4 ms·
Human Time-Frequency Acuity Beats the Fourier Uncertainty Principle
- jstanley 13y agoIntriguing title and abstract, but I don't really understand what this means, or its implications. Can anyone summarise for a layman?
- dekhn 13y agoSure. In general, if you have a time-domain signal (like a music file) you can break it up into little pieces and compute the frequencies in the pieces. For example, you could take a small part of a song, and say "this part of the song is a 400hz sound for 0.3 seconds". This is typically done with an algorith called the fourier transform, which is used to convert between time-domain and frequency-domain signals. However, as you make smaller and smaller time fragments, you pay a cost- less accuracy in the estimate of the frequency (because you have fewer samples to work with). In general, this relationship could be expressed as "accuracy of frequency * accuracy of time = a constant". Presumably, what they found is that human's auditory system is not doing simple operation like that but has the ability to pick out frequencies in short time segments (IE, while listening in real time) with better resolution that a short-time fourier transform. IE, somebody could estimate the frequency of a pitch faster than what you'd expect by the equation I gave above. None of this violates the laws of physics; the ear and brain would just need to do a different type of analysis. Probably more like wavelets.
- jstanley 13y agoGotcha, thanks. Is there a possibility that overlapping DFT windows could get you increased accuracy? I mean, instead of looking at each 0.3s individually, you could look at 0.3s segments, starting each segment 0.1s after the previous segment started so that there is some overlap.
- dekhn 13y agoI wish I knew.