# Re: Time scaling property of Fourier transform

Hi,

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
in

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

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.

.

## Relevant Pages

• Re: Time scaling property of Fourier transform
... One can find two different formulas of the time scaling property in the literature. ... The first formula uses the absolute value for 1/a, the second one does not use the absolute value for 1/a. ... the integral I obtain the second formula. ...
(comp.dsp)
• Time scaling property of Fourier transform
... I have a question about the time scaling property of the Fourier ... The first formula uses the absolute value for 1/a, ... the integral I obtain the second formula. ... please where the absolute value for 1/a comes from in the first formula. ...
(comp.dsp)