The aim of the paper is to compare Fourier methods and three parametric methods as techniques for the analysis of data acquired from a vibrating structure. The parametric methods include the Prony series, Recursive Least Squares, and Instrumental Variable Analysis. The methods are used to analyze simulated data as well as acceleration and force measurements obtained from a simple vibrating structure. The paper highlights the advantages and disadvantages of each method and shows that in certain circumstances the parametric methods provide useful alternatives to standard Fourier methods. The effect of noise on signal measurements for each method is also addressed, along with the problem of model order selection for the parametric approaches.