An improved mixed oscillator-and-external excitation model and methods for estimating the model parameters, for evaluating model quality, and for combining it with known in the art methods are disclosed. The improvement over existing oscillators allows the model to receive, as an input, all except the most recent point in the acquired data. Model stability is achieved through a process which includes restoring unavailable to the decoder data from the optimal model parameters and by using metrics to select a stable restored model output. The present invention is effective for very low bit-rate coding/compression and decoding/decompression of digital signals, including digitized speech, audio, and image data, and for analysis, detection, and classification of signals. Operations can be performed in real time, and parameterization can be achieved at a user-specified level of compression.