FIR and IIR techniques for bandlimited extrapolation of sequences

Abstract

The problem of extrapolating a finite length sequence into a band-limited sequence has been formulated in the past in terms of pseudoinverse techniques. Iterative and non-iterative algorithms for the extrapolation have also been proposed. All these algorithms, however, attempt to produce an ideally band-limited answer, which, in reality, is infinitely long and noncausal, and cannot be generated in finite time. In this paper the problem is converted to one of finding a finite length input to a practical FIR or IIR filter in such a way that a segment of the output matches the signal to be extrapolated. The fact that the generated signal is the output of a filter ensures that it is bandlimited to an extent determined largely by the filter quality. The advantage of this viewpoint is that we can exploit the rich literature which is available for efficient filter implementation (such as multistage and IFIR techniques, and efficient IIR techniques based on allpass building blocks).