Journal of the Institute of Electronics Engineers of Korea SP (대한전자공학회논문지SP)

The Institute of Electronics and Information Engineers (대한전자공학회)
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Analytic derivation of the finite wordlength errors in fixed-point implementation of SDFT

SDFT 고정소수점 연산에 대한 유한 비트 오차영향 해석

  • Chang, Tae-Gyu (School of Electrical Engineering, Chung-Ang University) ;
  • Kim, Jae-Hwa (School of Electrical Engineering, Chung-Ang University)
  • 장태규 (중앙대학교 전자전기공학부) ;
  • 김재화 (중앙대학교 전자전기공학부)
  • Published : 2000.07.25
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Abstract

Finite wordlength effect of the recursive implementation of SDFT(sliding-DFT) is analytically derived in this paper. Representation errors of the twiddle coefficients and the data registers are the two major causes of the spectral errors in the recursive implementation. The noise-to-signal ratio is analytically derived in terms of the coefficients wordlength, the data registers wordlength, and the DFT's block-length used in the computation Error dynamic equation is obtained from the recursive DFT and the probabilistic models for the coefficients error and the round-off error are introduced for the NSR derivation, The result of the NSR derivation is verified with the simulation data.

본 논문에서는 SDFT(sliding discrete-Fourier transform)을 순환식(recursive)으로 구현할 때 유한 비트 고정소수점 계산하여 발생하는 오차의 영향을 해석적으로 구하는 방법을 제시하고 이의 유도 과정을 기술하였다. 유한 비트 오차는 계수의 양자화 때문에 발생하는 계수오차와, 곱셈연산 후 반올림되는 유효자리 때문에 발생하는 반올림오차로 구성된다. 각각의 오차는 주파수 스펙트럼 추정오차를 야기 시키며, 이 스펙트럼 오차의 전력과 실제 스펙트럼의 전력 비(noise-to-signal power ratio NSR)를 진동계수를 표현하는 비트 수, DFT 값을 표현하는 비트 수, 그리고 DFT 구간길이에 대한 식으로 유도하였다. 유도과정은 SDFT 순환식(recursive equation)을 통해 유도한 오차방정식(error-dynamic equation)과 계수오차 및 반올림오차의 확률분포특성에 근거하였다. 해석적으로 유도한 NSR 결과를 시뮬레이션 실험을 통해 얻은 결과와 비교하여 타당성을 확인하였다.

Keywords

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