Time frequency resolution is a long debate in the DSP communities.
But modern models has proved that the resolution isn't limited by the DFT because usually we know more about the signal but its bandwidth.
Remark: Usually the counter argument is the Uncertainty Principle. In this context we should understand that it holds given all the knowledge we have is limited to the bandwidth of the signals.
Resolution, or the ability to see different signals as different components, is a function of the knowledge of the signal in question.
If you know nothing, then you probably have zero resolution as you can not infer anything form what you see.
If all you know is something about the signal bandwidth, then you're limited by the properties of the DFT once you apply it.
The magic happens when you add more information to the problem. Information either on the signal, the other signals or the properties of the system itself which is the case in the video.
By skimming through the video I'd describe their method as following:
- Apply DFT.
- Since the time interval (Time window) is known and modeled as multiplication with the original data one could infer the data in the DFT is a result of a convolution of the signal of interest and the DFT transform of the window.
- The above model leaves us with a Deconvolution problem. Which in many cases can be solved.
- Solving the deconvolution model using iterative method.
- Mitigating the noise amplification due to the deconvolution.
The nice thing about this model is that it almost, at least not explicitly, assumes nothing about the data. But if it almost assumes nothing, how can it beat the known limitations.
Well, there are assumptions which are buried in the deconvolution process. To name few:
- The SNR is quite high.
- The signal of interest is following the model of the deconvolution. Usually it means it is LPF, In many other cases smooth, etc...
- The artifacts by other surrounding signals are limited (Namely they don't match the "high pass pattern" of the deconvolution process).