LTI-part2.ppt signals and systems related

signals and systems

1. Properties of LTI Systems
Convolution is commutativenxnhnhnx 
h[n]x[n] y[n]
x[n]h[n] y[n] nhnxnhnxnhnhnx
2121 
Convolution is distributed over addition

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3. Parallel connectionof systems
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h n h n h n  
1 2 1 2
x n h n h n x n h n x n h n     

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5. Cascade connectionof systems
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h n h n h n
x[n]
h
1[n] h
2[n] y[n]
x[n]
h
2[n] h
1[n] y[n]
x[n]
h
1[n] ]h
2[n] y[n]
associative property  
1 2 1 2
x n h n h n x n h n h n      
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x n h n h n  
commutative

6. Stabilityof LTI Systems
LTI system is stable if the impulse response
is absolutely summable .
k
S h k


     





kk
knxkhknxkhny 
xBnx  
x
k
y n B h k


  
Causalityof LTI systems 0,0nnh

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