• Question: Do you know what Fourier series are in mathematics?

    Asked by to Ian, Naomi on 27 Jun 2014. This question was also asked by .
    • Photo: Naomi Osborne

      Naomi Osborne answered on 27 Jun 2014:


      I’ve used a machine called Fourier Transform Infrared Spectroscopy to analyse chemicals. This is where infrared wavelengths are passed through a material which excites the bonds in the chemical – the amount of infrared that’s been absorbed as well as the energy that’s released from the excited bonds is used to produce a graph. From this graph you can tell if the chemical is what you think it is – and Fourier Transform is used to produce it. But I’m not sure how – it’s some complicated maths! Hopefully someone who’s good at maths can help on this one!

    • Photo: Ian Stephenson

      Ian Stephenson answered on 27 Jun 2014:


      Absolutly!!!!

      While it might not seem particularly obvious Fourier is a really fundamental part of computer graphics. Most of the work I’ve done has depended on it, to some degree.

      The basic idea of Fourier is that rather than drawing a graph as values which change over tim, it can be made of up different frequencies.

      Imagine looking at an audio signal (in GarageBand or something). It would be a squiggle line that changes over time, representing the strength of the audio over time.

      However now imaging taking that same audio and drawing a bar graph showing how much bass, mid and treble there is (its spectrum).

      That’s exactly what a Fourier transform is – it converts between the waveform and the spectrum, and back again.

      It turns out we can do exactly the same thing to an image – fourier transform it to find its spectrum. We can then manipulate it in “frequency domain” (the spectrum) before transforming it back to a regular signal: “time/space domain”.

      For example if you want to blur an image, its a LOT of work to do a nice blur on the raw image, but if you Fourier transform it to “frequency domain” you can remove all the high frequencies really easily, and produce a really pretty blur – imagine turning down the high frequencies on some music.

      If you draw a line on the screen it can have jaggy edges, and again we can use Fourier to understand why this looks bad and how to make it better. We call this Anti-Aliasing.

      The work I did on Motion Blur was about removing the right set of high frequencies from the image, and keeping some of the others.

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