Dr. Burrus received teaching awards at Rice in 1969, 74, 75, 76, 80, and 1989, an IEEE S-ASSP Senior Award in 1974, a Senior Alexander von Humboldt Award in 1975, received a Senior Fulbright Fellowship in 1979, was elected Fellow of the IEEE in 1981, the IEEE S-ASSP Technical Achievement Award in 1986, and was a Distinguished Lecturer for the Signal Processing Society and for the Circuits and Systems Society from 1989 through 1992. He was awarded the IEEE S-SP Society Award in 1994, the Millineum Medal in 2000, and the SPIE Wavelet Pioneer Award in 2006. He served on the IEEE Signal Processing Society ADCOM and has coauthored five books and over 200 papers on digital signal processing.
Dr. Burrus has been conducting research in digital signal processing (DSP) for more than 30 years at Rice. His interests are in digital filter design and implementation, and in efficient signal processing algorithms. Significant work is being done in both time and frequency domain specifications for FIR and IIR filters. The design methods focuses on efficient approximation algorithms, and the implementation uses block processing, distributed arithmetic, and transform techniques. Recent work has been on constrained least squared approximation, iterative reweighted least squares algorithms, and new exchange algorithms for Chebyshev approximations. The results of the DSP group's research on filter design are used in commercial filter design systems and are described in Burrus' book on digital filter design. More information on this research program can be found in the filter design notes.
Very efficient fast Fourier transform (FFT) algorithms have been developed by Professor Burrus and his students at Rice. Two very important approaches that are different from the traditional Cooley-Tukey FFT have been the prime factor algorithm (PFA) and the number theoretic transform. Recent work has considered real-data transforms, the split-radix FFT, the Hartley transform, the QFT, and special cases for small number of data points and for prime lengths. A program has been written that will write specialized FFT programs. The work involves basic theory, practical computer programs, and applications. FFT algorithms developed at Rice have been implemented in commercial products and are described in Burrus' book on FFTs. More information on the research program in FFTs and other fast algorithms can be found in the FFT notes.
Since 1988, Professor Burrus and his group have been investigating the use of wavelets as expansion functions for signal analysis, representation and processing. Work has been done on efficient implementation of the discrete wavelet transform, on time-varying wavelets, on optimal wavelet bases, on filter banks, and on the use of frames and tight frames for redundant wavelet transforms. Recently work on nonlinear processing of redundant time-invariant wavelet transforms for denoising and compression has proven very effective. More information on the research program on wavelets can be found in the wavelet notes.
Since 1976, Professor Burrus has had a hobby interest in algorithms to factor high degree polynomials. In 2000, he and three other colleagues formed the "Polynomial Club" which has meet randomly to discuss polynomial factorization. We have recently factored a four million degree polynomial with random coefficients on four processors of an AMD cluster.
In addition to DSP research, Dr. Burrus has been interested in the use of technology to teach and facilitate learning. He and five colleagues at other universities have published a book of exercises using Matlab (from MathWorks) to teach DSP. He has been part of the Connexions Project since its founding in 1999 and is now its Senior Strategist.