Series expansion of the signum function of sine

[carbon9]

Hi,

I just read a physics paper and there it expands signum of a sine function as below:


sgn(sin(wt))=(4/pi)*{sin(wt)+(1/3)*sin(3wt)+(1/5)*sin(5wt)+...}

How can we expand sgn(sin(wt)) like this?

Thanks.

 

[jbunniii]

http://mathworld.wolfram.com/FourierSeriesSquareWave.html