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Consider three continuous-time systems S1, S2, and S3 whose responses to a complex

Chapter 3, Problem 3.17

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QUESTION:

Consider three continuous-time systems S1, S2, and S3 whose responses to a complex exponential input ei51 are specified as sl : ej5t --7 tej5t, S2 : ej5t ----7 ejS(t-1), S3 : ei51 ----7 cos(St). For each system, determine whether the given information is sufficient to conclude that the system is definitely not LTI.

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QUESTION:

Consider three continuous-time systems S1, S2, and S3 whose responses to a complex exponential input ei51 are specified as sl : ej5t --7 tej5t, S2 : ej5t ----7 ejS(t-1), S3 : ei51 ----7 cos(St). For each system, determine whether the given information is sufficient to conclude that the system is definitely not LTI.

ANSWER:

Step 1 of 3

The system can be expressed as follows:

Let is an arbitrary input to system and is corresponding output:

Now, consider the second input represented as a time shifted input :

Output corresponding to input is:

Here, . This system is not linear time variant system as LTI system will have as the output when is input.

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