ABSTRACT
This chapter discusses a harmonic inversion problem by considering a homogeneous ordinary differential equation (ODE). The inverse problem relative to the ODE consists of the exchanged roles of the knowns and unknowns. In the inverse problem, the ODE itself is unknown and so are the eigenroots and the accompanying boundary conditions. This inverse problem is the continuous version of the harmonic inversion. A retrieval of the ODE and the boundary condition is essential for unfolding the hidden dynamics that govern the evolution of an examined system. In signal processing, one deals with both continuous and discrete time signals. Any two functions of conjugate variables are linearly interrelated by the Fourier integral. Therefore, a linear combination of Lorentzians in the frequency domain leads to a sum of damped exponentials in the time representation, irrespective of continuous or discrete functions.
