Lipeng Ning, Romeil Sandhu, Tryphon Georgiou, and Allen Tannenbaum
International Symposium on Mathematical Theory of Networks and Systems
Publication year: 2016

In this note, we describe a methodology focused on spectral analysis of multivariable times-series as this may arise in processing signals originating in antenna and sensor arrays.  Traditional spectral analysis methods such as spectrograms and maximum entropy technique, are often severely constrained by the non-stationary nature of time-series, which necessitates very short observation records. Thus, our goal has been to develop natural regularization techniques that allow smooth interpolation of spectrograms in time, thereby improving resolution and robustness. Since power spectra are matrix-valued measure, we sought to develop geometric tools that are based on weak∗ continuous metrics, such as Wasserstein metrics, only for matrix-valued functions.