Fourier Analysis: Signal Representation & Non-Monochromatic Light/Sound

[cscott]

From what I understand, I can use Fourier Analysis to represent a periodic signal using a sum of sine waves. However, isn't this just a mathematical tool? Can I take any non-monochromatic light source and use Fourier Analysis to break it into a sum of the physically meaningfuly frequencies it's made of up? What about for sound?

 

[nrqed]

From what I understand, I can use Fourier Analysis to represent a periodic signal using a sum of sine waves. However, isn't this just a mathematical tool? Can I take any non-monochromatic light source and use Fourier Analysis to break it into a sum of the physically meaningfuly frequencies it's made of up? What about for sound?

It is a mathematical tool that can be applied to any function (that is physically reasonanble..there are some restrictions which are almost never of concern in physical applications) ...and if you include Fourier transforms, the function does not even have to be periodic.

Of course it can be applied to sound waves, electromagnetic waves, electric signals, the beating of a heart, and on and on. It is even applied to the probability waves of quantum physics.

 

[kyle8921]

Yes, Fourier Analysis is a mathematical tool that allows us to represent a periodic signal using a sum of sine waves. However, this tool has practical applications in the fields of physics and engineering, where it is used to analyze and understand complex signals such as non-monochromatic light and sound.

In the case of non-monochromatic light, Fourier Analysis can be used to break down the light into its constituent frequencies, which can then be used to understand the physical properties of the light source. This can be particularly useful in fields such as spectroscopy, where the analysis of light spectra can provide information about the composition and structure of materials.

Similarly, in the case of sound, Fourier Analysis can be applied to break down a complex sound wave into its component frequencies, which can then be used to understand the physical properties of the sound source. This can be useful in fields such as acoustics, where the analysis of sound spectra can provide information about the source of the sound and its surrounding environment.

In summary, Fourier Analysis is not just a mathematical tool, but a powerful tool that has practical applications in understanding and analyzing complex signals in various fields of science and engineering.