An analog LTI system with impulse response function h(t) = u(2 − t) + u(t − 2) is
presented with an input x(t) = t[u(t − 2) − u(t − 4)].
a) Determine and plot the system output y(t) = x(t) ∗ h(t).

The plot shows the following signals:

1. **Input signal \( x(t) \)** (first subplot): This function is non-zero between \( t = 2 \) and \( t = 4 \), following the form \( t \) in that interval.
2. **Impulse response \( h(t) \)** (second subplot): This function is non-zero between \( t = 0 \) and \( t = 2 \).
3. **Output signal \( y(t) = x(t) \ast h(t) \)** (third subplot): The result of the convolution, which is the system's output.

The output \( y(t) \) captures how the input signal is shaped by the system's impulse response.

Would you like more details or have any questions? Here are five related questions you might find useful:

1. How does the convolution operation work in general for LTI systems?
2. What are the properties of the unit step function \( u(t) \)?
3. How does the duration of the input affect the output in a convolution operation?
4. How would the system output change if the impulse response were a different shape?
5. What is the physical interpretation of an LTI system's impulse response?

**Tip:** The limits of integration in convolution depend on the intervals where both input and impulse response overlap. Understanding this can help simplify computations.

An analog LTI system with impulse response function h(t) = u(2 − t) + u(t − 2) is presented with an input x(t) = t[u(t − 2) − u(t − 4)]. a) Determine and plot the system output y(t) = x(t) ∗ h(t).

Explore the convolution of an LTI system with an impulse response function h(t) = u(2 − t) + u(t − 2) and an input x(t) = t[u(t − 2) − u(t − 4)]. Learn how to compute and plot the system output y(t), understanding key concepts in LTI systems, convolution, and the unit step function.

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