I am doing a frequency analysis. Reading some literature I have seen that when you perform an fft on a time history of a variable, the dimension of this variable remains the same also after the application of the fft.
In particular, in my case study I have a variable with dimension [L^2/T^2]. Once I perform a fft on this variable the dimensions remain [L^2/T^2].
Now I have two question: 1. Can you confirm that the dimensions does not change after a fft? 2. Can you help me to demonstrate this (the fact that the dimensions does not change after fft) very very rigorously? Unfortunately I have to demonstrate to someone that does not believe it. Thanks