A triangle wave is a non-sinusoidal 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 (4n−1)th harmonic by −1 (or changing its phase by π), 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:
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:
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