The wavenumber - frequency spectra of a pressure field beneath a turbulent boundary layer is considered, with the aim of removing the effect of the measuring device. A rotating antenna of aligned microphones has been used in previous studies and the measured spectra are shown to be a convolution of the true spectra with the transfer function of said antenna. Deconvolution algorithms are presented that were previously developed for other fields of studies. Test cases and processing of experimental data show that until a better convergence criteria is defined for the iterative process, a hybrid approach between deconvolution and angular interpolation of the antenna’s rotation could be the best compromise.