Restoration of Audio Recordings Corrupted by Nonlinear Distortions

Magnetic tape recordings suffer from nonlinear distortions, mainly due to saturation effects. We model the audio signals using a linear Autoregressive (AR) model with additive Gaussian noise and the recording procedure with a nonlinear measurement function. To analyze the nonlinearities we perform measurements on magnetic tape devices in saturation. Due to ferromagnetic effects a nonlinearity with memory has to be considered. For this reason we explore the capabilities of the Preisach model, suitable for hysteretic systems. We have used Sequential Monte Carlo (SMC) and Markov Chain Monte Carlo (MCMC) methods to filter the distorted tape recordings and restore the original audio signal, despite the nonlinearities in the measurements and possibly unknown parameters of the audio signal model. Moreover, the Expectation Maximization (EM) algorithm for combined parameter and state estimation is discussed. Simulations show promising results for restoring distorted audio signals in the near future.