Linear & Non-Linear Systems |Solved problems|
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This document discusses linear and nonlinear systems. It defines a linear system as one that satisfies the principles of superposition and homogeneity or scaling. The principles of homogeneity and superposition for a linear system are defined. Homogeneity means that scaling the input scales the output by the same factor. Superposition means that the output for the sum of two inputs is the sum of the outputs for each input individually. A linear system thus satisfies the property of linearity, where the output of scaled and summed inputs is the scaled and summed outputs. Nonlinear systems do not satisfy these properties.
![LINEAR AND NON LINEAR SYSTEMS
A linear system is one which satisfies the principle of superposition and homogeneity or
scaling
Consider a linear system characterized by the transformation operator T[]. Let x1, x2 are
the inputs applied to it and y1, y2 are the outputs. Then the following equations hold for a
linear system
y1(n) = T[x1(n)], y2 = T[x2(n)]
Principle of homogeneity:
T [a*x1(n)] = a*y1(n), T [b*x2(n)] = =b*y2(n)
Principle of superposition:
T [x1(n)] + T [x2(n)] = y1(n)+y2(n)
Linearity:
T [a*x1(n)] + T [b*x2(n)] = a*y1(n)+b*y2(n) .](https://image.slidesharecdn.com/lec20problemsinclassificationofsystems-linearandnonlinearsystems-200817082316/85/Linear-Non-Linear-Systems-Solved-problems-2-320.jpg)
Linear & Non-Linear Systems |Solved problems|
- 1. 15EE55C – DIGITAL SIGNAL PROCESSING AND ITS APPLICATIONS CLASSIFICATION OF SYSTEMS – LINEAR AND NON LINEAR SYSTEMS Dr. M. Bakrutheen AP(SG)/EEE Mr. K. Karthik Kumar AP/EEE DEPARTMENT OF ELECTRICAL AND ELECTRONICS ENGINEERING NATIONAL ENGINEERING COLLEGE, K.R. NAGAR, KOVILPATTI – 628 503 (An Autonomous Institution, Affiliated to Anna University – Chennai)
- 2. LINEAR AND NON LINEAR SYSTEMS A linear system is one which satisfies the principle of superposition and homogeneity or scaling Consider a linear system characterized by the transformation operator T[]. Let x1, x2 are the inputs applied to it and y1, y2 are the outputs. Then the following equations hold for a linear system y1(n) = T[x1(n)], y2 = T[x2(n)] Principle of homogeneity: T [a*x1(n)] = a*y1(n), T [b*x2(n)] = =b*y2(n) Principle of superposition: T [x1(n)] + T [x2(n)] = y1(n)+y2(n) Linearity: T [a*x1(n)] + T [b*x2(n)] = a*y1(n)+b*y2(n) .
- 3. LINEAR AND NON LINEAR SYSTEMS
- 4. LINEAR AND NON LINEAR SYSTEMS - PROCEDURE
- 5. LINEAR AND NON LINEAR SYSTEMS - PROCEDURE
- 6. PROBLEMS