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Signals and Systems (System Properties)

  1. Dec 30, 2011 #1
    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?
  2. jcsd
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