3 ms·
What tacos is trying to say is that in an FFT, you will have the same number of samples in the time domain and the frequency domain (weeeeellll, I'm simplifying
by demallien 12y ago
What tacos is trying to say is that in an FFT, you will have the same number of samples in the time domain and the frequency domain (weeeeellll, I'm simplifying a bit, half of those 'frequency domain' samples are actually phase information, so you really have half as many frequency domain samples as you do time domain). So, if you wish to have a high resolution in the frequency domain, implying lots of samples, you're going to have a total sample time that is quite long, and you won't be able to say exactly when each of the different frequencies was actually present in the sound.
Take a concrete example. Let's assume that I have a recording in PCM at 44.1kHz, and I want to see all of the frequencies present, to a resolution of 10Hz. Nyquist tells us that we only have 22.05kHz of signal present in the sample (well, one can hope, otherwise if the recording didn't filter out everything above that when coding to PCM, we're going to have a mess of aliasing going on, which is outside the scope of this post - just assume the person doing the encoding knew what they were doing, mkay...). So, 22.05kHz. And we want a resolution of 10Hz, so we're going to need 22.05kHz / 10Hz = 2205 samples.
Of course, we actually need double that in the time domain (we throw away the phase information remember), so we need 4410 samples in the time domain to get our 2205 samples in the frequency domain. 4410 samples at 44.1kHz sampling is equal to 0.1 seconds.
If I decide that I want a better frequency resolution, say down to 1Hz, then you quickly arrive at the conclusion that you will need a full second of samples. In other words, your resolution in the time domain has decreased as you improve the resolution in the frequency domain.
You can improve a bit on this situation by using a sliding window with a carefully chosen windowing function. The frequency information will still be smeared out in time, but the windowing function reduces the amplitude of a frequency the further it is from the centre of the sampling window, which sharpens up the smear a bit.