Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Fast generalized Fourier transforms
Theoretical Computer Science
Dynamics of Time-Varying Discrete-Time Linear Systems: Spectral Theory and the Projected System
SIAM Journal on Control and Optimization
The efficient computation of Fourier transforms on the symmetric group
Mathematics of Computation
Spectral Analysis of Boolean Functions as a Graph Eigenvalue Problem
IEEE Transactions on Computers
Spectral decision diagrams using graph transformations
Proceedings of the conference on Design, automation and test in Europe
Spectral Techniques in VLSI CAD
Spectral Techniques in VLSI CAD
Orthogonal Transforms for Digital Signal Processing
Orthogonal Transforms for Digital Signal Processing
Chrestenson Spectrum Computation Using Cayley Color Graphs
ISMVL '02 Proceedings of the 32nd International Symposium on Multiple-Valued Logic
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Discrete finite-valued functions are increasingly important in applications involving automation and control. In particular, it is evident that industry is focusing on “Systems-on-a-Chip” (SoC) where the integration of analog (infinite-valued) and digital (binary-valued) circuits must co-exist. As designers struggle with these interfacing issues, it is natural to consider the intermediate circuits that can be modeled as multi-valued, discrete logic-level circuits. This viewpoint is not unprecedented as such principles have been used for at least the past twenty years in telecommunications protocols. If an analogous approach is considered in control systems implemented in “Integrated Circuit” (IC) designs, it is proposed that spectral analysis may provide an important role and efficient methods for computing such mixed-radix function spectra are described here. These methods are formulated as transformations of word-level decision diagrams representing the underlying arithmetic expressions and can be implemented as graph traversal algorithms. The theoretical foundation of the spectral transform of a mixed-radix function is presented and the equivalence of the resulting spectrum and the spectrum of a Cayley graph is shown.