Restoration of a discrete-time signal segment by interpolation based on the left-sided and right-sided autoregressive parameters

This paper presents an algorithm for the interpolation of a missing signal segment on the assumption that the signal can be modeled as an autoregressive (AR) process. Unlike previous algorithms, the presented algorithm does not model the signal of the missing segment and the neighboring signal portions by a single AR-parameter vector. Instead, two separate vectors are used so that stationarity need no longer be assumed to extend beyond both sides of the missing segment. The relaxation of this stationarity assumption is essential when the duration of the missing segment is on the order of the short-time stationarity duration of the signal. The algorithm provides the optimal solution to the problem of interpolating a missing segment based on the left-sided and right-sided AR-parameter vectors. The solution is optimal in the sense of a least-squares residual. The algorithm is applied to speech and music signals and is compared with other restoration techniques.