Comments on: Spectral analysis with Fast Fourier Transform in Actionscript

By: stephan

stephan — Tue, 14 Apr 2009 20:46:08 +0000

Sources are available, see this blog post. I haven't had time to look further into Alchemy yet, but it still is on my wanted list. Pixel Bender might be an option, but the lack of loops might make its use very limited, as that would make it only suitable for short samples. But it's worth looking at, sure!

By: jkozniewski

jkozniewski — Tue, 14 Apr 2009 18:56:37 +0000

Hi,

You’ve mentioned Alchemy as an option of
computing FFT – have you made any tests if
it’s much faster than pure as3 ?
I’m wondering if PixelBender may be helpful here
i know that lack of loops support etc. would be a problem
but hm…. any thoughts on this ?
Are you planning to release sources any time soon ?
Regards !

By: stephan

stephan — Sun, 01 Mar 2009 19:29:17 +0000

Hamming window is next on the todo list To do 2-way FFT (with fun stuff in the middle) you have to do overlapping Hamming windows, otherwise you get an extra sound that can be quite nasty. The frequency of that added sound is the same as that of the base frequency of the FFT, so usually around 50Hz, and shaped like a square or a pulse. So basically you get a low sharp buzz extra. Problem is only that this requires the double number of transforms, so it’s twice as hard on the CPU. With my current findings that still leaves 20ms to do fun stuff. The Hamming window itself isn’t hard on the processor, as the curve can be precalculated and applied in a single run over one buffer.

By: vFragosop

vFragosop — Sun, 01 Mar 2009 18:30:55 +0000

Hmm.. that’s interesting..

I was talking to Ben Houston, the responsable for FFT algorithms in Math.NET library, and he suggested me the Hamming Function.

I don’t if Adobe took one of those Window functions in care. It’s an interesting topic anyway.

[Wiki has a great article about Hamming].

By: stephan

stephan — Thu, 26 Feb 2009 07:10:05 +0000

Actually that’s not a mistake, but the standard way a Fourier Transform works. My code does exactly the same thing, except that it’s more flexible in choice of resolution over time vs. frequency. The linear nature of the Fourier Transform (each ’slot’ takes up 1 frequency that is a multiple of the base frequency) is what makes it less suitable for accurately analysing audible content, as the human ear functions logarithmically. However it’s not very difficult to change the code such that it groups frequencies, with larger groups towards the higher frequencies. It’s basically a kind of post processing that is not very CPU-intensive. It does reduce the resolution in high frequencies, but as you say, that is already very high anyway. Unfortunately it doesn’t increase the resolution in low frequencies.
One way to increase the resolution in low frequencies, is by increasing the sample size. As the base frequency is a factor of the sample size, it will get half for each doubling of the sample size. However, that implies also halving the time resolution. So the more we wish to know about which frequencies occur in a sound, the less we know about when those frequencies occur. It’s a direct result of Heisenberg’s Uncertainty Principle.
In mathematics there’s another transform, called Wavelet Transform, that is a lot less well known than the Fourier Transform, but that does much better justice to the logarithmic nature of sound. There’s a number of explanations about that on the net, but they’re mostly quite mathematical, and haven’t found much application outside of science yet. So it seems like we’re stuck with Fourier for the time being.

By: vFragosop

vFragosop — Thu, 26 Feb 2009 00:37:22 +0000

That’s nice news! Thanks for reply.

One big mistake Adobe made, at least in my opinion, is dividing all the frequencies in 256 equal groups of N frequencies.
Normally, spectrum analyzers grows exponentially the N number of frequencies inside the groups.

0-20, 20-60, 60-100, 100-180, 180-320, 320-640… and so on..

This way, the graph looks more natural, since there’s just a few low frequencies and thousands of high frequencies.

By: stephan

stephan — Mon, 23 Feb 2009 07:15:58 +0000

I haven’t been adding much to it lately, but I’ve cleaned up the code, so I can upload the sources. Stay tuned, coming up soon!

By: vFragosop

vFragosop — Mon, 23 Feb 2009 05:15:58 +0000

Well, it’s just what i’m looking for.
Since computeSpectrum curves aren’t precise, having a decent fft code would be really great.
Hoping you’re still working on that. I could do it for myself, but my math skills are the same as an eight year old boy.
Please, let me know about any progress.

By: Shui

Shui — Wed, 28 Jan 2009 09:57:48 +0000

This is exactly what I was planning to do.
I’m looking forward to your results.