If all the harmonics composing a the signal are shifted by the same amount, this would be the same as sampling later or earlier in time. I think.
Take a simple pulse train as an example.
If Fourier is performed when the pulse is high for time t after 0, and flat for time t before the 0 it will have odd symmetry and only sin harmonics. If the same signal was sampled differently with half of the pulse left of y-axis and other half right of it, it would have even symmetry and contain only cos terms.
Each time actual signal is the same, just its Fourier representation is different.
Difference between these is only shifting all harmonics by 90 degrees. Why is Hilbert filter different in those regards?
I know square wave passed through Hilbert filter produces sideways curly braces like shape, so my fundamental understanding of something is wrong. Thanks for help.