Triangle Wave Information
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 (A3).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:
- where is the angular frequency.
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Triangle wave sound sample
5 seconds of anti-aliased triangle wave at 220 Hz
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Another definition of the triangle wave, with range from -1 to 1 and period 2a is:
- where the symbol represent the floor function of n.
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:
See also
Sine, square, triangle, and sawtooth waveformsReferences
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