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 autoregressive processes as well as on digitized music and speech signals. described by means of autoregressive processes. The only restrictions sk t T IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING,

Abstract. We describe an algorithm for the interpolation of burst errors in discrete-time signals that can be modelled as being band-limited. The algorithm correctly restores a mutilated signal that is indeed band-limited. The behavior of the algorithm when applied to signals containing noise or out-of-band components can be analysed satisfactorily with the aid of asymptotic properties of the discrete prolate spheroidal sequences and wave functions. The effect of windowing can also be described conveniently in terms of these sequences and functions.

An interpolation method for restoring burst errors in discrete-time, band-limited signals is presented. The restoration is such that the restored signal has minimal out-of-band energy. The filter coefficients depend only on the burst length and on the size of the band to which the signal is assumed to be band-limited. The influence of additive noise and the effect of violation of the band-limitedness assumption is analysed with the aid of discrete prolate spheroidal sequences and wave functions. It is indicated for what combinations of values for noise power, burst length and bandwidth the method is still stable enough to be practicable.

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