Logarithmic spacing of FFT bins
- by Mykel Stone
I'm trying to do the examples within the GameDev.net Beat Detection article ( http://archive.gamedev.net/archive/reference/programming/features/beatdetection/index.html ) I have no issue with performing a FFT and getting the frequency data and doing most of the article. I'm running into trouble though in the section 2.B, Enhancements and beat decision factors.
in this section the author gives 3 equations numbered R10-R12 to be used to determine how many bins go into each subband:
R10 - Linear increase of the width of the subband with its index
R11 - We can choose for example the width of the first subband
R12 - The sum of all the widths must not exceed 1024
He says the following in the article: "Once you have equations (R11) and (R12) it is fairly easy to extract 'a' and 'b', and thus to find the law of the 'wi'. This calculus of 'a' and 'b' must be made manually and 'a' and 'b' defined as constants in the source; indeed they do not vary during the song."
However, I cannot seem to understand how these values are calculated...I'm probably missing something simple, but learning fourier analysis in a couple of weeks has left me Decimated-in-Mind and I cannot seem to see it.
