Lecture 03 Convolution sum Integral meiling chen signals

Lecture #03 Convolution sum & Integral meiling chen signals & systems

Linear system Convolution Integral : LTI system meiling chen signals & systems … 2

Linear system LTI system I. C. =0 Impulse response Transfer function of the system Any input meiling chen LTI system I. C. =0 signals & systems Zero state response 3

Example : Graphical convolution Linear system (1) meiling chen signals & systems 4

Linear system (2) (3) meiling chen signals & systems 5

Linear system (4) (5) meiling chen signals & systems 6

Linear system Ans: meiling chen signals & systems 7

Convolution sum meiling chen signals & systems 8

LTI system Only true for linear system (linearity property) x[k] is a constant with respect to H (linearity property) Let Only true for time invariant system Convolution sum meiling chen signals & systems 9

convolution meiling chen signals & systems 10

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Example 2. 1 Impulse response meiling chen signals & systems 12

Example 2. 2 The input and impulse response are of infinite duration Consider a system with impulse response Find y[n] when the input is x[n]=u[n] meiling chen signals & systems 13

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