Refined instrumental variable estimation: maximum likelihood optimization of a unified Box–Jenkins model

For many years, various methods for the identification and estimation of parameters in linear, discretetime transfer functions have been available and implemented in widely available Toolboxes for MatlabTM. This paper considers a unified Refined Instrumental Variable (RIV) approach to the estimation of discrete and continuous-time transfer functions characterized by a unified operator that can be interpreted in terms of backward shift, derivative or delta operators. The estimation is based on the formulation of a pseudo-linear regression relationship involving optimal prefilters that is derived from an appropriately unified Box–Jenkins transfer function model. The paper shows that, contrary to apparently widely held beliefs, the iterative RIV algorithm provides a reliable solution to the maximum likelihood optimization equations for this class of Box–Jenkins transfer function models and so its en bloc or recursive parameter estimates are optimal in maximum likelihood, prediction error minimization and instrumental variable terms

Model-based analysis of noisy musical recordings with application to audio restoration

This thesis proposes digital signal processing algorithms for noise reduction and enhancement of audio signals. Approximately half of the work concerns signal modeling techniques for suppression of localized disturbances in audio signals, such as impulsive noise and low-frequency pulses. In this regard, novel algorithms and modifications to previous propositions are introduced with the aim of achieving a better balance between computational complexity and qualitative performance, in comparison with other schemes presented in the literature. The main contributions related to this set of articles are: an efficient algorithm for suppression of low-frequency pulses in audio signals; a scheme for impulsive noise detection that uses frequency-warped linear prediction; and two methods for reconstruction of audio signals within long gaps of missing samples. The remaining part of the work discusses applications of sound source modeling (SSM) techniques to audio restoration. It comprises application examples, such as a method for bandwidth extension of guitar tones, and discusses the challenge of model calibration based on noisy recorded sources. Regarding this matter, a frequency-selective spectral analysis technique called frequency-zooming ARMA (FZ-ARMA) modeling is proposed as an effective way to estimate the frequency and decay time of resonance modes associated with the partials of a given tone, despite the presence of corrupting noise in the observable signal.reviewe