Separation of stationary and time-varying systems and its application to the restoration of gramophone recordings

The motivation for developing the technique described arose from a desire to restore old gramophone recordings which were spectrally distorted during the original recording process. This distortion was caused by the horn used to focus the sound. White noise tests on an original recording horn suggest that its frequency response contains several strong resonances which are modeled as a stationary autoregressive subsystem. The signal to be recovered is modeled as a time-varying autoregressive subsystem. Given knowledge of the parameters of the overall system, it is shown how the two systems can be separated to obtain the parameters of the horn distortion subsystem. An inverse filter can then be designed to recover the original signal. Initial results from experiments on subsystem separation are presented using a simple technique to identify the overall system. Better methods for the overall system identification stage are discussed