FMsignal

FMsignal, commonly written as an FM signal, is a type of modulated signal used in communications in which the instantaneous frequency of a carrier varies in accordance with a modulating waveform. It is a form of angle modulation and is more robust to amplitude noise than amplitude-modulated signals.

Mathematically, if the carrier is f_c and the modulating signal is m(t), the instantaneous frequency is f_i(t) = f_c + k_f m(t), where k_f is the frequency sensitivity. The transmitted signal can be written as s(t) = A cos(2π ∫ f_i(τ) dτ) = A cos(2π f_c t + 2π k_f ∫ m(τ) dτ). For a sinusoidal modulator m(t)=M cos(2π f_m t), this becomes s(t)=A cos(2π f_c t + β sin(2π f_m t)) with β = Δf / f_m and Δf = k_f M, the peak frequency deviation.

Bandwidth and modulation index: The peak deviation Δf and the message bandwidth f_m determine the modulation index β = Δf / f_m. Carson's rule gives an approximate total bandwidth B ≈ 2(Δf + f_m). Narrowband FM corresponds to smaller β, while wideband FM uses larger β and provides higher fidelity.

Generation and demodulation: FMsignals are produced by frequency-sensitive oscillators such as voltage-controlled oscillators or phase-locked loops that adjust the carrier frequency in response to the input. Demodulation is accomplished with discriminators, PLL-based demodulators, or quadrature detectors that recover the original information signal.

Applications: FMsignal is widely used in broadcast radio (FM), aviation and public-safety communications, and various data-link and professional communications channels. Its resilience to amplitude noise and interference is a primary advantage over amplitude-modulated schemes.