Detection of multiplicative noise in stationary random processes using second- and higher order statistics

This paper addresses the problem of detecting the presence of colored multiplicative noise, when the information process can be modeled as a parametric ARMA process. For the case of zero-mean multiplicative noise, a cumulant based suboptimal detector is studied. This detector tests the nullity of a specific cumulant slice. A second detector is developed when the multiplicative noise is nonzero mean. This detector consists of filtering the data by an estimated AR filter. Cumulants of the residual data are then shown to be well suited to the detection problem. Theoretical expressions for the asymptotic probability of detection are given. Simulation-derived finite-sample ROC curves are shown for different sets of model parameters

Acoustic features of piano sounds

To date efforts of music transcription indicate the need for modelling the data signal in a more comprehensive manner in order to improve the transcription process of music performances. This research work is concerned with the investigation of two features associated with the reproduced sound of a piano; the inharmonicity factor of the piano strings and the double decay rate of the resulting sound. Firstly, a simple model of the inharmonicity is proposed and the factors that affect the modelled signal are identified, such as the magnitude of the inharmonicity, the number of harmonics, the time parameter, the phase characteristics and the harmonic amplitudes. A formation of a socalled “one-sided” effect appears in simulated signals, although this effect is obscured in real recordings potentially due to the non-uniformly varying amplitudes of the harmonic terms. This effect is also discussed through the use of the cepstrum by analysing real piano note recordings and synthesized signals. The cepstrum is further used to describe the effect of the coupled behaviour of two strings through digital waveguides. Secondly, the double decay rate effect is modelled through coupled oscillators and digital waveguides. A physical model of multiple strings is also presented as an extension to the simple model of coupled oscillators and various measurements on a real grand piano are carried out in order to investigate the coupling mechanism between the strings, the soundboard and the bridge. Finally, a model, with reduced dimensionality, is proposed to represent the signal model for single and multiple notes formulated around a Bayesian framework. The potential of such a model is illustrated with the transcription of simple examples of real monophonic and polyphonic piano recordings by implementing the Metropolis-Hastings algorithm and Gibbs sampler for multivariate parameter estimation