전자공학회논문지CI (Journal of the Institute of Electronics Engineers of Korea CI)

대한전자공학회 (The Institute of Electronics and Information Engineers)
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복소연산이 없는 Polynomial 변환을 이용한 2차원 고속 DCT

Two dimensional Fast DCT using Polynomial Transform without Complex Computations

  • Park, Hwan-Serk (Myongji University, Electronics, Information & Communication Engineering) ;
  • Kim, Won-Ha (Myongji University, Electronics, Information & Communication Engineering)
  • 발행 : 2003.11.01
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초록

본 논문은 2차원 Discrete Cosine Transform (2D-DCT)의 계산을 새로운 Polynomial 변환을 통하여 1차원 DCT의 합으로 변환하여 계산하는 알고리즘을 개발한다. 기존의 2차원 계산방법인 row-column 으로는 N×M 크기의 2D-DCT에서 3/2NMlog₂(NM)-2NM＋N＋M의 합과 1/2NMlog₂(NM)의 곱셈이 필요한데 비하여 본 논문에서 제시한 알고리즘은 3/2NMlog₂M＋NMlog₂N-M-N/2＋2의 합과 1/2NMlog₂M의 곱셈 수를 필요로 한다. 또한 기존의 polynomial 변환에 의한 2D DCT는 Euler 공식을 적용하였기 때문에 복소 연산이 필요하지만 본 논문에서 제시한 polynomial 변환은 DCT의 modular 규칙을 이용하여 2D DCT를 ID DCT의 합으로 직접 변환하므로 복소 연산이 필요하지 않다.

This paper develops a novel algorithm of computing 2 Dimensional Discrete Cosine Transform (2D-DCT) via Polynomial Transform (PT) converting 2D-DCT to the sum of 1D-DCTs. In computing N${\times}$M size 2D-DCT, the conventional row-column algorithm needs 3/2NMlog$_2$(NM)-2NM＋N＋M additions and 1/2NMlog$_2$(NM) additions and 1/2NMlog$_2$(NM) multiplications, while the proposed algorithm needs 3/2NMlog$_2$M＋NMlog$_2$N-M-N/2＋2 additions and 1/2NMlog$_2$M multiplications The previous polynomial transform needs complex operations because it applies the Euler equation to DCT. Since the suggested algorithm exploits the modular regularity embedded in DCT and directly decomposes 2D DCT into the sum of ID DCTs, the suggested algorithm does not require any complex operations.

키워드

참고문헌

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