# Time resolution of the Short Time Fourier Transform (STFT)

I'm struggling to figure out how the time points of an STFT are calculated, and I can't find a definitive answer. Let's say I have a 4Hz stationary signal and I'm going to use a 64 second window with 3 second overlap. So that's a 256 point window and a 12 point overlap.

Assuming I start at time=0, take the first 64 seconds, and perform the FFT/Power Spectrum Density/etc... Can I then say that is the value at t=32? Is the next window, after the 3 second slide localized at t=35, and so on?

If so, and I really wanted to start at t=0, would I then effectively start at t=-32, fill the first 128 points with zeros and take the first 128 points from my signal, thus centering on t=0?

• If you have a 4 Hz signal then you need to sample it at a rate > 8 Hz (Nyquist/Shannon). Or do you really mean a 4 Hz sample rate (assumes signal bandwidth < 2 Hz) ? Mar 15, 2012 at 10:39

There is no single "time instant" associated with a short-time Fourier transform. As you noted, if you perform a DFT on data collected from $t = 0$ to $t = 64$, then there isn't a single point in time that you can associate with the output from that DFT; it is a function of every sample in its time interval.