A triangle wave is a nonsinusoidal waveform named for its triangular shape.
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:
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Another definition of the triangle wave, with range from 1 to 1 and period 2a is:
Also, the triangle wave can be the absolute value of the sawtooth wave:
The triangle wave can also be expressed as the integral of the square wave:
