(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Indicate following properties for the system with the given input-output equation:

-Linearity, Causality, Time Invariance, memoryless or not

and explain why?

2. Relevant equations

y(t) = ∫^{t}_{-∞}(t - λ) x(λ) dλ

3. The attempt at a solution

lets say X(t) is the antiderivative of x(t), then:

y(t) = t ∫^{t}_{-∞}x(λ) - ∫^{t}_{-∞}λ x(λ) dλ

= t (X(t) - X(-∞)) - (t X(t) - X(t) - (-∞ X(-∞) - X(-∞)))

now we have the relation between y(t) and X(t) but how can we obtain the relation between y(t) and x(t) to find out about the causality and memory properties?

can this be a clue or I am doing wrong?

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# Signals and Systems (System Properties)

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