A minimal example is below. I'm trying to reverse function y1d.
ClearAll["Global`*"] (* clear all symbols *)
f0d = 3.5*10^9;
f1d = 500*10^6;
T = 0.1*10^-6;
kd = (f1d - f0d)/T;
phi0 = 0;
chplusd[t_] := E^(I*2*\[Pi]*((kd*t^2)/2 + f0d*t + phi0))
fsig1 = 3*10^9;
x[t_] := Cos[2*Pi*fsig1*t]
s1d[t_] := x[t]*chplusd[t]
snd[t_] := E^(-I*2*\[Pi]*(f0d*t + phi0))
y2d[t_] := s1d[t]*snd[t]
Grid[{{Plot[{Re[y2d[t]]}, {t, 0, T}, PlotRange -> All, Exclusions -> None, GridLines -> Automatic, ImageSize -> Full]}, {Plot[{Re[y2d[T - t]]}, {t, 0, T}, PlotRange -> All, Exclusions -> None, GridLines -> Automatic, ImageSize -> Full]}}]
chmoinsd[t_] := E^(-I*2*\[Pi]*((kd*t^2)/2 + f0d*t + phi0))
y1dtemp = Convolve[y2d[to]*UnitStep[to], chmoinsd[to]*UnitStep[to], to, t, Assumptions -> t >= 0]
y1d[t_] := y1dtemp
Grid[{{Plot[{Re[y1d[t]]}, {t, 0, T}, PlotRange -> All, Exclusions -> None, GridLines -> Automatic, ImageSize -> Full]}, {Plot[{Re[y1d[T - t]]}, {t, 0, T}, PlotRange -> All, Exclusions -> None, GridLines -> Automatic, ImageSize -> Full]}}]
The problem starts in the line with the Convolve function, because I can reverse function y2d.
Before, I tried the below two lines in place of the last three lines of the above code, but it does not work and I don't understand why.
y1d[t_] := Convolve[y2d[to]*UnitStep[to], chmoinsd[to]*UnitStep[to], to, t, Assumptions -> t >= 0]
Grid[{{Plot[{Re[y1d[t]]}, {t, 0, T}, PlotRange -> All, Exclusions -> None, GridLines -> Automatic, ImageSize -> Full]}, {Plot[{Re[y1d[T - t]]}, {t, 0, T}, PlotRange -> All, Exclusions -> None, GridLines -> Automatic, ImageSize -> Full]}}]