# Mismatched Estimation of Polynomially Damped Signals

## TL;DR

This paper introduces a mismatched estimation method for polynomially damped sinusoidal signals that simplifies the signal model, enabling efficient and predictable parameter estimation despite the complexity and unknown components.

## Contribution

The work proposes a novel mismatched estimation approach using simplified models to efficiently estimate parameters of complex polynomially damped signals.

## Key findings

- The method provides statistically predictable estimates.
- It reduces computational complexity in parameter estimation.
- Applicable to signals with unknown components.

## Abstract

In this work, we consider the problem of estimating the parameters of polynomially damped sinusoidal signals, commonly encountered in, for instance, spectroscopy. Generally, finding the parameter values of such signals constitutes a high-dimensional problem, often further complicated by not knowing the number of signal components or their specific signal structures. In order to alleviate the computational burden, we herein propose a mismatched estimation procedure using simplified, approximate signal models. Despite the approximation, we show that such a procedure is expected to yield predictable results, allowing for statistically and computationally efficient estimates of the signal parameters.