Can two functions have the same frequency domain representation?

[sanjaysan]

Hi,

I stumbled upon the following two functions which have the same freq domain representation,
1/(j.pi.f)

1.signum(t) = u(t) - u(-t)

2. 2u(t)

what is the reasoning behind them having the same f domain representation?

 

[lurflurf]

well
2u(t)-1=signum(t)

 

[sanjaysan]

thanks,that answers my question:)