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Spectrum analysis and resolution enhancement by band limited extrapolation

Knowledge of the bandwidth of a signal allows for extrapolation over a time interval that can be many times the length of the given segment. Computer results, utilizing a version of a one-step small-matrix minimum-energy procedure, have shown that such extrapolation is feasible in the presence of noise and coarse (5-bit) quantization. It is shown here, however, that such a minimum-energy procedure cannot produce enhanced spectral resolution even in the absence of noise. By generalizing a unifying model for such procedures to include non-minimum energy bandlimited extrapolation, a new algorithm is proposed that allows for tradeoffs to be made between enhanced spectral resolution and reduced sensitivity to out-of-band noise. This algorithm may also be utilized in two dimensions to enhance the spatial resolution of an aperture-limited sensor when viewing a region of limited extent. However, resolution enhancement by bandlimited extrapolation appears to be practical only if the resolution is extremely poor to begin with.