Method and apparatus for signal decomposition, analysis, reconstruction and tracking

A system and method for representing quasi-periodic ("qp") waveforms, for example, representing a plurality of limited decompositions of the qp waveform. Each decomposition includes a first and second amplitude value and at least one time value. In some embodiments, each of the decompositions is phase adjusted such that the arithmetic sum of the plurality of limited decompositions reconstructs the qp waveform. Data-structure attributes are created and used to reconstruct the qp waveform. Features of the qp wave are tracked using pattern-ecognition techniques. The fundamental rate of the signal (e.g., heartbeat) can vary widely, for example by a factor of 2-3 or more from the lowest to highest frequency. To get quarter-phase representations of a component (e.g., lowest frequency "rate" component) that varies over time (by a factor of two to three) many overlapping filters use bandpass and overlap parameters that allow tracking the component's frequency version on changing quarter-phase basis.