Additive Synthesis (Square, Sawtooth, and Triangle Waves)

A short animation illustrating additive synthesis of three common waves, using Fourier Series.

Clearly visible in the first two partially synthesized waves is the Gibbs phenomenon. The triangle wave's Fourier Series converges much more quickly.

Category:

Science & Technology

Tags:

• fourier
• series
• additive
• synthesis
• sawtooth
• wave
• square
• triangle

[edringsina]

i wish the sounds would be on here.

[atomictraveller]

i wish you'd first gone over the idea of adding two sines together.. done a point by point example of what it means to add two sines, and also maybe done sort of a [fundamental] + [nth harmonic] = [result] kinda dealie.. :)

[xr280xr]

@Ciaran55 I believe harmonic is the base frequency multiplied by a whole number (as now I see is already posted...). In other words, a harmonizing frequency. You might also hear it referred to as an overtone.

[Desmaad]

Notice how the waveforms become passable at 12 harmonics.

[ScrewedUpDNA21]

What equation did you use for the triangle wave???

[zepp89]

8 months later but... a harmonic is a whole number multiple of the fundamental frequency.

[Ciaran55]

what is a harmonic??

[eerereps]

you've nailed it! esp in the triangular one! it was almost pure!