To sketch the signal \( x(t) u(l - t) \), we need to break down and understand the components of the signal:

### Components:

1. **\( x(t) \)**: This is the main signal that varies with time \( t \).
2. **\( u(l - t) \)**: This is a **unit step function**, where \( u(t) \) is defined as:
   \[
   u(t) = \begin{cases} 
   1 & \text{if } t \geq 0 \\
   0 & \text{if } t < 0 
   \end{cases}
   \]
   In this case, the argument is \( (l - t) \), so the unit step function shifts to trigger at \( t = l \). The signal is non-zero only when \( t \leq l \).

### Behavior of the signal \( x(t) u(l - t) \):

- For \( t \leq l \): The unit step function is 1, so the signal is simply \( x(t) \).
- For \( t > l \): The unit step function is 0, so the signal becomes 0.

### Steps to Sketch:

1. Sketch \( x(t) \) normally.
2. Apply the unit step function \( u(l - t) \), which limits the signal to the interval \( (-\infty, l] \).
3. After \( t = l \), the signal will be zero.

Do you have more details about the form of \( x(t) \) (e.g., is it a sine wave, exponential, etc.)? If it's a general signal, we can sketch it based on this logic.

Would you like further details or clarifications?

### Related Questions:
1. How would the graph change if \( x(t) \) were a ramp function?
2. What would happen if the unit step was \( u(t - l) \) instead?
3. Can you explain the physical meaning of \( x(t) u(l - t) \)?
4. How would the signal behave if \( l \) were negative?
5. How does the Fourier transform of a unit step function look?

**Tip:** The unit step function is often used to model switching behavior in signals, turning a signal on or off at a specific time.

Learn how to sketch the signal x(t) u(l - t) by analyzing its components and understanding how the unit step function affects the signal. This guide breaks down the key concepts in signal processing and unit step functions, suitable for university-level students.

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