Module 2 : Signals in Frequency Domain
Lecture 20 : Properties of Fourier Transform
 
Scaling of the independent variable by a real constant a

When a > 0 or a < 0

or

Hence the scaling of the independent variable is a self-dual operation.

Consider

Hence, x(t) and |a|1/2 x(at) have the same energy. Therefore such scaling is called energy normalized scaling of the independent variable.