Discrete convolution by means of forward and backward modeling

An approach to discrete convolution is presented which obviates the zero assumption. The method is structurally similar to the method of J.P. Burg (Stanford Univ., May 1975), which estimates the autocorrelation coefficients of a series in a manner which does not require a predefinition of the behavior of the signal outside of the known interval. The basic principle of the present approach is that each term of the convolution is recursively determined from previous terms in a manner consistent with the optimal modeling of one signal in terms of the other. The recursion uses forward and backward modeling together with the algorithm of M. Morf et al. (ibid., vol.ASSP-25, p.429-43, Oct. 1977) for computation of the prediction error filter. The method is illustrated by application to the computation of the analytic signal and its derivative