High sample rate recursive filtering can be achieved by transforming the original filters to higher-order filters using the scattered look-ahead computation technique (which relies upon pole-zero cancellation). Finite word-length implementation of these filters leads to inexact pole-zero cancellation. This necessitates a thorough study of finite word effects in these filters. Theoretical results on roundoff and coefficient quantization errors in these filters are presented. It is shown that to maintain the same error at the filter output, the word length needs to be at most increased by log/sub 2/ log/sub 2/ 2M bit for a scattered look-ahead decomposed filter (where as M is the level of loop pipelining). This worst case corresponds to the case when all poles are close to zero. For M between two and eight, the word length needs to be increased only by 1 or 2 bit. Contrary to common beliefs, it is concluded that pole-zero canceling scattered look-ahead pipelined recursive filters have good finite word error properties.
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机译:通过使用分散的超前计算技术(依赖零极点消除)将原始滤波器转换为高阶滤波器,可以实现高采样率递归滤波。这些滤波器的有限字长实现导致不精确的零极点消除。这就需要对这些滤波器中的有限词效应进行深入研究。给出了这些滤波器中舍入和系数量化误差的理论结果。结果表明,要在滤波器输出端保持相同的误差,对于散布的超前分解滤波器,字长最多需要增加log / sub 2 / log / sub 2 / 2M位(其中M是循环流水线级别)。最坏的情况对应于所有极点都接近零的情况。对于介于2和8之间的M,字长仅需增加1或2位。与普遍的看法相反,得出的结论是零极点消除的分散前瞻流水线式递归滤波器具有良好的有限字错误特性。
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