1. Approaching a sawtooth wave

We have that for the function of a saw tooth wave through a Fourier series, it develops...

$S(t) = \frac {2}{\pi}\sum_{k=1}^{\infin} {(-1)}^{k} \frac {\sin (2\pi kft)}{k}$

However, another way of approaching this function is through...

$S(t) = \frac {|sin (t)|} {tan (t)}$

Note: This trig. function in a "inverse saw tooth wave"

Realizing there exists a "bend" between minima's and maxima's, how can I approach this trigonometric function to produce a sawtooth wave? Curious.

2. Re: Approaching a sawtooth wave

Originally Posted by brianjesusdiaz
We have that for the function of a saw tooth wave through a Fourier series, it develops...

$S(t) = \frac {2}{\pi}\sum_{k=1}^{\infin} {(-1)}^{k} \frac {\sin (2\pi kft)}{k}$

However, another way of approaching this function is through...

$S(t) = \frac {|sin (t)|} {tan (t)}$

Note: This trig. function in a "inverse saw tooth wave"

Realizing there exists a "bend" between minima's and maxima's, how can I approach this trigonometric function to produce a sawtooth wave? Curious.
1. That is not the Fourier series of a saw tooth wave.

2. In the second there is nothing to converge.

CB