Signal analysis based on a redundant expansion of the signal

The wide scope of patterns embedded in biological signals and the precision of their characterization motivates decompositions over large and redundant dictionaries of waveforms. Moreover, fast algorithms and reasonable CPU and RAM requirements make digital implementations attractive. In the case of complex biomedical signals the basis is a minimal set of vectors that is not rich enough to reveal the wide scope of patterns embedded in the signal. In the presented paper a decomposition in which time-frequency information is part of the information about the signal in the transform domain is considered. A multiple decomposition of a discrete time signal into different and mutually related unitary bases of the given vector space C^M is discussed and a possible fast computation of the redundant decomposition for signal detection/classification applications is outlined