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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.
Signal-flow graphs are weighted, directed graphs. He used these to analyse circuits containing mutual couplings and active networks. The weight of a directed edge in these graphs represents a gain, such as possessed by an amplifier. In general, signal-flow graphs, unlike the regular directed graphs described above, do not correspond to the ...
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 ...
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.
The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms , images , or other types of data streams . An example of a closed-loop block diagram, from which a transfer function may be computed, is shown below: