Minimum variance interpolation and spectral analysis

Interpolation and spectral analysis of signals from finite number of samples is considered. When the observed data is of finite length, interpolation and spectral analysis of bandlimited signals using Shanon's framework leads to erroneous results. In spectral analysis this phenomenon is known as the spectral leakage problem. In this paper we address this issue from a minimum variance estimation perspective, and treat the generic case where the signal is not necessarily bandlimited. In contrast to traditional windowing based methods, the minimum variance framework leads to a convolutive transformation of the data, which employs a linear predictor. Simulations indicate a significant improvement in the performance.