Theory

1. The sensitivity of calibrated hydrophones is generally available in discrete steps that do not exactly match FFT data frequencies. To convert voltages to pressures, the sensitivity values \(M(f)\) are first interpolated to match the frequencies at which the calibration points are acquired.

2. Given a recorded voltage signal \(V(t)\) and its associated Fourier transform \(\mathscr{F}[V(t)]\), the Fourier transform is converted to a one sided spectrum and then divided by the interpolated sensitivities, yielding \(\frac{\mathscr{F}[V(t)]}{M(f)}\).

3. The pressure values are obtained by performing an inverse Fourier transform on the above division, giving \(p(t) = \mathscr{F}^{-1}\left[\frac{\mathscr{F}[V(t)]}{M(f)}\right]\).

The process is described in the paper Lebon et al. (2018) Experimental and numerical investigation of acoustic pressures in different liquids. Ultrasonics Sonochemistry (42) 411-421. doi:10.1016/j.ultsonch.2017.12.002.