Enhancement of the time resolution of limited-band signals

An expression is derived for the spectral power density of signals minimizing the normalized time-resolution function when the variance of the time estimate and the sidelobe level are prescribed. It is shown that as the variance of the time estimate increases the sidelobe level of the signal at the output of the matched filter decreases to -40 dB. The synthesized signals assure, for the prescribed sidelobe level, lower values of the normalized time-resolution function and lower values of the variance of the time estimate than signals whose spectral power density has the form k + (1 - k) cos-squared z.