SUMMARYDelay-and-sum array microphones consisting of a linear array of microphones can achieve a sharp directivity at high frequencies. A disadvantage is that the directivity depends on the frequency. In order to resolve this problem, an array microphone using a fan filter has been proposed. However, in order to form a sharp beam at a low frequency, it is necessary to increase the filter order and the array length. In this paper, we report improvement of the directivity of an array microphone realizing a narrow beam with a relatively low order of the filter by means of a two-dimensional frequency domain design. Employing two microphones, a first-order pressure-gradient microphone is formed. The spacing of the microphones is set for high sensitivity and broad bandwidth in the operating frequency range. The amplitude characteristics are obtained in the two-dimensional frequency domain. These microphone units are placed along a line and are cascaded to a two-dimensional fan filter so that the load is distributed. In the proposed configuration, a cardioid microphone is cascaded with an axially symmetric fan filter in a configuration that forms a single broadside beam. Another configuration forms a single beam in the endfire direction by cascading the bidirectional microphone to a diagonally symmetric fan filter. Deterioration of the pressure-gradient microphone is compensated for by the two-dimensional FIR filter. As a result, the directional characteristics of the pressure-gradient microphone are reflected in the array microphone and a sharp directivity not dependent on the frequency is obtained over a wide frequency range.