The formulation of output autocorrelation function of a digital beamformer into an infinite series leads naturally to the introduction of “quantizer functions” of various orders as a convenient vehicle in the evaluation of beamformer performance corresponding to different input quantizer designs. For arrays operating in a Gaussian ambient noise field, the quantizer function of a general nonuniform quantizer is defined and evaluated in terms of “reduced Hermite polynomials,” which facilitate less costly machine computation via their unique recursion formulae. A rigorous proof of the convergence of the series of quantizer functions is given to ensure confidence in numerical results. Examples of the use of quantizer functions given are (i) determination of optimum step sizes of 2‐, 3‐, and 4‐bit uniform quantizers which yield maximum array gain for a typical array, (ii) calculation of directivity patterns of digital beamformer with input signals of arbitrary bandwidth, and (iii) evaluation of the effect of post filtering on the directivity patterns of digital beamformers. The special case of 1 bit per channel quantization (DIMUS) was especially discussed in detail with respect to both array gain and directivity patterns. The use of quantizer functions can also be extended to the solution of active‐sonar problems involving sine‐wave signals, and a brief example was given to illustrate the partial recovering of clipping loss in DIMUS by post filtering.