# math topic related to orthogonal frequency division multiplexing (OFDM)

#### donut

Joined May 23, 2012
51
Reading about OFDM and it states that orthogonal frequencies can exist and not interfere with one another because of the fact that a sinusoidal wave multiplied by another sinusoid of a different harmonic is 0.

How can you demonstrate mathematically that a sinusoidal wave multiplied by another sinusoid of a different harmonic is 0? Unfortunately the book does show a mathematical expression.

#### WBahn

Joined Mar 31, 2012
26,056
By doing the math.

First, however, you need to realize that when they say the result is zero, they mean that the average value goes to zero over a sufficiently long period of time. This is because the average value is exactly zero over any time period that is an integral number of periods of both waveforms.

Consider

x = sin(mwt)
y = sin(nwt)

Now consider

z = x*y

What is the average value of any period T that is a multiple of the periods of both x and y?