Is the phase difference between recorded sounds from left and right ear the same as the phase difference between their HRTF? Pardon my ignorance if my question is silly. Lets say I did a binaural recording and found the phase difference between right and left channel. If the recording was done in anechoic chamber, where there is no reverberation, can I say that this phase difference is same as the phase difference between their HRTFs which they were filtered by (on their way from speaker to my ear)?
Consider a signal with a particular frequency at phase $\alpha$. Passing this through the two filter paths changes the phase of the frequency to $\alpha + L$ and $\alpha + R,$ where $L$ and $R$ are the values of the phase frequency responses of the two HRTF filters at the particular frequency. Yes, the phase difference $(\alpha + R) - (\alpha + L)$ is equal to $R - L,$ which you call more simply the "phase difference" between the HRTF's.