Beginning with Winograd's work on the arithmetic complexity of signal processing algorithms such as convolution, digital filtering, and the discrete Fourier transform, there has been much work devoted to the application of algebraic methods in the design and implementation of signal processing algorithms. Various computer algebra systems have been utilized to implement these and related ideas.
More recently, ideas from group theory and multivariate polynomial algebra have been used to provide new insights into the mathematical structure of signal processing algorithms. These ideas have been successfully applied in the design of filters and signal transforms. As examples we mention the use of Groebner bases in wavelet design as well as the derivation of fast signal transforms using techniques from computational representation theory.
This session is devoted to exploring areas in signal and image processing for which algebra and algebraic computation may be beneficial. This session follows up on the session Applications of Computer Algebra to Signal Processing from ACA '99 in El Escorial, Spain. Copies of the slides from the talks in the previous session are available at ACA '99 session summary on the SPIRAL website.