A band-limited signal extrapolation algorithm using waveform synthesis digital filter

An extrapolation algorithm for discrete bandlimited signals is proposed. The bandlimited condition is satisfied by using an ideal bandlimited signal as an excited signal. A waveform synthesis digital filter is used to extrapolate fractionally observed data, using the bandlimited excited signal. Therefore, the proposed method reduces the extrapolation problem to a digital filter estimation problem. Digital filter coefficients are obtained by solving linear equations, which are formulated to minimize the mean-square error between a part of the extrapolated signal and the fractionally observed data. The modified Gram-Schmidt (MGS) procedure is applied to finding the least-square solution of the filter coefficients, due to its superior numerical stability. The recursive version of the MGS procedure is suited to real-time hardware implementation. The proposed algorithm is shown to have good performance in extrapolating the fractional data, observed in a single as well as multiple time windows. This concept is applicable not only to the signal extrapolation but also to the spectral estimation