Fourier series representation uses an infinite number of harmonics. Which statement best describes this idea?

Fourier series representation uses an infinite number of harmonics. Which statement best describes this idea?

• A. A single pure tone.
• B. A sum of an infinite number of sines and cosines.
• C. A finite sum of harmonics.
• D. A non-periodic signal representation.

Answer: (B)

Fourier series expresses a periodic signal as a combination of sinusoidal components whose frequencies are integer multiples of the fundamental frequency. In theory, this decomposition uses an infinite number of sine and cosine terms with various amplitudes and phases, so the original waveform is the sum of infinitely many harmonics. This is why complex waveforms can be built from simple building blocks, and why the exact representation relies on an infinite series (even though, in practice, a finite number of terms can give a good approximation). The other ideas don’t fit: a single pure tone is just one sine, not the complete signal; a finite sum is just a truncated approximation; and non-periodic signals are described by the Fourier transform, not the Fourier series.

Fourier series expresses a periodic signal as a combination of sinusoidal components whose frequencies are integer multiples of the fundamental frequency. In theory, this decomposition uses an infinite number of sine and cosine terms with various amplitudes and phases, so the original waveform is the sum of infinitely many harmonics. This is why complex waveforms can be built from simple building blocks, and why the exact representation relies on an infinite series (even though, in practice, a finite number of terms can give a good approximation). The other ideas don’t fit: a single pure tone is just one sine, not the complete signal; a finite sum is just a truncated approximation; and non-periodic signals are described by the Fourier transform, not the Fourier series.