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)

Here's the plot of the system output \( y(t) = x(t) \ast h(t) \):

- **For \( 2 \leq t < 4 \)**, the output \( y(t) \) increases linearly from 0 to 2.
- **For \( 4 \leq t < 6 \)**, the output \( y(t) \) decreases linearly from 2 to 0.
- The output \( y(t) \) is zero outside the interval \( 2 \leq t < 6 \).

Would you like any further details or have any questions?

Here are five related questions you might consider:

1. How would the output change if the impulse response was delayed by a different time shift?
2. What happens to the output if the input signal \( x(t) \) is a different function, like a sine wave?
3. Can you derive the output analytically for other types of piecewise functions?
4. How does the shape of the output relate to the duration and shape of the input signal?
5. What would the output look like if the system were non-linear?

**Tip:** When dealing with convolutions in piecewise functions, breaking the problem into intervals where each function is non-zero simplifies the calculation significantly.

Understand how to compute the output of an LTI system given specific impulse response function and input signal. This problem involves convolution of piecewise functions and requires plotting the system output. Explore detailed steps and implications of the solution.

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