Signal recovery by discrete approximation and a Prony-like method

摘要

We introduce an algorithm which combines ideas of Prony’s approach to recover signals from given samples with approximation methods. We solve two overdetermined systems of linear equations with linear programming methods and calculate the zeros of a suitable ‘Prony-like’ polynomial. We get the bandwidth m, the frequencies as well as the amplitudes and some other characteristics of the signal. Especially, it is reconstructed if sufficient many (at least 2m) samples are given.If we have too few samples or if they are too much noised, we get an approximation of the original noiseless signal. Even if we have sufficient many but possible erroneous samples the obtained signal interpolates at least m of them (usually the low-noised or noiseless ones) and, of course, all samples if the signal is recovered.The described method behaves well to moderate sampling errors and is resistant to outliers in the samples which can be detected, filtered off or corrected during the calculations to improve the quality of the computed signal.