Aliasing in Modal Parameter Estimation

Experimentalists are familiar with the aliasing that happens in data acquisition when the sampling rate is less than twice the highest frequency of energy in the signal to be sampled. Much effort has been made over the years using a combination of analog and digital filters to make sure that the higher frequencies are filtered out to avoid or minimize the effect of this aliasing. Much less talked about is the aliasing that occurs in modal parameter estimation, or curvefitting, when the residual effects of out of band modes violate the assumptions of the finite dimensional parametric model that the experimentalist uses to curvefit the acquired digitized data. While the out of band energy has been filtered out of the now band limited data, the tails, sometimes called residual flexibility and inertial restraint of the out of band modes are still present in the data. This article will look at some classes of modal parameter estimation algorithms and show by theory and example that the algorithms based on continuous time or Laplace domain formulations are superior to the discrete time domain or z domain models in that they give results which are not contaminated by the aliasing effect of these residuals. In addition, it will introduce the Alias Free Polyreference Method, which uses orthogonal polynomials in the infinite frequency domain, corresponding to a family of orthogonal Green's functions in the continuous time domain.