A triangle wave is a non-sinusoidal waveform named for its triangular shape.
A bandlimited triangle wave pictured in the time domain (top) and frequency domain (bottom). The fundamental is at 220 Hz (A2).Like a square wave, the triangle wave contains only odd harmonics. However, the higher harmonics roll off much faster than in a square wave (proportional to the inverse square of the harmonic number as opposed to just the inverse).
It is possible to approximate a triangle wave with additive synthesis by adding odd harmonics of the fundamental, multiplying every (4nā1)th harmonic by ā1 (or changing its phase by Ļ), and rolling off the harmonics by the inverse square of their relative frequency to the fundamental.
This infinite Fourier series converges to the triangle wave:
|
|||||
| Problems listening to this file? See media help. | |||||
See also
Sine, square, triangle, and sawtooth waveformsCategories: Fourier series
|
