A tunable high resolution spectral estimator is disclosed as a method and apparatus for encoding and decoding signals, signal analysis and synthesis, and for performing high resolution spectral estimation. The invention is comprised of an encoder coupled with either or both of a signal synthesizer and a spectral analyzer. The encoder processes a frame of a time-based input signal by passing it through a bank of lower order filters and estimating a plurality of lower order covariances from which a plurality of filter parameters may be determined. Coupled to the encoder, through any appropriate data link or interface including telecommunication links, is one or both of a signal synthesizer and a spectral analyzer. The signal synthesizer includes a decocer for processing the covariances and a parameter transformer. The signal synthesizer includes a decoder for processing the covariances and a parameter transformer for determining filter parameters for an ARMA filter. An excitation signal is processed through the ARMA filter to reproduce, or synthesize, a representation of the input filter. The spectral analyzer also includes a decoder which processes the covariances for input to a spectral plotter to detemine the power frequency spectrum of the input signal. The invention may be used in a myriad of applications including voice identification, doppler-based radar speed estimation, time delay estimation, and others.