ECE2026 L9: Periodic Signals and Harmonics (Introduction to Signal Processing, Georgia Tech course)

Today I learned what paying attention means.

Another (intuitive) way to express the fact that harmonic signals can only have integer multiples of the fundamental is to use a time-domain example from wavetable synthesis. Imagine we have a waveform defined as the fundamental plus an overtone at the 1.5th harmonic. Draw that waveform and you’ll see we have a huge discontinuity between the start and end point of the single-cycle waveform. Such discontinuities throw off sawtooth like harmonics. Should we animate the fractional component (the 0.5) across a wavetable (say from 0 to 1 - the next harmonic), we will hear the “sync” synth sound. I know you’re teaching systems and signals, but this is how I explain it to sound designers who ask, “can single-cycle waveforms have non-integer harmonics?”

Hey aaron, I invented a new maths symbol yesterday that is an upgraded and more flexible edition of SUM. I can email it after making a proper infographic on how to use that👍🏻