What does a Fourier series representation of a periodic signal consist of?

• A. A signal is a sum of sines and cosines.
• B. A signal is represented by a single frequency component only.
• C. A signal is a product of sines and cosines.
• D. A signal cannot be represented in the frequency domain.

Answer: (A)

The idea being tested is that any periodic signal can be built by adding together simple sinusoidal waves. In a Fourier series, a periodic signal is represented as a sum of sinusoids—sines and cosines (or, equivalently, complex exponentials)—at discrete frequencies that are integer multiples of the fundamental frequency. Each term has its own amplitude and phase, and the orthogonality of the sine and cosine functions over one period makes the coefficients unique, so the original waveform can be exactly reconstructed by summing these components. A single frequency component would only describe a pure tone; most periodic signals contain many harmonics, so the full representation requires a sum of multiple sinusoidal terms. It’s not a product of sines and cosines, and this formulation directly provides a view in the frequency domain, showing which frequencies contribute to the signal.