variety of applications that require the lower-dimensional transformation of high-dimensional MBRs.