This problem involves analyzing a linear time-invariant (LTI) system's response to given input signals based on the provided figures. Let’s go through each part of the problem.

Problem Analysis

1. Given Information:

   • An LTI system has an input (excitation) that corresponds to the signal in figure (i), and it produces the output (response) shown in figure (ii).

2. Questions:

   • (a) Determine the response when the excitation is the signal in figure (iii).
   • (b) Determine the response when the excitation is the signal in figure (iv).
   • (c) For a different LTI system where $x(t) = u(t)$ produces $y(t) = u(-1 - t)$, outline the response for the input in figure (v).

Approach to Solution

1. Using Convolution for LTI Systems: Since the system is LTI, the response to any new input can be determined using convolution if the impulse response is known. Here, we need to deduce the system's behavior based on the response to previous signals.

2. Scaling and Shifting Properties: For parts (a) and (b), use the scaling and time-shifting properties of the system’s response based on the given figures.

3. Reversal Property in Part (c): The given output $y(t) = u(-1 - t)$ suggests a time reversal and shift property that can be applied to the response.

Let me solve each part:

Solution Outline

1. (a) Analyze how the response to the signal in (i) transforms into the response shown in (ii) and then apply this to the signal in (iii).
2. (b) Similarly, apply the system's transformation to the signal in (iv).
3. (c) Use the transformation $y(t) = u(-1 - t)$ with the signal in (v) to sketch the response.

Would you like detailed steps and visualizations for each part?

Follow-up Questions

1. How is convolution applied in LTI systems to determine the output for various inputs?
2. What does time reversal of a signal imply in an LTI system response?
3. How does scaling in the time domain affect the response in an LTI system?
4. Can we deduce the impulse response of the system given the inputs and outputs in this problem?
5. How would the response change if the system was not time-invariant?

Tip

In LTI systems, convolution with the impulse response characterizes the output completely.