# Friday Math Movie – Sine Wave to Square Wave using Fourier Series

By Murray Bourne, 14 Nov 2008

We learned about sine waves in elementary trigonometry:

The idea behind the **Fourier Series** is to add sine curves with different amplitudes and frequencies and the resulting curve can be either a square wave, a sawtooth wave or many other interesting periodic shapes. You can see more on this concept in this Introduction to Fourier Series.

This week’s movie begins with a pure sine wave tone and then the other sine curves are added to it to produce something very close to a square wave (with the odd wiggle here and there) as the number of added curves becomes very large.

**Warning:** The final square wave tone may be pretty loud.

See the 3 Comments below.

26 Nov 2008 at 1:14 pm [Comment permalink]

Your work is very awsome..^^ please show us your solution in solving higher dimension^^

16 Mar 2011 at 9:46 pm [Comment permalink]

Sir.

building a square wave from sine wave is easy as square wave is periodic.how to claculate fourier series of

y=x? it dont have period as it doesnt repeat itself.

17 Mar 2011 at 2:37 pm [Comment permalink]

@gagangc: The original function has to be periodic – otherwise you can’t form a Fourier Series!