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timofeeve [1]
3 years ago
5

Linear Time Invariant Systems For each of the systems below an input x(t) and the output y(t) are plotted. Determine whether eac

h of these are linear time invariant (LTI) systems, and can be described by a convolution. Provide an argument for your answer. Note that some cases are described in the time domain, and some in the frequency domain.
Engineering
1 answer:
STALIN [3.7K]3 years ago
4 0

Answer:

The system can be described by a convolution

Explanation:

Thinking process:

If we consider a discrete input to a linear time-invariant system, then the system will be periodic with respect to the period, say N. This therefore, means that the output must also  be periodic. The proof is as follows:

The LTI system can be written for the system where:

y (n+N) = ∑h(k)x(n + N - k)

            = ∑h(k)x(n-k)\\= y(n)

From the proof, it turns out that y(y + N) = y(n) for any value of n, then the output will be the periodic with the period N.

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