A simple commutativity condition for block decimators and expanders

Didier Pinchon (1) , Pierre Siohan (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 Orange Labs, 35512 Cesson-Sévigné, France

Commutativity rules are essential for building multirate signal processing systems. In this short and self-contained paper, we focus on theinterchangeability of block decimators and expanders. We, formally, prove that commutativity between these two operators is possible if and only if the data blocks are of an equal length corresponding to the greatest common divisor of the integer decimation and expansion factors.

Mots clés: Expansion; Decimation; Commutativity; Block sampling

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Didier Pinchon, Pierre Siohan. A simple commutativity condition for block decimators and expanders. Digital Signal Processing, 2014, 35, p.124-128. ⟨10.1016/j.dsp.2014.08.010⟩. ⟨hal-00851242v2⟩