Roger Pridham and collaborators William Knight and Steven Kay document a comprehensive treatment of digital signal processing for sonar in a review article titled: Digital Signal Processing for Sonar, PROCEEDINGS OF THE IEEE, VOL. 69, NO. 11, NOVEMBER 1981. The article describes sonar processing from the water to the display. Pridham, et al., describe analog to digital conversion, filtering (analog and digital), detection, classification and localization (bearing and range estimation, Kalman tracking) and human interface. Active and passive sonar examples are worked out in detail to solidify the readers knowledge of the exposition. The hardware and software implementations discussed seem dated compared with the current state of the art for sonar. However, these do not detract and actually enhance understanding of legacy sonar applications.
One standout feature is a general formula for the beamwidth of a line array versus steering angle (IIB-57). The formula is approximate but more exact than most textbooks provide. The formula is good from broadside to endfire. The effect of aperture shading can be treated as a multiplicative factor (from Harris) on this equation. The formula can be applied to a two-dimensional panel array as an approximation (via a Mills cross equivalency). Finally, the formula is usable in an estimate of array directivity versus target angle.
Pridham identifies spatial transform processing as a form of beamforming along with the time delay and phase shift methods. The article also discusses adaptive beamforming and presents it in terms of bearing response (the power output of a beam scanned past a target). Another standout is the extensive discussion of digital sampling, complex spectra and aliasing. Perhaps most interesting is the date of the review, 1981. Many low-frequency active and passive sonars were digitized by this time. Studies were performed yearly documenting the current analog to digital conversion state of the art. Today, mid and higher frequency sonars are fully digital. At some point in the future, radio frequency communications and radar will realize the full impact of digitization.