SEMPO: Singularity Expansion Method - Parameter Optimizer

SEMPO is a python toolbox to extracts the poles, zeros and residues in the complex frequency plane from arbitrary spectra acquired along the real frequency axis. This set of tools allows us to determine the modes of a linear physical system from its spectral response only, without any a priori knowledge. It is based on the description of the physical response as a meromorphic function through the Singularity Expansion Method (SEM). This analytical expansion of the response function in the complex frequency plane motivates the use of what is known as the Cauchy method, as well as the use of an auto-differentiation-based optimization approach to retrieve the complex poles, zeros and residues from the knowledge of the spectrum over a finite and real spectral range.