e178-L6.ppt

e178-L6.ppt - Linear Systems: Discrete case & 2D...

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Linear Systems: Discrete case & 2D Required Reading: 3.4 ECE 178: Linear Systems Review 2 Linear systems-review Discrete case & 2D 2D impulse function Line function Step function Linear systems and Shift invariance Impulse Response of LSI Systems 2-D Convolution
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ECE 178: Linear Systems Review 3 2-D Systems X(n1,n2) n1 n2 ECE 178: Linear Systems Review 4 Impulse Function(Kronecker Delta) δ (n1,n2)=1 if n1=0 and n2=0. =0 otherwise. n1 n2
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ECE 178: Linear Systems Review 5 Line Impulse δ T (n1,n2)=1 for all n1=0. =0 otherwise. n1 n2 ECE 178: Linear Systems Review 6 Unit Step Function u(n1,n2)=1 for all n1,n2>0. =0 otherwise. n1 n2
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7 “ System” An input-output relationship is called a system if there is a unique output for any given input. Y(n1,n2) = T[X(n1,n2)] X Y T ECE 178: Linear Systems Review 8 Linear Systems The linearity of a system T is defined as Linearity: T[a X 1 (n1,n2) + b X 2 (n1,n2)] = a Y 1 + b Y 2 (i.e., principle of superposition holds). Are these linear?
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e178-L6.ppt - Linear Systems: Discrete case & 2D...

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