MHB Uncovering the Hidden Significance of Fourier Series in Physics and Engineering

[matqkks]

If we have a simple periodic function (square wave) which can be easily written but the Fourier series is an infinite series of sines and cosines. Why bother with this format when we can quite easily deal with the given periodic function? What is the whole point of dealing this long calculation of the Fourier coefficients? Does it tell us something that is useful?

 

[Kiwi1]

In many areas of physics and engineering you will find that the Fourier components can actually be measured. Arguably they actually exist.

For example if you inject a 50 Hz square wave of current into an electrical circuit and then measure that current with a test instrument that is only sensitive to 150 Hz then the reading on the test instrument will match the value found for the third harmonic by Fourier analysis.

Similarly if you pass a square wave signal through a filter that allows low frequencies to pass more easily than high frequencies then you can decompose the signal into Fourier components, work out how much each component is attenuated by the filter and then add the attenuated components back together to work out what the signal shape will be after passing through the filter.

Maybe soldiers walk across a bridge in step with each other. If the bridge is resonant at one of the harmonics of their walking frequency then the bridge can be destroyed. The Fourier components have very real consequences.