(Linearity and Time Invariance)
(Linearity and Time Invariance)
Line 2: Line 2:
 
Given system:
 
Given system:
 
Input       Output
 
Input       Output
 +
 
X0[n]=δ[n]   ->  Y0[n]=δ[n-1]
 
X0[n]=δ[n]   ->  Y0[n]=δ[n-1]
  

Revision as of 09:48, 12 September 2008

Linearity and Time Invariance

Given system: Input Output

X0[n]=δ[n] -> Y0[n]=δ[n-1]

X1[n]=δ[n-1] -> Y1[n]=4δ[n-2]

X2[n]=δ[n-2] -> Y2[n]=9 δ[n-3]

X3[n]=δ[n-3] -> Y3[n]=16 δ[n-4]

... -> ...

Xk[n]=δ[n-k] -> Yk[n]=(k+1)2 δ[n-(k+1)] -> For any non-negative integer k

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