Question:
Signal flow graphs:
Signal flow graphs:
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Signal Flow Graphs (SFGs). A graphical representation of linear system equations. Nodes represent variables, branches represent gains/transfer functions, arrows show signal flow direction (cause/effect). Applicable only to linear systems. Convertible to/from block diagrams.
Updated On: May 7, 2025
- They apply to linear systems
- The equation obtained may or may not be in the form of cause or effect
- Arrows are not important in the graph
- They cannot be converted back to block diagram
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The Correct Option is A
Solution and Explanation
Signal Flow Graphs (SFGs) are a graphical method used to represent and analyze systems described by linear algebraic or differential equations
(1) SFGs are specifically designed for representing linear systems, particularly Linear Time-Invariant (LTI) systems, where the principle of superposition holds
This statement is correct
(2) The equations represented by SFGs inherently depict cause-and-effect relationships, where the signal at a node is the sum of signals coming into it via branches, each representing a gain or transfer function (effect = gain \(\times\) cause)
This statement is incorrect
(3) The arrows (directed branches) are crucial in an SFG; they indicate the direction of signal flow and the dependence of one variable on another
This statement is incorrect
(4) Signal Flow Graphs and Block Diagrams are interconvertible methods for representing linear systems
An SFG can be derived from a block diagram and vice-versa
This statement is incorrect
Therefore, the correct statement describing signal flow graphs is that they apply to linear systems
(1) SFGs are specifically designed for representing linear systems, particularly Linear Time-Invariant (LTI) systems, where the principle of superposition holds
This statement is correct
(2) The equations represented by SFGs inherently depict cause-and-effect relationships, where the signal at a node is the sum of signals coming into it via branches, each representing a gain or transfer function (effect = gain \(\times\) cause)
This statement is incorrect
(3) The arrows (directed branches) are crucial in an SFG; they indicate the direction of signal flow and the dependence of one variable on another
This statement is incorrect
(4) Signal Flow Graphs and Block Diagrams are interconvertible methods for representing linear systems
An SFG can be derived from a block diagram and vice-versa
This statement is incorrect
Therefore, the correct statement describing signal flow graphs is that they apply to linear systems
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