The rectangular pulse function, often denoted as \( \text{rect}(t) \), is a simple, piecewise function that is frequently used in signal processing. If the rectangular pulse is defined to exist between \( t = 0 \) and \( t = 1 \), the function can be expressed mathematically as:

\[
\text{rect}(t) = 
\begin{cases} 
1 & \text{for } 0 \leq t \leq 1, \\
0 & \text{otherwise}.
\end{cases}
\]

This means that the function is equal to 1 when the time \( t \) is between 0 and 1, inclusive, and 0 elsewhere.

Would you like further details about how the rectangular pulse is used in various contexts like Fourier transforms or signal processing?

Here are 5 relative questions to explore further:
1. How is the Fourier transform of the rectangular pulse computed?
2. What is the role of the rectangular pulse in time-domain versus frequency-domain analysis?
3. How does the width of the pulse affect its behavior in different applications?
4. Can the rectangular pulse be generalized to higher dimensions, such as 2D pulses?
5. How is the rectangular pulse related to other windowing functions in signal processing?

**Tip**: The area under a rectangular pulse is important, often representing a measure of total energy or power in signals.

Understand the rectangular pulse function defined between 0 and 1, commonly used in signal processing. Explore how it behaves in the time-domain, its formula, and its applications in Fourier transforms and energy computation. Suitable for undergraduate students studying signal processing and piecewise functions.

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