A Welch method approximation of the Thomson multitaper spectrum estimator

The Thomson multitaper estimator has become successful for spectrum analysis in many application areas. From the aspect of efficient implementation, the so called Welch or WOSA-Weighted Overlap Segment Averaging, has advantages. In the Welch estimator, the same, time-shifted, window is applied to the data-sequence. In this submission, the aim is to find a Welch estimator structure which has a similar performance as the Thomson multitaper estimator. Such a estimator might be more advantageous from real-time computation aspects as the spectra can be estimated when data samples are available and a running average will produce the subsequent averaged spectra. The approach is to restructure the corresponding co-variance matrix of the Thomson estimator to the structure of a Welch estimator and to find a mean square error approximation of the covariance matrix. The resulting window of the Welch estimator should however fulfill the usual properties of a spectrum estimator, such as low-pass structure and well suppressed sidelobes.