Triangle Wave Article Index for
Triangle
Limousines in
Triangle
Website Links For
Triangle
 

Information About

Triangle Wave




Like a Square Wave , the triangle wave contains only odd Harmonic s. 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 (4nāˆ’1)th harmonic by āˆ’1 (or changing its phase by \pi), 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:

:x_\mathrm{triangle}(t) = rac {8}{\pi^2} \sum_{k=1}^\infty \sin \left( rac {k\pi}{2} ight) rac{ \sin (kt)}{k^2}


SEE ALSO

, Square , Triangle , and Sawtooth waveforms]]