If the integral of the square of a signal s(t) is finite, what is the signal called?

A signal for which the integral of its square is finite is referred to as an energy signal. This definition arises from the analysis of signals in the context of signal processing and communications. Energy signals are characterized by having a finite total energy, which is mathematically represented as the integral of the square of the signal over all time.

When you compute the integral of the square, you're essentially quantifying the total energy of the signal across its duration. If this value is finite, it indicates the signal does not extend indefinitely in energy, therefore classifying it distinctly as an energy signal. In contrast, signals that do not meet this criterion typically either have infinite energy or are periodic with finite power but infinite energy.

This understanding establishes energy signals as those that can manifest in forms like pulses or other transient waveforms that dissipate energy over time, as opposed to power signals, which maintain a consistent average power over time and may stretch indefinitely.