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Starting with a prescribed configuration realizing the denominator of a given transfer function, this paper presents a systematic procedure for obtaining the noise-optimal realization, where the basic configuration is kept invariant. This procedure, in turn, is based on the identification of the maximal independent node sets of the given configuration. Thus a major objective of this paper is to develop effective algorithms for determining the independent sets of nodes and maximal independent sets of nodes of any arbitrary digital filter configuration. The entire low-noise design method is illustrated by means of an example.