Reduction of the power consumed by highperformance filters is the ultimate objective of all digital signal processing (DSP) practitioners. However, low power consumption and high-performance are often contradictory design goals. This paper uses a technique involves extending the applicability of the Noble identity in commuting downsamplers with 'sparse transfer functions,' which can be expressed as a function of ZM, where M = 2,3,4,.... More precisely, the transfer functions are relaxed so that they can be expressed as a function of Z1. This commuting relation, termed the generalized Noble identity (GNI), substantially reduces the power consumption of a filter. The GNI is applied to elaborately designed lowpass filters (LPFs) and achieves a favorable compromise between contradictory design goals.