Introduction
If there was ever a mathematical idea that applies itself to almost everything in everyday life but is almost unknown outside the scientific world, the Fourier Transform has to be it.
Dreamed up by the French mathematician and physicist Jean-Baptiste Joseph Fourier in 1822, the Fourier Transform is so useful that you will probably be using a piece of technology that implements it right now as you read this blog post. But what does the Fourier Transform do and why am I writing about it in a blog which is meant to be for music and recording?
“The Fourier Transform decomposes a function of time into the frequencies that make it up” -Wikipedia
Put simply, the Fourier Transform takes any every day signal, sound for example, and tells you which frequencies (notes) are present in that signal.
“So what?” I hear you say.
“Ahaaaaa!!!!” I reply. The moment we know what frequencies are present in our signal, we can analyze, understand and manipulate that signal in an almost unlimited number of ways.
If you’re wondering just what use that is to us in the music world, then look at the following list of just a small number of its applications:
- EQ Filters
- Noise Reduction Tools
- Pitch Correction Tools
- Guitar Tuners
- Streaming Media Players
- MP3 Files
- Spectrum Analyzers
- Vocoders
- Voice Recognition
… and many many more
The Fourier Transform, or rather my lack of understanding of how it does what it does, has been something of an irritation for me ever since I was studying for my Electrical and Electronic Engineering degree back in my days at university. It was the maths that really got me. My eyes would always begin to glaze over the moment the amount of Greek on the lecturer’s blackboard began to outweigh the amount of English and I would simply lose the plot. I once went up to one of my lecturers and asked him to draw a picture of what he was trying to explain as all the Thetas and Omegas meant nothing to me. However, no picture was forthcoming, and understanding eluded me.
Over my years working as an Electronics engineer, I’ve locked horns with the business end of the Fourier Transform more than once. By first using it, then having to implement it in different projects, each time I met it, my understanding grew a little more. Lately it has been very useful to me in my recording work and I have decided that now, finally, is the time to lay my demons to rest and try and crack it once and for all!
With research and scripting now complete, the filming stage has commenced. To get a taster of the style of video that will appear in the course, Click Here to watch a video on Euler’s Identity which will introduce the module on on complex numbers, the language used to express the Fourier Transform. Unfortunately, I cannot promise to not use any maths at all in the course (at the end of the day, the Fourier Transform is a mathematical formula) but every equation will be illustrated by diagrams and animations to explain how and what the maths is doing and how it affects the real world.
Click here to reserve your free sample module from the course which will be emailed to you the moment the course goes live.
I have watched many hours of videos on Youtube which attempt to explain the Fourier Transform, but I have never yet found one that does so in the visual way my brain craves so much. Hopefully I will finally succeed in doing that in mine and if you, dear reader, come away from the video course a little wiser on the subject than you went in, then I will have succeeded in my endeavors.
It is going to take me some time to finish researching, scripting and editing the video, so I am going to use my blog as a quick way to post my progress, share with you the things that I’m learning and of course link to the course once it is complete.
Over the next few blog posts, I am going to be ducking under the bonnet of the Fourier Transform, finding out exactly how it works, and putting that knowledge to use by seeing how its different aspects are echoed in the tools we use. So for instance, next time you’re looking at the bars of your spectrum analyzer plugin dancing around in time with the music you’re playing, when you flick your eye over to some of the parameters your analyzer lets you play around with, you’ll have a better idea of what things like the “FFT Size” setting means and how changing the value contained therein can help you better find that annoying frequency you’re looking for.
So here’s to a Bon Voyage together and don’t forget to comment if you have any questions or suggestions that could help the finished product.
