Smart copying-a new approach to reconstruction of audio signals
The paper presents a new approach to reconstruction of audio signals, referred to as "smart copying". Smart copying is an intelligent version of the "cut and paste" technique which amounts to replacing the missing fragment with a similar one extracted from the material preceding or succeeding the gap. The paper presents an optimal, from the statistical point of view way of crossfading the inserted fragment into the projection-based reconstruction obtained using the maximum a posteriori approach. First, a general reconstruction formula is derived allowing one to estimate unknown samples from the known (neighboring) ones. Then, it is shown that the unknown excitation appearing in the analytical reconstruction formula can be replaced with the natural excitation waveform extracted from the available portions of the signal. It is shown that the reconstruction can be carried out recursively using the appropriately configured variable-order Kalman filter. Finally, a simplified reconstruction scheme is derived, allowing one to reduce dramatically computational costs when filling very large gaps.