We discuss the design and implementation of a compiler that translates form
ulas representing signal processing transforms into efficient C or Fortran
programs. The formulas are represented in a language that we call SPL, an a
cronym from Signal Processing Language. The compiler is a component of the
SPIRAL system which makes use of formula transformations and intelligent se
arch strategies to automatically generate optimized digital signal processi
ng (DSP) libraries. After a discussion of the translation and optimization
techniques implemented in the compiler, we use SPL formulations of the fast
Fourier transform (FFT) to evaluate the compiler. Our results show that SP
IRAL, which can be used to implement many classes of algorithms, produces p
rograms that perform as well as "hard-wired" systems like FFTW.