一种定点DCT运算的最大误差估算方法

APPROACH TO ESTIMATE THE MAXIMUM ERRORS USING FIXED POINT DCT

DCT运算广泛地应用在数字信号处理领域 .某些情况下 ,必须用定点运算来完成 DCT运算 ,此时会遇到两个问题 :一个是对某种快速 DCT算法 ,如何从精度和溢出两方面综合考虑 ,选择一个最佳的预定标方案 ,达到在不产生溢出条件下 ,尽量降低结果误差 ;另一个是如何从多个快速 DCT算法中选择出最合适的一个 .本文结合快速 DCT运算中乘法运算的某些特点 ,在单个定点乘法误差模型基础上 ,从控制运算结果的最大误差角度 ,就分别保留乘法结果的低半部分和高半部分两种不同的定点乘法结果处理方法 ,对定点 DCT运算的最大误差情况进行分析 ,以指导前述两个问题的解决 .

DCT (Discrete Cosine Transform) is extensively used in the field of digital signal process, especially for image process. In some cases, fixed point computation has to be resorted to in DCT process, during which, two problems are often encountered. One is how to pre determine the best scaling scheme for the fast DCT algorithm that used based on the consideration of both precision and overflow so as to minimize the resulted errors without causing overflow. The other is how to choose the best alternative among several feasible fast DCT algorithms. It is impractical to derive the probability distribution function of the errors that occur in the fixed point fast DCT, because the derivation concerns the specific computation process. In this paper, from the point of error control, potential maximum errors are analyzed and calculated in the execution of two different fixed point multiplication methods. One is to retain the low half portion, the other is to retain the high half portion. Analysis is based on an error model of isolated fixed point multiplication and the features of fast DCT algorithm, of which one of the multiplier is constant. Conclusions thus obtained are applicable to data scaling and precision allocation, and are useful in the determination of the best alternative among several satisfactory fast speed DCT algorithms.