Design of the 2nd order Digital Filter with Minimum Coefficient Quatization Error

최소계수 양자화 오차를 갖는 2차 디지틀 필터의 설계

When digital filters are implemented on a computer or with spectial purpose hardware, they unavoidably suffer from errors due to finite wordlength implementation. These errors are classified into coefficient quantiz ation error and roundoff error. The synthesizing method for realizations with minimum coefficient quantization error and minimum roundoff error has been studied. In this paper, it is shown that there is an equivalent transform relation between realizations with minimum coefficient quatization error and minimum roundoff error. To show tha validity of this equivalent transform, we derived the 2nd order digital filter with minimum coefficient quantization error from the 2nd order digital filter with minimum roundoff error and proved the efficiency of realization with minimum coefficient quantization error by simulation.

디지틀 필터를 전용 하드웨어나 범용 계산기에 의해서 實現할 때 有限 語長 實現에 기인해서 量子化 誤差(演算, 誤差, 係數 量子化 誤差)가 필연적으로 발생하며, 또한 이러한 量子化 誤差의 最小化를 위한 等價 變換 行列이 연구되었다. 본 논문에서는 演算 誤差 最小 實現과 係數 量子化 誤差 最小 實現과의 상호 등가 변환할 수 있는 等價 變換行列을 유도하고 유도된 等價 變換 行列의 유효성을 나타내기 위해서 演算 誤差 最小型 2차 디지틀 필터로부터 係數 量子化 誤差 最小型 2차 디지틀 필터를 설계하고 시뮬레이션하였다.