Algebraic Signal Processing Theory: Foundation and 1-D Time

Algebraic Signal Processing Theory

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A,M,Φ), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and Φ generalizes the concept of the z-transform to bijective linear mappings from a vector sp...

Algebraic Signal Processing: Modeling and subband Analysis

Traditional linear signal processing is based on viewing signals as sequences or functions in time that flow in one direction, from past through present into future. Somewhat surprisingly, the assumption that the most basic operation that can be performed on a signal is a time shift, or “delay,” is sufficient to derive many relevant signal processing concepts, including spectrum, Fourier transf...

D Speech Signal Processing

consisted of seven Ph.D. students (five of whom were located at the department), a part-time (20%) researcher (forskarassistent), two guest researchers, and a professor. The group performs research encompassed within speech processing, signal processing, and source coding and teaches two undergraduate courses (Information Theory and Source Coding, and Digital Speech Signal Processing), in addit...

Joseph D . Lakey Time – Frequency Methods for Signal Processing

Algebraic D-groups and Differential Galois Theory

We discuss various relationships between the algebraic Dgroups of Buium, 1992, and differential Galois theory. In the first part we give another exposition of our general differential Galois theory, which is somewhat more explicit than Pillay, 1998, and where generalized logarithmic derivatives on algebraic groups play a central role. In the second part we prove some results with a “constrained...