In a single-tone frequency-modulated (FM) signal, at what spacing do the spectral sidebands occur relative to the carrier?

Introduction / Context:
Understanding the FM spectrum is essential for bandwidth estimates (Carson’s rule) and interference control. A single-tone FM signal creates an infinite set of sidebands whose positions are harmonically related to the modulating frequency f_m.

Given Data / Assumptions:

• Single-tone modulation at frequency f_m.
• Carrier frequency f_c with deviation Δf.
• Standard narrow/wideband FM spectral structure.

Concept / Approach:

The FM spectrum contains components at f_c ± k f_m where k = 1, 2, 3, … . Amplitudes are given by Bessel functions of the first kind and depend on the modulation index, but the frequency spacing is strictly f_m regardless of index.

Step-by-Step Solution:

Verification / Alternative check:

Fourier expansion of a single-tone FM signal explicitly yields harmonics spaced by f_m around f_c.

Why Other Options Are Wrong:

• Four times, twice, half: incorrect spacing factors.
• Random spacing: amplitudes vary with index, but frequencies remain harmonic multiples of f_m.

Common Pitfalls:

Confusing sideband spacing with bandwidth growth from larger deviation; bandwidth increases, but spacing remains f_m.

Final Answer:

Exactly the modulating frequency (integer multiples of f_m)