Why would a time shifted signal have a higher maximum frequency than an unshifted one? I´m reading the book Numerical Simulation of Optical Wave Propagation by Jason Schmidt.
In section 2.1-2.2, the author performs the FFT of a centered and a shifted Gaussian pulse and makes the statement that the time shifted signal has a higher maximum frequency than the unshifted one. For that reason more samples are required in getting the shifted signal spectrum.
Why does the time shifted image have a higher highest frequency? I don´t understand.
How much I should increase my sampling rate for a given time shift?
Thanks for your attention.
Carolina Rickenstorff
I was able to take a look at the book.
You are right it says: &quot;The highest significant frequency in the shifted Gaussian signal is higher than that in the centered Gaussian&quot;.  I think this is misleading.
Looking at Figs 2.2 and 2.3 I can only think that the author is saying that in Fig 2.3 the phase is &quot;significant&quot; across the whole spectrum, while in Fig 2.2 phase is zero everywhere.
However, the magnitude curves are identical. If magnitude is zero then phase is irrelevant. (i.e. atan (small/small)).  The required sample interval is governed by the magnitude spectrum. That is the required sample interval is not affected by a simple time shift, as stated by the above commenters. If this wasn't the case, then real-data analog-to-digital conversion would be pretty difficult!