New answers tagged group-delay
4
A real-valued system that doesn't distort the shape of the input signal must have the following input-output relation:
$$y(t)=Ax(t-t_0)\tag{1}$$
with arbitrary real-valued constants $A>0$ and $t_0$.
In the frequency domain, Eq. $(1)$ corresponds to
$$Y(\omega)=Ae^{-j\omega t_0}X(\omega)\tag{2}$$
Consequently, the corresponding system is an LTI system ...
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