A waveform-matched waveform interpolation (WMWI) technique is presented which offers improved signal analysis over standard WI coders and, in the unquantised case, perfect reconstruction. In WMWI, an accurate representation of speech evolution is formed by extracting consecutive pitch periods of a time-warped, constant pitch residual. A pitch track optimisation technique is described which ensures that the critically sampled pitch periods can be effectively decomposed into a slowly evolving and rapidly evolving waveform, allowing efficient quantisation.