The high resolution concept : its reality and its limits

摘要

Since a few years, high resolution methods appeared in the field of signal processing . They allow to separate twoudsignais in cases where classical processing fails . In spectral analysis, they distinguish the sinusoïdal componentsudseparated by less than the Fourier transform resolution . A computation of theoretical and practical limits is realized .udFor this, the frequency estimation error for two sinuoïds is first derived front the Cramer-Rao bounds . Front theudexact formula thus obtained, the influence of différent parameters is analyzed (phase différence, signal to noiseudratio) . On the basis of this estimation error, an intuitive criteria is introduced and used to derive the theoreticaludlimits of high resolution . Then, these results are compared with those obtained by three spectral analysis methods:udthe first two ones are based on an autoregressive modelisation, the last one on the filter matched to two sinusoïds .udFinally, the computations are generalized to any kind of signal .