Restoration of clipped sound signals -a weighted Fourier series and AR approach

Sound signals can be distorted in many dierent ways, one of them is called clipping. A clipped sound signal diers from a non-clipped signal in the way that the amplitudes of the sound wave that are higher than a certain amplitude threshold has been partially lowered or completely lowered to the threshold, the latter is called hard clipping. Since data is lost when a signal is clipped, there is an interest in restoring the signal. For a hard clipped signal, it is often impossible to perfectly restore the signal. In this thesis two dierent methods for partially restoring a symmetrically hard clipped signal are suggested. The two methods considered are a weighted Fourier series (WFS) t and an autoregressive (AR) model approach. Both methods attempt to restore the signal by solving optimization problems designed to min- imize the errors of the respective model. Evaluation and comparison of the two methods showed that the AR method typically performed better than the WFS method. The AR method was eec- tive at restoring the signal, while the WFS method stuck close to the clipped signal, which might be due to dierences in their optimization problems