How is the number of harmonics typically estimated in a Fourier series representation?

• A. Include only the first harmonic.
• B. Take as many harmonics as needed until the amplitude of a harmonic drops to about 1/10th of the first harmonic.
• C. The harmonics must all have equal amplitude.
• D. Include all harmonics up to infinity.

Answer: (B)

When building a Fourier series approximation, you break a periodic signal into sinusoids at multiples of the fundamental frequency, then decide how many terms to keep. Higher harmonics usually have smaller amplitudes, and the Fourier coefficients decay for smoother signals, so you don’t need infinitely many terms to get a good fit. A practical rule of thumb is to keep adding harmonics until the next one’s amplitude drops to about one-tenth of the first harmonic. This choice gives a good balance: you capture the main shape of the waveform without spending effort on components that contribute only a tiny amount. Although the exact Fourier representation would include all harmonics to infinity, in practice a finite number is used because those tiny harmonics add little noticeable detail. Including only the first harmonic misses important waveform features, and harmonic amplitudes are not typically equal, so a simple equal-amplitude assumption wouldn’t describe real signals.