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 will lead to inexact pole-zero cancellation. This necessitates a thorough study of finite word effects in these filters. In this correspondence, we present theoretical results on roundoff and coefficient quantization errors in these filters. We show that (to maintain the same error at the filter output) the word length needs to be at most increased by log2 log2 2M b for a scattered look-ahead decomposed filter (where M is the level of loop pipelining). This worst case corresponds to the case when all poles are close to zero. For M between 2 and 8, the word length needs to be increased only by 1 or 2 b. Contrary to common belief, we conclude that pole-zero canceling scattered look-ahead pipelined recursive filters have good finite word error properties.
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