Triangle wave
From Freepedia
A triangle wave is a basic kind of non-sinusoidal waveform named for its triangular shape.
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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), and so its sound is smoother than a square wave and is nearer to that of a sine wave.
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 <math>\pi</math>), 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:
- <math>x_\mathrm{triangle}(t) = \frac {8}{\pi^2} \sum_{k=1}^\infty \sin \left(\frac {k\pi}{2}\right)\frac{ \sin (kt)}{k^2}</math>
| Image:Gnome-speakernotes.png | Triangle wave sound sample (info) |
| 5 seconds of triangle wave at 1 kHz | |
| Problems listening to the file? See media help. |
