Evaluation of Efficient Compression Properties of the Complete Oscillator Method, Part 1: Canonical Signals

The paper describes a highly efficient coding scheme based on the Complete Oscillator Method (COM). The COM has a number of powerful theoretical properties which enable it to provide very compact models for a wide range of deterministic signals. Several of these properties are studied here. The theoretical COM is shown to model and synthesize exactly all types of stationary signals, irrespective of the dimension of the system that generated it, using only one model parameter. The exact representation property independent of data dimension extends to certain amplitude-variable signals as well. The COM also reconstructs with high fidelity a number of other classes of nonstationary signals for which the exact representation cannot be guaranteed. One such class encompasses frequency-modulated signals presented here. The theoretical results obtained under idealized conditions are related to practical discrete implementations, where the COM is shown to be robust to deviations from the ideal conditions. In non-ideal conditions, increasing the order of the COM to two terms, four parameters total, delivers near exact models in many cases. The compact representation property of the COM is illustrated on several canonical waveforms, which provide representative examples for each class of signal studied here.