This article deals with the fixed-point computation of the sum-of-products, necessary for the implementation of several algorithms, including linear filters. Fixed-point arithmetic implies output errors to be controlled. So, a new method is proposed to perform accurate computation of the filter and minimize the word-lengths of the operations. This is done by removing bits from operands that don't impact the final result under a given limit. Then, the final output of linear filter is guaranteed to be a faithful rounding of the real output.