Signal-flow graph: Difference between revisions

Revision as of 12:53, 6 June 2025

Revision as of 12:54, 6 June 2025

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=== Signal-flow graphs for design synthesis ===

Signal-flow graphs have been used in [[Design Space Exploration|Design Space Exploration (DSE)]], as an intermediate representation towards a physical implementation. The DSE process seeks a suitable solution among different alternatives. In contrast with the typical analysis workflow, where a system of interest is first modeled with the physical equations of its components, the specification for synthesizing a design could be a desired transfer function. For example, different strategies would create different signal-flow graphs, from which implementations are derived.<ref>{{Cite journal|title = ARCHGEN: Automated synthesis of analog systems|last1 = Antao|first1 = B. A. A.|date = June 1995|journal = IEEE Transactions on Very Large Scale Integration (VLSI) Systems |doi = 10.1109/92.386223|volume = 3|issue = 2|pages = 231–244|last2 = Brodersen|first2 = A.J.}}</ref>

Another example uses an annotated SFG as an expression of the continuous-time behavior, as input to an architecture generator<ref>{{Cite book |last1 = Doboli|first1 = A.|date = May 2000|doi = 10.1109/ISCAS.2000.856026 |last2 = Dhanwada|first2 = N.|last3 = Vemuri|first3 = R. | title=2000 IEEE International Symposium on Circuits and Systems. Emerging Technologies for the 21st Century. Proceedings (IEEE Cat No.00CH36353) | chapter=A heuristic technique for system-level architecture generation from signal-flow graph representations of analog systems |volume = 3|pages = 181–184|isbn = 978-0-7803-5482-1|citeseerx = 10.1.1.59.304|s2cid = 13948702}}</ref>

== Shannon and Shannon-Happ formulas ==

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[[William W. Happ]] generalized the Shannon formula for topologically closed systems.<ref name=Happ66>{{Cite journal|title = Flowgraph Techniques for Closed Systems|last = Happ|first = William W.|date = 1966|journal = IEEE Transactions on Aerospace and Electronic Systems|doi = 10.1109/TAES.1966.4501761|pages = 252–264|volume=AES-2|issue = 3|bibcode = 1966ITAES...2..252H|s2cid = 51651723}}</ref> The Shannon-Happ formula can be used for deriving transfer functions, sensitivities, and error functions.<ref name=Potash />

For a consistent set of linear unilateral relations, the Shannon-Happ formula expresses the solution using direct substitution (non-iterative).<ref name=Potash>{{cite journalbook |last1 =Potash|first1 = Hanan|first2 = Lawrence P.|last2 = McNamee| title=Proceedings of the 1968 23rd ACM national conference | chapter=Application of unilateral and graph techniques to analysis of linear circuits |year =1968 |pages=367–378 |chapter-url =https://www.deepdyve.com/lp/association-for-computing-machinery/application-of-unilateral-and-graph-techniques-to-analysis-of-linear-b8r753Bq03 |doi=10.1145/800186.810601|s2cid =16623657|doi-access =free}}</ref><ref name=NASAP-70>{{Cite book|title = NASAP-70 User's and Programmer's manual|last1 = Okrent|first1 = Howard|publisher = School of Engineering and Applied Science, University of California at Los Angeles|year = 1970|___location = Los Angeles, California|pages = 3–9|first2 = Lawrence P.|last2 = McNamee|chapter-url = https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19710025849.pdf|chapter = 3. 3 Flowgraph Theory}}</ref>

NASA's electrical circuit software NASAP is based on the Shannon-Happ formula.<ref name=Potash /><ref name=NASAP-70 />

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| first2 =Alan V.

| last2 =Oppenhiem

| title =2011 Digital Signal Processing and Signal Processing Education Meeting (DSP/SPE)

| chapter =Inversion of nonlinear and time-varying systems

| year = 2011

| pages =283–288