In signals and systems, which statement best defines a bandlimited signal in practical communication engineering terms?

Introduction:
A core idea in signals and systems and communication engineering is the notion of a bandlimited signal. This concept explains when and why sampling, filtering, and spectrum allocation work as expected. The question asks for the most accurate engineering definition of a bandlimited signal.

Given Data / Assumptions:

• We consider deterministic signals with well-defined Fourier transforms.
• “Finite frequency interval” means there exists B > 0 such that the spectrum is zero for |f| > B.
• Real-world hardware approximates bandlimiting via filters with finite roll-off.

Concept / Approach:
A signal x(t) is bandlimited if its Fourier transform X(f) = 0 for |f| > B. This property underlies ideal sampling: if the highest frequency is B, perfect reconstruction is possible when sampling at rate > 2B (Nyquist rate), assuming ideal conditions.

Step-by-Step Solution:

Verification / Alternative check:
The definition does not mention modulation, number of receivers, or network topology. It focuses purely on spectral support of the signal. Therefore, the correct choice must reference finite bandwidth.

Why Other Options Are Wrong:

• Transmission without modulation: possible for short links but unrelated to the spectral definition.
• Simultaneous transmission to many stations: describes a distribution method, not spectrum confinement.
• All of the above: false because the prior two are not definitions of bandlimitedness.
• None of the above: incorrect because one option is correct.

Common Pitfalls:
Confusing implementation methods (baseband, broadcast) with spectral properties; assuming “finite energy” implies “finite bandwidth” (it does not).

Final Answer:
A bandlimited signal has zero spectral content outside a finite frequency band.