A time-limited rectangular pulse defined by f(t) = 0 for t < 0, f(t) = E for 0 ≤ t ≤ a, and f(t) = 0 for t > a is best described as which type of standard signal?

Introduction / Context:
Standard test signals—step, impulse, ramp, and pulse—are frequently used in systems and signal analysis. Correct classification helps in understanding system responses and Fourier/Laplace transforms. Here, the signal is nonzero only over a finite interval [0, a] with amplitude E, which is a classic rectangular pulse.

Given Data / Assumptions:

• f(t) = 0 for t < 0.
• f(t) = E for 0 ≤ t ≤ a.
• f(t) = 0 for t > a.

Concept / Approach:
A rectangular pulse can be written as the difference of two step functions: f(t) = E[u(t) − u(t − a)]. It is time-limited (finite duration) and has finite energy. It is not a single step (which stays at E forever after t ≥ 0), nor a shifted step at t = a alone (that would be zero until t ≥ a and then E thereafter).

Step-by-Step Solution:

Verification / Alternative check:

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Final Answer: