# Help with a rather specific implementation of FFT Library?

So, I guess what I'm trying to do here is properly understand the FFT library posted here by Open Music Labs, done in C++. I believe I understand the Fourier transform, but the FFT has some nuance that I'm not quite familiar with. From what I understand, the FFT takes a amplitude vs. time signal and transforms it into its constituent frequencies like a normal Fourier transform, but it only does so at given points that break down the signal into the Arduino's clock speed divided by the number of bins decided on, for the sake of efficiency. Thus each bin actually accounts for a number of frequencies that is also equal to the clock speed divided by bin number. I'm correct so far, right?

So here's my question. I have a very specific application of the FFT that requires reading only frequencies at roughly 0-100 Hz. Everything else I don't need, and I want to know how to achieve such high resolution. I imagine that because the number of bins seems to be capped at around 512, that there must be some sort of way to decrease the clock speed to an exorbitantly low number in order to read these frequencies. How might I go about doing that? Or maybe there is a better way to apply the transform to the data at such low frequencies through some other method outside of FFT?

Second, I'm wondering how performing multiple FFTs simultaneously will affect performance, and if there is some way I can export this data to another program in order to do the heavy lifting regarding data storage, seeing as I imagine performing many FFTs all at once will decimate the available memory on the Arduino itself if all of those values aren't being kept on my computer.

Thanks in advance for any insight you guys might be able to provide

• You are mixing things. There is the “Fourier transform” (FT), the “discrete Fourier transform” (DFT) and the “fast Fourier transform” (FFT). DFT is a generalization of FT for finite sets of data points. FFT is an efficient algorithm for computing a DFT when the number of data points is a power of two. The binning is a feature of the DFT arising from the finite nature of your data set, it has nothing to do with efficiency. “0-100 Hz” is a frequency range, not a resolution. What resolution do you need? – Edgar Bonet Mar 4 '16 at 9:20