A method and apparatus for prediction in a speech-coding system is provided herein. The method of a 1st order long-term predictor (LTP) filter, using a sub-sample resolution delay, is extended to a multi-tap LTP filter, or, viewed from another vantage point, the conventional integer-sample resolution multi-tap LTP filter is extended to use sub-sample resolution delay. This novel formulation of a multi-tap LTP filter offers a number of advantages over the prior-art LTP filter configurations. Particularly, defining the lag with sub-sample resolution makes it possible to explicitly model the delay values that have a fractional component, within the limits of resolution of the over-sampling factor used by the interpolation filter. The coefficients of such a multi-tap LTP filter are thus largely freed from modeling the effect of delays that have a fractional component. Consequently their main function is to maximize the prediction gain of the LTP filter via modeling the degree of periodicity that is present and by imposing spectral shaping.