Improved oscillator-based source modeling methods for estimating model parameters, for evaluating model quality for restoring the input from the model parameters, and for improving performance over known in the art methods are disclosed. An application of these innovations to speech coding is described. The improved oscillator model is derived from the information contained in the current input signal as well as from some form of data history, often the restored versions of the earlier processed data. Operations can be performed in real time, and compression can be achieved at a user-specified level of performance and, in some cases, without information loss. The new model can be combined with methods in the existing art in order to complement the properties of these methods, to improve overall performance. The present invention is effective for very low bit-rate coding/compression and decoding/decompression of digital signals, including digitized speech and audio signals.