Sawtooth Wave ○꠹｜appendage｜___｜20260628174208-01-•

Sawtooth wave	…
A bandlimited sawtooth wave1 pictured in the time domain (top) and frequency domain (bottom). The fundamental is at 220 Hz (A${}_3$).	…
General information	…
General definition	$x(t)=2\left(t-\lfloor t+\frac{1}{2}\rfloor \right),t-\frac{1}{2}\notin \mathbb{Z}$
Fields of application	Electronics, synthesizers
Domain, codomain and image	…
Domain	$\mathbb{R}\setminus \left\{n-\frac{1}{2}\right\},n\in \mathbb{Z}$
Codomain	$\left(-1,1\right)$
Basic features	…
Parity	Odd
Period	1
Specific features	…
Root	$\mathbb{Z}$
Fourier series	$x(t)=-\frac{2}{\pi }\sum _{k=1}^{\infty }\frac{{\left(-1\right)}^k}{k}\sin \left(2\pi kt\right)$

(echo:: @ ᯤ)

Footnotes

1. Kraft, Sebastian; Zölzer, Udo (5 September 2017). “LP-BLIT: Bandlimited Impulse Train Synthesis of Lowpass-filtered Waveforms”. Proceedings of the 20th International Conference on Digital Audio Effects (DAFx-17). 20th International Conference on Digital Audio Effects (DAFx-17). Edinburgh. pp. 255–259. ↩