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Error spectrum shaping is used in digital filters to reduce roundoff noise. There are several other filter structures which can also reduce roundoff noise. Are these methods of noise reduction in any way related? This paper shows that optimal error spectrum shaping is a method of increasing the word length of accumulators and internal variables, i.e., it is, in its optimum form, extended precision arithmetic. Furthermore there is no hardware advantage to be gained with optimum ESS as compared to traditional methods of implementing extended precision arithmetic.