Is a “rolling” FFT possible and could it be of use?

Question

Lately I have been experimenting with audio and FFTs, specifically the Minim library in Processing (basically Java, not that its particularly important for this question). What I have come to understand is that with a buffer/sample size N and sample rate K, after performing a forward FFT, I will get N frequency bins (only N/2 usable data and in fact Minim only returns N/2 bins) linearly spaced representing the spectrum from 0 to K/2 HZ.

With Minim (as well as other typical FFT implementations) you wait to gather N samples, and then perform the forward transformation, then wait for N more samples, and so on. In order to get a reasonable frame-rate (for audio visualizations, beat detection, etc.), I must use a small sample size relative to the sampling frequency.

The problem with this, though, is that a small sample size results in a very low resolution for the low end of the spectrum when I compute logarithmically spaced averages (Since a bass octave is much narrower than a high pitched octave).

I was wondering if a possible way to squeeze more apparent resolution would be to perform FFTs more often than every N samples on a slightly larger sample size than I am currently using. (I.E. with input buffer of size 2048, every 100 samples, add those samples to the input buffer and remove the oldest 100 samples, and perform a FFT). It seems like this would possibly create a rolling-average type of affect (which I can live with) but I'm not too sure.

What would be the pros and cons of this approach? Are there any other ways I could increase my apparent resolution while still being able to do real-time visualization and analysis?

Answer 1

That approach goes by the name Short-time Fourier transform. You get all the answers to your question on wikipedia: https://en.wikipedia.org/wiki/Short-time_Fourier_transform

It works great in practice and you can even get better resolution out of it compared to what you would expect from a rolling window by using the phase difference between the fft's.

Here is one article that does pitch shifting of audio signals. The way how to get higher frequency resolution is well explained: http://www.dspdimension.com/admin/pitch-shifting-using-the-ft/

Answer 2

We use the approach you describe, which we call overlapping, to make sure all the rows of a spectral waterfall are filled in. Overlap can be used to provide spectra that are spaced as closely as a single sample interval.

The primary disadvantage is the extra processing to produce all those spectra.

On the positive side, while the time resolution of each spectra is still constrained by FFT size, looking at closely spaced adjacent spectra seems to provide a kind of a visual interpolation that, I think, lets you see the data with higher precision.

Answer 3

One common way this is done is to use multiple lengths of windowed FFTs on the same data, short FFTs for good time resolution, much longer FFTs for better frequency resolution of lower frequencies. Then the problem for visualization becomes picking the best FFT result out of several possible at each plot point (such as the highest contrast sub-block, etc.) and blending them attractively.

Most modern processors (in PCs and mobile phones, etc.) can easily do multiple lengths (dozens) of FFTs still in real-time for audio.