`Perfect reconstruction´ time-scaling filterbanks

A filterbank-based method of time-scale modification is analyzed for elemental signals including clicks, sines, and AM-FM sines. It is shown that with the use of some basic properties of linear systems, as well as FM-to-AM filter transduction, “perfect reconstruction” time-scaling filterbanks can be constructed for these elemental signal classes under certain conditions on the filterbank. Conditions for perfect reconstruction time-scaling are shown analytically for the uniform filterbank case, while empirically for the nonuniform constant-Q (gammatone) case. Extension of perfect reconstruction to multi-components signals is shown to require both filterbank and signal-dependent conditions and indicates the need for a more complete theory of “perfect reconstruction” time-scaling filterbanks