Frequency Extrapolation through Sparse Sums of Lorentzians

Abstract. Sparse sums of Lorentzians can give good approximations to functions consisting of linear combination of piecewise continuous functions. To each Lorentzian, two parameters are assigned: translation and scale. These parameters can be found by using a method for complex frequency detection in the frequency domain. This method is based on an alternating projection scheme between Hankel matrices and finite rank operators, and have the advantage that it can done in weighted spaces. The weighted spaces can be used to partially revoke the effect of finite band-width filters. Apart from frequency extrapolation the method provides a way of estimating discontinuity locations.