Suppose I have a very low frequency pattern of sound. For example a 10 second music file. Then 10 seconds of silence. Then the same 10 second music file repeated again. The whole sequence repeats every 20 seconds so it would make sense to say it has frequency 1/20 Hz.
The pattern is being played in the presence of a lot of noise. And for simplicity we assume the noise does not have the same sort of repeating structure as the music, at least on the same scale.
You would expect if we gather a large number of 20 second samples it should be possible to process them such that the noise cancels out and we recover the music. A less optimistic goal would be to simply determine if there is a 20-second recurring track behind the noise. In the second case we don't care about recovering the music. We just care that a repeating pattern exists.
Is there anything in Fourier theory or in signal processing practice that suggests this is possible? Naievely I'd expect something to show up low down on the Spectogram if we set the time sampling window to be on the order of minutes. But I have (a) no reason to suspect this should be visually interesting as a long stripe down at the 1/20 Hz range and (b) no reason to suspect standard DFT tools would even detect a standing wave of such low frequency.