Abstract A generalisation of the linear prediction for fractional steps is reviewed, widening well-known concepts and results. This prediction is used to derive a causal interpolation algorithm. A reconstruction algorithm for the situation where averages are observed is also presented. 1 INTRODUCTION The relevance of linear prediction in modern Signal Processing is a well-established fact. The one-step prediction has several practical applications, namely in Telecommunications and Speech Processing, for example, sampling rate conversion, equalization, and speech coding and recognition. The d-step prediction (d positive integer) is useful in Geophysical Signal Processing. The basic idea underlying the proposed algorithm is to develop a system capable of linear predicting the signal over instant times, in between the current ones, without converting the signal to the continuous-time domain. The new samples would fit in between the original samples. The algorithm uses the Maximum Entropy Method to obtain the spectrum of the original integer sampled signal. Using this spectrum estimate, it is possible to derive the coefficients of the fractional predictor. The simulations present in this work will show that, from the fractional linear prediction method, it is possible to perform the multirate conversion either for a higher or lower rate. In section 2, a fractional delay and lead concepts review takes place. These concepts are the base for the theory of fractional linear prediction that is described in section 3. An algorithm is proposed, for the computation of the optimum predictor coefficients. In section 4, some examples to illustrate the behaviour of the algorithm, are presented. At last some conclusions are outlined. 2 FRACTIONAL DELAY AND LEAD We will base our algorithm on the theory of the fractional linear systems [1]. The starting point is the definition of fractional delay and lead [1]: x n+α = [ ] [ ] ∑ ∞ + -∞ = - + - + m m m n m n x α π α π ) ( sin (2.1) where α∈R and n ∈Z. This equation expresses a relation between two signals x n and y m = x n+α defined in the sets Z and { m: m=n+ α, n ∈Z and α∈R}, respectively. So, we are relating two signals defined over two different time grids, obtained, one from the other by a fractional translation. The NEW RESULTS ON FRACTIONAL LINEAR PREDICTION Manuel D. Ortigueira Carlos J. C. Matos Instituto Superior Técnico/INESC and UNINOVA Campus da FCT da UNL, Quinta da Torre, 2825 - 114 Monte da Caparica, Portugal, Mail: mdo@uninova.pt UNINOVA and Escola Superior de Tecnologia, Instituto Politécnico de Setúbal, Setúbal, Portugal, Mail: cmatos@est.ips.pt