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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.
Mason's gain formula (MGF) is a method for finding the transfer function of a linear signal-flow graph (SFG). The formula was derived by Samuel Jefferson Mason, [1] for whom it is named. MGF is an alternate method to finding the transfer function algebraically by labeling each signal, writing down the equation for how that signal depends on ...
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]
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.
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 ...
Figure 1 shows a block diagram that leads to the asymptotic gain expression. The asymptotic gain relation also can be expressed as a signal flow graph. See Figure 2. The asymptotic gain model is a special case of the extra element theorem. Figure 2: Possible equivalent signal-flow graph for the asymptotic gain model
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 signal-flow graph for these equations are shown in the second figure to the right. The arrangement of feedback loops in the signal flow-graph inspired the name leapfrog filter. [1]: 286 The signal flow graph is manipulated to convert all current nodes into voltage nodes and all the impedances and admittances into dimensionless transmittances.