The potential effectiveness of the detection of pulsed signals in the non-uniform sampling

We consider a non-uniform time quantization of the optimal form of the signal by shifting one of the samples in the neighborhood of the point at which the minimum eigenvalue of the covariance matrix of the noise is equal to zero. Shown, that in testing simple hypotheses, arbitrarily large value of the signal-to-noise- ratio is achieved by this shift on the output of the discrete matched filter at finite energy of the signal and noise power. We discuss some aspects of the ill conditioning of the problem and the a priori of uncertainty.