The Fourier series concept states that any periodic signal can be represented as ...

• A. Any periodic signal can be represented as a sum of harmonics sine and cosine; the coefficients constitute the spectrum.
• B. Only non-periodic signals can be expressed as a spectrum.
• C. The spectrum is continuous for periodic signals.
• D. Fourier series only uses sine terms, not cosine.

Answer: (A)

A periodic signal can be built from a sum of sine and cosine components at harmonic frequencies. In Fourier series, a signal with period T0 has a fundamental frequency ω0 = 2π/T0 and can be written as x(t) = a0/2 + Σ[n=1 to ∞] [a_n cos(nω0 t) + b_n sin(nω0 t)]. The coefficients a_n and b_n tell you how much of each harmonic is present, and they are found by integrating over one period. The spectrum is the set of these coefficients mapped to their corresponding frequencies nω0; for periodic signals this spectrum is discrete, a line spectrum at multiples of ω0. This matches the statement that any periodic signal can be represented as a sum of harmonics and that the coefficients form the spectrum. Note that non-periodic signals also have spectra, but those are continuous rather than discrete, and Fourier series uses both sine and cosine terms (not only sine).