Multidimensional systems and signal processing, Robust control, Image processing, Wavelet and filter bank, Signal processing for communication, Convolutional code design.
Digital Signal Processing
Multidimensional signal processing has become more popular lately due to its efficiency and greater degree of freedom in the design. However, the design and analysis of multidimensional systems are generally more complicated and requires thorough understanding of abstract algebra. Applications of multidimensional DSP include image compression, video coding, multi-sensor system design, filter bank design and wavelet.
Multidimensional System/Robust Control
Over several decades, great effort has been invested in the finding of a multivariate (n-D) polynomial matrix factorization algorithm. The problem has been completely solved only for the bivariate case. Recently with the usage of Groebner basis and conventional algebra, some n-D matrix factorization algorithms have been developed for some special cases. The general problem however, remains open. The solution to this problem will simultaneously solve many other important problems and can be directly applied to the multidimensional system realization and synthesis.
Signal Processing for Communication and Coding Theory
Many signal processing techniques such as adaptive filtering and spectral analysis are used to improve the fidelity of the transmission and reception of digital signals. Unlike source coding, channel coding is used for the purpose of protecting the transmitted bit stream from erroneous receiving. Correction and detection of error bits by means of algebraic coding techniques such as 1-D and 2-D convolutional code are usually employed. Topics of interest include: adaptive filtering, power spectrum estimation, array processing, 2-D convolutional code design, and application-specific coding design.