Adaptive interpolation of discrete-time signals that can be modeled as autoregressive processes

This paper presents an adaptive algorithm for the restoration of lost sample values in discrete-time signals that can locally be are that the positions of the unknown samples should be known and that they should be embedded in a sufficiently large neighborhood of known samples. The estimates of the unknown samples are obtained by minimizing the sum of squares of the residual errors that involve estimates of the autoregressive parameters. A statistical analysis shows that, for a burst of lost samples, the expected quadratic interpolation error per sample converges to the signal variance when the burst length tends to infinity. The method is in fact the first step of an iterative algorithm, in which in each iteration step the current estimates of the missing samples are used to compute the new estimates. Furthermore, the feasibility of implementation in hardware for real-time use is established. The method has been tested on artificially generated auto-regressive processes as well as on digitized music and speech signals. described by means of autoregressive processes. The only restrictions sk t T I. INTRODUCTION HIS paper treats the problem of restoring (or interpolating) unknown or lost sample values in a discrete-time signal. An algorithm is presented that is capable of restoring satisfactorily unknown samples with known positions occurring in bursts and more general patterns. Examples of both cases are shown in Fig. 1. To restore the unknown samples, the algorithm uses the information contained in the known neighboring samples. Until rather recently, the problem of estimating unknown sample values in discrete-time signals in real time could only be solved by relatively simple, nonadaptive methods, such as Lagrange-type curve fitting. These methods are not well suited for signals primarily containing harmonic components, especially not when the number of samples in the periods of the harmonic components is less than the number of unknown samples. For instance , linear interpolation gives already audible interpolation errors for bursts in digital audio signals of length 5. Because of the progress made in the field of chip design , one can now contemplate more complicated real-time restoration methods that may also involve some sig