One of the most important issues for engineering and multimedia is how to process digital signals in a fast manner. Many digital signal transforms are available, including discrete Fourier transform, discrete cosine transform, Hartley transform, and Haar transform. Fast algorithms for computing such transforms are based on matrix factorization and sparse matrices manipulation. This paper presents “a computer algebra framework to automatically derive and implement algorithms for digital signal processing.”

The reader will find the general presentation of the entire process, starting with the transform and ending with fast FORTRAN or C executable code (section 1). After a presentation of the mathematical background, the algorithm used for factoring a matrix with symmetry is outlined. The last part of the second section describes a library for symbolic manipulation of group representations and structured matrices, called AREP. Examples of factorizations for different transforms are also included. For translating the matrix expressions into efficient imperative-style numerical programs (FORTRAN or C), the SPL language is used. The constructs of the SPL language, which provides tools for generating programs and interfacing with MATLAB, GAP, and Maple, are presented in section 3.

To illustrate the performance of the approach, the automatic implementation of an 8-point discrete cosine transform is presented, in great detail, in section 4. The paper ends with some remarks concerning future work, and a list of references. Hypertext links for AREP and SPL are also included.

The authors announce results that are interesting for digital signal engineers, academic professionals, and those interested in computer algebra and applications. The presentation is clear, and the list of references is helpful.