(→Linearity and Time Invariance) |
(→Linearity and Time Invariance) |
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=Linearity and Time Invariance= | =Linearity and Time Invariance= | ||
Given system: | Given system: | ||
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Input Output | Input Output | ||
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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 | ||
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| + | =Time Invariant System?= | ||
| + | Suppose the system is defined as the third line where input is <math>X_2[n]=δ[n-2]</math> and output: <math>Y_2[n]=9 δ[n-3]</math> with a time delay of . Using the same method as in Part D, we can determine whether this system is time invariant or not. | ||
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| + | δ[n] -> time delay -> δ[n-3] -> system -> 16δ[n-4] | ||
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| + | δ[n] -> system -> δ[n-1] -> time delay -> δ[n-4] | ||
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| + | Since both cascades produce different outputs, this system is NON-time invariant. | ||
Revision as of 10:57, 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
Time Invariant System?
Suppose the system is defined as the third line where input is $ X_2[n]=δ[n-2] $ and output: $ Y_2[n]=9 δ[n-3] $ with a time delay of . Using the same method as in Part D, we can determine whether this system is time invariant or not.
δ[n] -> time delay -> δ[n-3] -> system -> 16δ[n-4]
δ[n] -> system -> δ[n-1] -> time delay -> δ[n-4]
Since both cascades produce different outputs, this system is NON-time invariant.
