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A signal-flow graph or signal-flowgraph (SFG), invented by Claude Shannon, [1] but often called a Mason graph after Samuel Jefferson Mason who coined the term, [2] is a specialized flow graph, a directed graph in which nodes represent system variables, and branches (edges, arcs, or arrows) represent functional connections between pairs of nodes.
Signal-flow graph connecting the inputs x (left) to the outputs y that depend on them (right) for a "butterfly" step of a radix-2 Cooley–Tukey FFT. This diagram resembles a butterfly (as in the morpho butterfly shown for comparison), hence the name, although in some countries it is also called the hourglass diagram.
An example of a signal-flow graph Flow graph for three simultaneous equations. The edges incident on each node are colored differently just for emphasis. An example of a flow graph connected to some starting equations is presented. The set of equations should be consistent and linearly independent. An example of such a set is: [2]
Mason's Rule is also particularly useful for deriving the z-domain transfer function of discrete networks that have inner feedback loops embedded within outer feedback loops (nested loops). If the discrete network can be drawn as a signal flow graph, then the application of Mason's Rule will give that network's z-domain H(z) transfer function.
A multi-input, multi-output system represented as a noncommutative matrix signal-flow graph. In automata theory and control theory, branches of mathematics, theoretical computer science and systems engineering, a noncommutative signal-flow graph is a tool for modeling [1] interconnected systems and state machines by mapping the edges of a directed graph to a ring or semiring.
A propagation graph is a signal flow graph in which vertices represent transmitters, receivers or scatterers. Edges in the graph model propagation conditions between vertices. Propagation graph models were initially developed by Troels Pedersen, et al. for multipath propagation in scenarios with multiple scattering, such as indoor radio ...
It is similar to a block diagram or signal-flow graph, with the major difference that the arcs in bond graphs represent bi-directional exchange of physical energy, while those in block diagrams and signal-flow graphs represent uni-directional flow of information. Bond graphs are multi-energy domain (e.g. mechanical, electrical, hydraulic, etc ...
Flow graph (mathematics), a directed graph linked to a set of linear algebraic or differential equations; Flow network, a directed graph where each edge has a capacity and receives a flow; Signal-flow graph, a directed graph with nodes as system variables and branches as node connections