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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. | 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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Revision as of 09:57, 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.
