Physically Informed Subtraction of a String's Resonances from Monophonic, Discretely Attacked Tones : a Phase Vocoder Approach

A method for the subtraction of a string's oscillations from monophonic, plucked- or hit-string tones is presented. The remainder of the subtraction is the response of the instrument's body to the excitation, and potentially other sources, such as faint vibrations of other strings, background noises or recording artifacts. In some respects, this method is similar to a stochastic-deterministic decomposition based on Sinusoidal Modeling Synthesis [MQ86, IS87]. However, our method targets string partials expressly, according to a physical model of the string's vibrations described in this thesis. Also, the method sits on a Phase Vocoder scheme. This approach has the essential advantage that the subtraction of the partials can take place \instantly", on a frame-by-frame basis, avoiding the necessity of tracking the partials and therefore availing of the possibility of a real-time implementation. The subtraction takes place in the frequency domain, and a method is presented whereby the computational cost of this process can be reduced through the reduction of a partial's frequency-domain data to its main lobe. In each frame of the Phase Vocoder, the string is encoded as a set of partials, completely described by four constants of frequency, phase, magnitude and exponential decay. These parameters are obtained with a novel method, the Complex Exponential Phase Magnitude Evolution (CSPME), which is a generalisation of the CSPE [SG06] to signals with exponential envelopes and which surpasses the nite resolution of the Discrete Fourier Transform. The encoding obtained is an intuitive representation of the string, suitable to musical processing

Two-dimensional spectrum estimation using the radon transform

An alternative approach to two-dimensional power spectrum estimation incorporating the Radon transform in conjunction with each of the one-dimensional periodogram, Blackman-Tukey, and Autoregressive parameter estimation algorithms is examined. The Radon transform is used to express a two-dimensional data set in terms of its projections onto a set of one-dimensional radial lines, effectively reducing the two-dimensional estimation problem to a series of one-dimensional problems. The resulting two-dimensional power spectrum estimates are compared to the known power spectra for a variety of data types. The Radon transform approach combined with autoregressive parameter estimation can provide a high-resolution power spectrum estimate, effectively surpassing the resolution limitations of the Fourier methods without the cumbersome implementations of the more direct high resolution estimation methods in two dimensions

Harmonic Sinusoid Modeling of Tonal Music Events

PhDThis thesis presents the theory, implementation and applications of the harmonic sinusoid modeling of pitched audio events. Harmonic sinusoid modeling is a parametric model that expresses an audio signal, or part of an audio signal, as the linear combination of concurrent slow-varying sinusoids, grouped together under harmonic frequency constraints. The harmonic sinusoid modeling is an extension of the sinusoid modeling, with the additional frequency constraints so that it is capable to directly model tonal sounds. This enables applications such as object-oriented audio manipulations, polyphonic transcription, instrument/singer recognition with background music, etc. The modeling system consists of an analyzer and a synthesizer. The analyzer extracts harmonic sinusoidal parameters from an audio waveform, while the synthesizer rebuilds an audio waveform from these parameters. Parameter estimation is based on a detecting-grouping-tracking framework. The detecting stage finds and estimates sinusoid atoms; the grouping stage collects concurrent atoms into harmonic groups; the tracking stage collects the atom groups at different time to form continuous harmonic sinusoid tracks. Compared to standard sinusoid model, the harmonic model focuses on harmonic groups of atoms rather than on isolated atoms, therefore naturally represents tonal sounds. The synthesizer rebuilds the audio signal by interpolating measured parameters along the found tracks. We propose the first application of the harmonic sinusoid model in digital audio editors. For audio editing, with the tonal events directly represented by a parametric model, we can implement standard audio editing functionalities on tonal events embedded in an audio signal, or invent new sound effects based on the model parameters themselves. Possibilities for other applications are suggested at the end of this thesis.Financial support: European Commission, the Higher Education Funding Council for England, and Queen Mary, University of Londo

Design, Evaluation, and Application of Heart Rate Variability Analysis Software (HRVAS)

The analysis of heart rate variability (HRV) has become an increasingly popular and important tool for studying many disease pathologies in the past twenty years. HRV analyses are methods used to non-invasively quantify variability within heart rate. Purposes of this study were to design, evaluate, and apply an easy to use and open-source HRV analysis software package (HRVAS). HRVAS implements four major categories of HRV techniques: statistical and time-domain analysis, frequency-domain analysis, nonlinear analysis, and time-frequency analysis. Software evaluations were accomplished by performing HRV analysis on simulated and public congestive heart failure (CHF) data. Application of HRVAS included studying the effects of hyperaldosteronism on HRV in rats. Simulation and CHF results demonstrated that HRVAS was a dependable HRV analysis tool. Results from the rat hyperaldosteronism model showed that 5 of 26 HRV measures were statistically significant (p\u3c0.05). HRVAS provides a useful tool for HRV analysis to researchers