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Comment by omegalulw | Hacker News Reader

I'm confused about the first point. Is it simply restating that Fourier coefficients are complex numbers?

Basically yes, but his statement is mixing up things a bit. The Discrete Fourier Transform transforms a complex vector of length N to another complex vector of length N. In the latter, each of the N elements corresponds to a frequency "bin" and, like complex numbers in general, can be represented either by a real and an imaginary part (like Cartesian coordinates), or by a phase (==atan(Im/Re)) and a magnitude (==sqrt(Re^2+Im^2)) (like polar coordinates). Obviously, whichever you choose, you need both components for unambiguous representation.

I made a video about the FFT a few months ago that I hope might offer another perspective to help understand these concepts: https://www.youtube.com/watch?v=iyjIVSnrPSo&t=271s

The FFT segment starts at 4:30 (linked), the specific part about phase and magnitude is at 5:45, and the part about negative vs. positive frequencies starts at 6:35.

Making quality animations drive the point home is not so easy to pull off, so thanks for sharing. Both interesting and impressive.

Thanks for taking a look!

Very nice video, the 3d animations and colors make it look very professional. What tool(s) did you use to create the video? Ruby? OpenGL? A custom synthesizer?

All of the above. I have a custom animation system written in Ruby that talks to some visualization software I wrote using C and OpenGL. The synthesizer is also in Ruby, and the core audio code for that is on GitHub. I use Inkscape for overlay graphics, and reboot into Windows for VEGAS for editing and compositing.

...and thanks for checking out the video!

I've never tried Ruby, but would love to try out that synth and its visualizations. Do you plan on making them available?

You can try the synthesizer and other audio code if you're using Linux.

Here's an earlier version of the synthesizer (licensed under AGPL3). The MIDI CCs for controlling different parameters are listed in the source code. You'd want to clone the repo, run through the installation instructions in the mb-sound repo, do a bundle update mb-sound, then run bundle exec bin/complex_synth.rb. https://github.com/mike-bourgeous/mb-surround/blob/3823de44a...

Here's the core sound repo (licensed under BSD) with some examples for getting started: https://github.com/mike-bourgeous/mb-sound

I don't plan on making the visualizations available, in part because the system is too convoluted and they probably only work in my specific environment.

Very nice, thanks a lot, will try it out. Does the synth have gui?

No, just MIDI CC controls. I control it with a hardware keyboard, but anything that can generate note events and MIDI CC changes can be wired in with jackd and a patchbay like Patchage.

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