Convolution sum & Integral

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Presentation transcript:

Convolution sum & Integral Lecture #03 Convolution sum & Integral

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

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

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

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

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

Linear system Ans: meiling chen signals & systems

Convolution sum meiling chen signals & systems

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

convolution meiling chen signals & systems

meiling chen signals & systems

Example 2.1 Impulse response meiling chen signals & systems

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

meiling chen signals & systems

meiling chen signals & systems

meiling chen signals & systems