Why would a time shifted signal have a higher maximum frequency than an unshifted one?
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!