Current LPC synthesizers have a problem when the driving function is periodic; an output synthesized from LPC analysis has spectral properties which are not identical to those of the analyzed input. These distortions prevent a vocoder from being truly transparent for many voiced sounds. An iterative method, which modifies the conventional LPC coefficients such that the autocorrelation function of the output becomes identical to that of the input, is presented. A methodology for keeping the increased computational cost to a minimum is also to be discussed.

This paper presents the theory for a rapidly converging adaptive linear digital filter. The filter weights are updated for every new input sample. This way the filter is optimal (in the minimum mean square error sense) for all past data up to the present, at all instants of time. This adaptive filter has thus the fastest possible rate of convergence. Such an adaptive filter, which is highly desirable for use in dynamical systems, e.g., digital equalizers, used to require on the order of N2 multiplications for an N-tap filter at each instant of time. Recent “fast” algorithms have reduced this number to like 10 N. One of these algorithms has the lattice form, and is shown here to have some interesting properties: It decorrelates the input data to a new set of orthogonal components using an adaptive, Gram-Schmidt like, transformation. Unlike other fast algorithms of the Kalman form, the filter length can be changed at any time with no need to restart or modify previous results. It is conjectured that these properties will make it less sensitive to digital quantization errors in finite word-length implementation.

The set of PARCOR parameters of an autoregressive process is found sequentially and iteratively. It is proven that the equations are decoupled to the first order for small changes in the parameter values. Sequential calculation of the parameters is therefore possible. Using the sign Decorrelator the number of calculations is drastically reduced with little degradation of the performance. Simulation results are given for a specific example. The simulation shows that the system converges and the predietion residual is small and comparable to the excitation of the autoregressive process.

An algorithm for computing the prediction coefficient for a time series is discussed. The algorithm uses stochastic approximation, but with absolute values rather than square magnitudes. The number of computations is reduced drastically, while the added error is relatively small.