I have one question concerning phase rotation of signals and I am not sure wether it works or not:

Let's assume we have a zero-phase wavelet x(t) i.e. Ricker wavelet. Unfortunately, in our experiment, the wavelet y(t) we use is not zero phase anymore but rotated by an phase angle $\Psi$. Yet, we still can clearly identify the peak of the wavelet at x(T).

Question: Is it possible to derive the position of the peak of the corresponding zero-phase wavelet $x(t)$ from $y(\tau)$?

My first steps are: 1) equation Ricker wavelet: $$ x(t)=(1-2 \pi^2 f^2 t^2) e^{-\pi^2 f^2 t^2} $$

2) equation rotated Ricker wavelet

$$ y(\tau)=(1-2 \pi^2 f^2 \tau^2) e^{(-\pi^2 f^2 \tau^2 - \Psi \tau)} $$

My assumption was setting $y(t) = x(t)$ and solve for $t$ since $\tau,f,\Psi$ are known. Unfortunately the amplitude of the wavelet changes with the phase rotation. How can I account for this?

please help!


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