An Algorithm Design Environment for Signal Processing

The computer is used in signal processing primarily for numerical calculations. Re-cently, a number of signal-processing environments have evolved which simplify the ini-tial creation of a signal-processing algorithm from a series of low-level signal-processing blocks. Despite this progress, the majority of the design process is generally completed without computer support: the analyses of the properties of the selected algorithm are generally completed by hand as is the manipulation of the algorithm to find efficient, in-put/output equivalent implementations. This thesis explores some of the issues involved providing software tools for the symbolic analysis and rearrangement of signal-processing algorithms as well as for the initial algorithm selection. A software environment is developed, supporting numeric signal-processing compu-tations as well as symbolic analysis and manipulation of signal-processing expressions. The areas in which this thesis contribute lie primarily in the symbolic manipulation of signal-processing expressions. To allow for the efficient manipulation of a variety of "regular " algorithms, such as polyphase and FFT structures, correspondence constraint