The generation of Fourier transforms of a time varying signal by frequency‐dependent beam steering of focused surface acoustic waves (SAWs) is described. This transform is accomplished by using a focusing array of phased SAW interdigital transducers (IDT) to generate, focus, and angularly disperse the acoustic waves according to the input signal frequencies. The spectrum is retrieved at the output by an array of independent SAW IDTs placed along the focal arc. Substrate anisotropy affects SAW diffraction, but need not present a problem when properly accounted for. This paper discusses the rationale for the design of the input transducer and its effect on the acoustic diffraction pattern, frequency response, and sidelobe suppression on an anisotropic substrate.