Learning Timbre Analogies from Unlabelled Data by Multivariate Tree Regression

This is the Author's Original Manuscript of an article whose final and definitive form, the Version of Record, has been published in the Journal of New Music Research, November 2011, copyright Taylor & Francis. The published article is available online at http://www.tandfonline.com/10.1080/09298215.2011.596938

Computational Tonality Estimation: Signal Processing and Hidden Markov Models

PhDThis thesis investigates computational musical tonality estimation from an audio signal. We present a hidden Markov model (HMM) in which relationships between chords and keys are expressed as probabilities of emitting observable chords from a hidden key sequence. The model is tested first using symbolic chord annotations as observations, and gives excellent global key recognition rates on a set of Beatles songs. The initial model is extended for audio input by using an existing chord recognition algorithm, which allows it to be tested on a much larger database. We show that a simple model of the upper partials in the signal improves percentage scores. We also present a variant of the HMM which has a continuous observation probability density, but show that the discrete version gives better performance. Then follows a detailed analysis of the effects on key estimation and computation time of changing the low level signal processing parameters. We find that much of the high frequency information can be omitted without loss of accuracy, and significant computational savings can be made by applying a threshold to the transform kernels. Results show that there is no single ideal set of parameters for all music, but that tuning the parameters can make a difference to accuracy. We discuss methods of evaluating more complex tonal changes than a single global key, and compare a metric that measures similarity to a ground truth to metrics that are rooted in music retrieval. We show that the two measures give different results, and so recommend that the choice of evaluation metric is determined by the intended application. Finally we draw together our conclusions and use them to suggest areas for continuation of this research, in the areas of tonality model development, feature extraction, evaluation methodology, and applications of computational tonality estimation.Engineering and Physical Sciences Research Council (EPSRC)

Multichannel sampling of finite rate of innovation signals

Recently there has been a surge of interest in sampling theory in signal processing community. New efficient sampling techniques have been developed that allow sampling and perfectly reconstructing some classes of non-bandlimited signals at sub-Nyquist rates. Depending on the setup used and reconstruction method involved, these schemes go under different names such as compressed sensing (CS), compressive sampling or sampling signals with finite rate of innovation (FRI). In this thesis we focus on the theory of sampling non-bandlimited signals with parametric structure or specifically signals with finite rate of innovation. Most of the theory on sampling FRI signals is based on a single acquisition device with one-dimensional (1-D) signals. In this thesis, we extend these results to the case of 2-D signals and multichannel acquisition systems. The essential issue in multichannel systems is that while each channel receives the input signal, it may introduce different unknown delays, gains or affine transformations which need to be estimated from the samples together with the signal itself. We pose both the calibration of the channels and the signal reconstruction stage as a parametric estimation problem and demonstrate that a simultaneous exact synchronization of the channels and reconstruction of the FRI signal is possible. Furthermore, because in practice perfect noise-free channels do not exist, we consider the case of noisy measurements and show that by considering Cramer-Rao bounds as well as numerical simulations, the multichannel systems are more resilient to noise than the single-channel ones. Finally, we consider the problem of system identification based on the multichannel and finite rate of innovation sampling techniques. First, by employing our multichannel sampling setup, we propose a novel algorithm for system identification problem with known input signal, that is for the case when both the input signal and the samples are known. Then we consider the problem of blind system identification and propose a novel algorithm for simultaneously estimating the input FRI signal and also the unknown system using an iterative algorithm