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==Time Invariance== | ==Time Invariance== | ||
| − | + | Assuming the subscript <math>k</math> denotes a time shift in the input signal, <math>Y_k[n]=(k+1)^2\delta[n-(k+1)]</math> is <b>not</b> time invariant. As the input goes through a time shift, the output amplitude change is related to the square in the shift in time. | |
==Linearity== | ==Linearity== | ||
Since the system is linear, the required input will be <math>X[n]=u[n]</math>. An input of a <math>\delta</math> functional produces an output of a time-shifted <math>\delta</math> functional, so an input of a unit step function will produce an output of a time-shifted unit-step function. | Since the system is linear, the required input will be <math>X[n]=u[n]</math>. An input of a <math>\delta</math> functional produces an output of a time-shifted <math>\delta</math> functional, so an input of a unit step function will produce an output of a time-shifted unit-step function. | ||
Latest revision as of 08:59, 9 September 2008
Time Invariance
Assuming the subscript $ k $ denotes a time shift in the input signal, $ Y_k[n]=(k+1)^2\delta[n-(k+1)] $ is not time invariant. As the input goes through a time shift, the output amplitude change is related to the square in the shift in time.
Linearity
Since the system is linear, the required input will be $ X[n]=u[n] $. An input of a $ \delta $ functional produces an output of a time-shifted $ \delta $ functional, so an input of a unit step function will produce an output of a time-shifted unit-step function.
