Papers by Matthieu Hodgkinson
A new method for the analysis of inharmonic instrumental tones is presented. The method exploits ... more A new method for the analysis of inharmonic instrumental tones is presented. The method exploits an equation derived from the well-know inharmonic series equation, where the inharmonicity coefficient is balanced with the frequencies and numbers of any two partials extracted from a pseudo-harmonic series. A serial search for increasingly deviating spectral peaks is aided with the integrated refinement of increasingly
1 [email protected] 2 [email protected] 3 [email protected] Abstract— The recently intr... more 1 [email protected] 2 [email protected] 3 [email protected] Abstract— The recently introduced Complex Spectral Phase Evolution (CSPE) algorithm is a super-resolution technique for the estimation of the exact frequency values of sinusoidal components in a signal. However, if a component of the signal does not exist within the entire data set, it cannot be identified out by CSPE algorithm, even though it still may be visible in the FFT magnitude spectrum. In this paper, we identify the source of this problem and propose a novel approach to resolve this issue. Specifically, we will show how to use a window apodization function to improve the CSPE algorithm. Experimental results are presented to illustrate the performance enhancement.
This paper investigates a number of digital methods to produce the Analog subtractive synthesis e... more This paper investigates a number of digital methods to produce the Analog subtractive synthesis effect of 'Hard Synchronisation.' While the original effect is produced by an explicit waveform phase reset, other approaches are given that produce an equivalent output. In particular, based on measurements taken from a real-analog synthesizer , a comb filtering model is proposed. This description ties in with earlier work but here an explicit structure is provided. This filter-based approach is then shown to be far more computationally efficient than the synchronisation by phase reset. This efficiency is at a minor cost as it is shown that it has a minimal impact on the sonic accuracy.
A new method for the analysis of inharmonic instrumental tones is presented. The method exploits ... more A new method for the analysis of inharmonic instrumental tones is presented. The method exploits an equation derived from the well-know inharmonic series equation, where the inharmonicity coefficient is balanced with the frequencies and numbers of any two partials extracted from a pseudo-harmonic series. A serial search for increasingly deviating spectral peaks is aided with the integrated refinement of increasingly reliable inharmonicity coefficient and fundamental frequency estimates. This firsthand approach to the problem of evaluating inharmonic spectra brings about an unprecedented level of simplicity, efficiency and accuracy .
A closed form method for Exponential Plus Constant (EPC) curve fitting is introduced. The method,... more A closed form method for Exponential Plus Constant (EPC) curve fitting is introduced. The method, referred to as Fourier-based Exponential Plus Constant Fitting (FEPCF), returns estimates of the EPC coefficients for user-input sets of equidistant time values and corresponding data points. An analytical expression for the exponent's coefficient is found through algebraic manipulation of the Fourier series of the EPC, taken over a finite time interval. The unknown is therefore approximated through the Discrete Fourier Transform (DFT) of the input sequence, itself used as an approximation of Fourier series. The discrepancy between Fourier series and DFT, byproduct of aliasing, is reduced with sine windowing. This is the essential contribution of the paper – the exponent coefficient found, what remains of the problem can be approached with standard linear least squares. FEPCF was motivated by the need for a measuring tool for the time-modeling of fundamental frequency and inharmonicity coefficient of tension-modulated strings. Care is however taken in the mathematical formulation of the method to facilitate its transportation to other fields of science. MATLAB function implementation and a demonstration of FEPCF can be downloaded from the address http://www.cs.nuim.ie/~matthewh/.
This paper introduces a spectral model for plucked, steel string tones, based on functional model... more This paper introduces a spectral model for plucked, steel string tones, based on functional models for time-varying fundamental frequency and inharmonicity coefficient. Techniques to evaluate those analytical values at different time indexes are reviewed and commented. A method to evaluate the unknowns of the fundamental frequency and inharmonicity coefficient functions and match the data of a given tone is presented. Frequency tracks can thereafter be deployed and traced for all values of time. Their accuracy is discussed, and applications for the model are suggested .
Thesis Chapters by Matthieu Hodgkinson
A method for the subtraction of a string's oscillations from monophonic, plucked-or hit-string to... more 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.
Uploads
Papers by Matthieu Hodgkinson
Thesis Chapters by Matthieu Hodgkinson