Certain changes in pulse shape do not affect the resolution capability of a sonar system. These changes can be expressed as mathematical transformations that leave invariant important properties of the wide‐band ambiguity function. Such transformations provide a large number of signal and filter functions, all of which satisfy a given range‐Doppler resolution requirement. The sonar designer can then choose the signal and filter that best satisfy other system constraints (e.g., ease of signal generation and filter synthesis, clutter suppression capability, and peak power).