(New page: =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] ...) |
(→Linearity and Time Invariance) |
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Input Output | Input Output | ||
X0[n]=δ[n] -> Y0[n]=δ[n-1] | X0[n]=δ[n] -> Y0[n]=δ[n-1] | ||
| + | |||
X1[n]=δ[n-1] -> Y1[n]=4δ[n-2] | X1[n]=δ[n-1] -> Y1[n]=4δ[n-2] | ||
| + | |||
X2[n]=δ[n-2] -> Y2[n]=9 δ[n-3] | X2[n]=δ[n-2] -> Y2[n]=9 δ[n-3] | ||
| + | |||
X3[n]=δ[n-3] -> Y3[n]=16 δ[n-4] | X3[n]=δ[n-3] -> Y3[n]=16 δ[n-4] | ||
| + | |||
... ... | ... ... | ||
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Xk[n]=δ[n-k] -> Yk[n]=(k+1)2 δ[n-(k+1)] -> For any non-negative integer k | Xk[n]=δ[n-k] -> Yk[n]=(k+1)2 δ[n-(k+1)] -> For any non-negative integer k | ||
Revision as of 10:46, 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
