Electrical Engineering ⇒ Topic : Linear and Nonlinear Systems

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Linear and Nonlinear Systems If a system satisfies the property of homogeneity and the property of superposition, the system is said to be linear. Homogeneity Let the system produces output y(t) for an input x(t). If the input is scaled 'a' times, the output will also be scaled by 'a' times for all values of 'a' and x(t). Therefore, we can write mathematically as follows: x(t) → y(t) ax(t) → ay(t) Superposition If two inputs x_{1}(t) and x_{2}(t) are applied to a system simultaneously, the overall output will be the combined effects of x_{1}(t) and x_{2}(t). x_{1}(t) + x_{2}(t) → y_{1}(t) + y_{2}(t) Combining these properties, we can write the following for a linear system: If x_{1}(t) → y_{1}(t) and x_{2}(t) → y_{2}(t), then a_{1}x_{1}(t) + a_{2}x_{2}(t) → a_{1}y_{1}(t) + a_{2}y_{2}(t) If any system does not satisfy the above two conditions, the system is called nonlinear. Usually,nonlinearity arises in a physical system due to nonlinear input and output relation of its components.  
 
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