Dose it can be used for real-time application in processing low frequency signal?

[GUIMINLONG]

First, I would like to express my sincere gratitude and respect for the contributions of the authors of this project.

Below is my question.

When I tried to use the output of fcwt input to my model, I found that to obtain a clear spectrum on low frequency, the signal input to fcwt should long enough. For example, if the target frequency is 20 Hz， the duration of the input signal should larger than 1/20Hz=0.05 s. Otherwise, lower frequency spectrum will blur. Dose this means that the conflict between frequency resolution and time resolution still exist?

Or is that mean, for the processing low frequency(f) signal, the input segment duration delta_t should always satisfy that delta_t>1/f. And the high efficient of fcwt only ensure real time processing of with frequency satisfy f>1/delta_t. (Because Heisenberg uncertainty principle?). From what I know, one of the advantage of cwt above stft is it high frequency resolution at low frequency, if limitation of Heisenberg uncertainty still hold, what the advantage of fcwt above stft for real-time using, especially for the processing of low frequency signal.

My question may seems weird, but it is what confuse me now. Any one familiar with are welcome to share your opinion.

[fastlib]

The Heisenberg uncertainty principle is something we cannot break. In fact, no algorithm that does single passes can circumvent this and those that claim they can do better (e.g., superresolution) are wrong. It's a core principle in physics. The only way to achieve super-resolution is by doing multiple CWT passes (see this paper). Yet, even then, it's questionable if the output of those algorithms actually reflect physical meaning.

That aside, the advantage of CWT over STFT has nothing to do with the Heisenberg uncertainty principle, it has to do with the fact CWT does not use fixed size windows to analyse the signal. As such, CWT 'adapts' its resolution to the frequency its analysing. Higher frequencies are analysed at a higher time resolution. STFT cannot do that. STFT only looks at a small part of the signal and then performs a FFT that has a fixed time resolution for all frequencies. Consequently, when you want to analyse low frequencies that need, following Heisenberg uncertainty principle, large time windows, your time resolution in the higher frequencies also diminishes and vice versa.

Does this answer your question?