This paper discuss an approach to implementing and optimizing fast signal transforms based on a domain-specific computer language, called SPL. SPL programs, which are essentially mathematical formulas, represent matrix factorizations, which provide fast algorithms for computing many important signal transforms. A special purpose compiler translates SPL programs into efficient FORTRAN programs. Since there are many formulas for a given transform, a fast implementation can be obtained by generating alternative formulas and searching for the one with the fastest execution time. This paper presents an application of this methodology to the implementation of the FFT.