Estimation of the Complex Amplitudes Associated to the Common Poles in a Multichannel Signal

Recently, certain solutions have been proposed to solve the common poles estimation problem in a multichannel exponentially damped sinusoidal (EDS) signal. In this work, we tackle the closely related problem consisting of the estimation of the complex amplitudes associated to the common poles of a multichannel EDS signal. Our approach is based on the estimation of an oblique projector on the space of the estimated/common poles along the space of the unknown/non-common poles. We derive three projection/estimation schemes. The first one is based on a sequential (channel by channel) processing of the data while the others are based on joint estimation of the complex amplitudes.