A sound source can generally be characterized by three physical properties: timbre, loudness, and directivity. Although loudspeakers give a faithful reproduction of timbre and loudness, their own directivity can conflict with the directivity of the source they aim at reproducing. A general method to optimize the reproduction of any given directivity pattern with a set of independently driven sources is described. At each frequency the synthesized directivity is obtained by looking for the optimal linear combination of the elementary sources, from which the resulting acoustic field can be predicted. This method is applied to a particular source with 12 loudspeakers grouped into a few subsets in order to fit the first spherical harmonics. The comparison between the prediction and the experimental measurements shows excellent agreement. However, the synthesized figures only fit the spherical harmonics in a limited frequency range, which depends strongly on the characteristics of the electroacoustical set (number, position, and directivity of sources). The interest and the limitations of this method are discussed for various types of applications, such as the reproduction of the directivity of instruments, loudspeaker clusters design, and echo cancellation. Finally, an attempt is made to illustrate the perceptual effects of the directivity by analyzing the variations of room acoustics criteria measured with the different synthesized directivity patterns.