Auto-regressive spectral line analysis of piano tones

Abstract

Three auto-regressive spectral estimation methods are experimentally tested with a view to musical applications: the Maximum Entropy method, Marple's MODCOVAR algorithm, and an efficient version of Prony spectral line estimation due to Cybenko. A performance analysis measuring the maximum relative error of their frequency estimates for a signal consisting of three sinusoids under variations of the model order (up to 20), signal length (60 to 200 samples) and noise level shows that unless the model order is close to 2/3 of the number of data points (i.e. when it is nearly ill-conditioned), Marple's algorithm gives by far the best results. In a separate experiment, Marple's algorithm was applied to recorded piano sounds; some preliminary results are shown which demonstrate its potential for fast multicomponent analysis.