🔍 Key Concepts

• Fourier series representation of periodic waves • How harmonics (integer multiples of a fundamental frequency) add together to form complex wave shapes • Which common waveforms (sine, square, sawtooth, cosine) can be built from a sum of many sine waves at harmonic frequencies

💭 Think About

• Which waveform is already just a single pure sine at the fundamental frequency, with no additional harmonics? Eliminate that choice. • Think about which non-sinusoidal waveforms are typically demonstrated in electronics or signals courses as being made up of a full series of harmonics (1st, 2nd, 3rd, etc.), not just odd harmonics. • Between the remaining complex wave shapes, which one is known to require all harmonics (both even and odd) in its Fourier series expansion?

✅ Before You Answer

• Be clear on what fundamental frequency means versus harmonics (integer multiples of that frequency). • Identify which listed waveforms are pure sinusoids (single frequency only) versus composite periodic waves (sum of many harmonics). • Recall or look up which standard waveforms (square vs sawtooth) use only odd harmonics and which use all harmonics in their Fourier series.