A sonar system that includes a new comb-like waveform constructed by modulating the tines of a comb spectrum according to a set of Hermite functions defining a Hermite Function Space (HFS), and a processing method that reduces the sidelobes of the ambiguity function associated with the normally-processed HFS comb waveform. Noise-limited performance remains high, because the waveform is designed to be power-efficient; range ambiguity is superior to the highly-rated sinusoidal frequency-modulation (SFM) waveform; and reverberation-limited performance is equal to or better than that offered by any other waveform designed for this purpose. The full Doppler sensitivity normally associated with pulsed CW can be realized by the application to HFS signals of the constrained, regularized deconvolution method of this invention. The deconvolutionally-processed Hermite-function comb waveform offers better reverberation-limited performance than does the triplet-pair comb waveform or any of its predecessors, while maintaining a noise-limited performance equal to the best of these.