TITLE: Intuition behind the scaling property of Fourier Transforms
QUESTION [7 upvotes]: I had a course in PDE last year where we used fourier transforms extensively; I understand the rules of manipulation and can prove the scaling theorem directly from the definition using a substitution, but I don't really have any good intuitive argument as to why "compressing" a function causes an expansion of its fourier transform, and vice versa.  I have been trying to gain solid intuition behind the various properties of the fourier transform; but have not gotten far with this one.  If anyone knows of a website / book or a slick argument that covers this; it'd be greatly appreciated.  Thanks!

REPLY [15 votes]: Intuitively, One way to think about it is that compressing a sinusoid, increases its frequency.  So compessing a sum of sinusoids will expand the frequency spectrum.