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Signal restoration for linear systems with weighted inputs. Singular value analysis for two cases of low-pass filtering

The a priori knowledge that the input of a linear system is weighted by some kind of profile function can be exploited for restoring the output signal by means of the singular value technique. The authors determine the analytic expression of the singular system for two typical cases in which the system behaves like a low-pass filter and the profile function has the same form as the impulse response of the filter. The analysis leads us to predict the performance of the restoration process in the presence of noise. It is shown that under suitable conditions the resolution of the restored signal can be twice that of the unrestored output.