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Chapter 2 Linear Time-Invariant Systems - Engineering

ELG 3120 Signals and Systems Chapter 2 1/2 Yao Chapter 2 Linear Time-Invariant Systems Introduction Many physical Systems can be modeled as Linear Time-Invariant (LTI) Systems Very general signals can be represented as Linear combinations of delayed impulses. By the principle of superposition, the response ][ny of a discrete-time LTI system is the sum of the responses to the individual shifted impulses making up the input signal ][nx. Discrete-Time LTI Systems : The Convolution Sum Representation of Discrete-Time Signals in Terms of Impulses A discrete-time signal can be decomposed into a sequence of individual impulses. Example: nx[n]21-1-1-2-3-41234 Fig.

Systems Let h k [n] be the response of the LTI system to the shifted unit impulse d[n − k], then from the superposition property for a linear system, the response of the linear system to the input x[n] in Eq. (2.2) is simply the weighted linear combination of these basic responses: ∑ ∞ =−∞ = k y[n] x[k]h k [n]. (2.3)

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