Re: Time scaling property of Fourier transform
- From: "cyrus0824" <ca48@xxxxxxxxxxx>
- Date: Thu, 08 Oct 2009 09:17:04 -0500
Hi,in
I have a question about the time scaling property of the Fourier
transform.
One can find two different formulas of the time scaling property in the
literature. These formulas are:
1. x(at) <-> 1/|a| X(f/a)
2. x(at) <-> 1/a X(f/a)
The first formula uses the absolute value for 1/a, the second one does
not use the absolute value for 1/a.
In fact, when I try to prove this property using the substitution rule
the integral I obtain the second formula. Could somebody explain me
please where the absolute value for 1/a comes from in the first formula.
Anatol
Hi Anatol, this may be very late to reply, but I came across your thread
after having puzzled over this one myself. I believe that when you do your
change of variables in the integral, you have to take the determinant of
the Jacobian...in this case that becomes 1/|a|...perhaps this is a more
fundamental way than was described earlier (which attempts to verify from
other relationships...)
Cyrus.
.
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