Modal analysis of the input impedance of wind instruments. Application to the sound synthesis of a clarinet

International audienceThis paper investigates the modal analysis of wind instruments as seen from the input of their air column. Beside the treatment of analytical models, a particular emphasis is given to the analysis of measured input impedances. This requires special care because the measurements cover only a limited frequency band and are affected by some unknown errors. This paper describes how the Prony analysis and the Least Squares Complex Exponential (LSCE) classical techniques can be used in this context and how the main pitfalls can be avoided in their application. A physically acceptable method of reconstruction of the low frequency band is proposed. A technique using fictitious points in the high frequency range is described in order to ensure the passivity of the resonator in the whole frequency band. The principles of a real-time synthesis of clarinet sounds based on the modal representation of the resonator is given as an application, with a method to efficiently handle the modal representation during the transition between fingerings

Analysis and resynthesis of polyphonic music

This thesis examines applications of Digital Signal Processing to the analysis, transformation, and resynthesis of musical audio. First I give an overview of the human perception of music. I then examine in detail the requirements for a system that can analyse, transcribe, process, and resynthesise monaural polyphonic music. I then describe and compare the possible hardware and software platforms. After this I describe a prototype hybrid system that attempts to carry out these tasks using a method based on additive synthesis. Next I present results from its application to a variety of musical examples, and critically assess its performance and limitations. I then address these issues in the design of a second system based on Gabor wavelets. I conclude by summarising the research and outlining suggestions for future developments

Hardward and algorithm architectures for real-time additive synthesis

Additive synthesis is a fundamental computer music synthesis paradigm tracing its origins to the work of Fourier and Helmholtz. Rudimentary implementation linearly combines harmonic sinusoids (or partials) to generate tones whose perceived timbral characteristics are a strong function of the partial amplitude spectrum. Having evolved over time, additive synthesis describes a collection of algorithms each characterised by the time-varying linear combination of basis components to generate temporal evolution of timbre. Basis components include exactly harmonic partials, inharmonic partials with time-varying frequency or non-sinusoidal waveforms each with distinct spectral characteristics. Additive synthesis of polyphonic musical instrument tones requires a large number of independently controlled partials incurring a large computational overhead whose investigation and reduction is a key motivator for this work. The thesis begins with a review of prevalent synthesis techniques setting additive synthesis in context and introducing the spectrum modelling paradigm which provides baseline spectral data to the additive synthesis process obtained from the analysis of natural sounds. We proceed to investigate recursive and phase accumulating digital sinusoidal oscillator algorithms, defining specific metrics to quantify relative performance. The concepts of phase accumulation, table lookup phase-amplitude mapping and interpolated fractional addressing are introduced and developed and shown to underpin an additive synthesis subclass - wavetable lookup synthesis (WLS). WLS performance is simulated against specific metrics and parameter conditions peculiar to computer music requirements. We conclude by presenting processing architectures which accelerate computational throughput of specific WLS operations and the sinusoidal additive synthesis model. In particular, we introduce and investigate the concept of phase domain processing and present several “pipeline friendly” arithmetic architectures using this technique which implement the additive synthesis of sinusoidal partials

Implementation and optimization of the synthesis of musical instrument tones using frequency modulation

Im Bereich der elektronischen Musik hat die Frequenzmodulation (FM) als eine effiziente Methode zur Klangsynthese in jüngster Zeit enorm an Bedeutung gewonnen. In der vorliegenden Arbeit werden Methoden zur Grundfrequenzschätzung und zur FM-Synthese für Musikinstrumentenklänge untersucht, bewertet und optimiert. Dazu wurde im Rahmen dieser Arbeit eine FM Analyse- und Syntheseumgebung entwickelt, in welcher die hier betrachteten Verfahren implementiert wurden. Zur Grundfrequenzschätzung in Musiksignalen wurde ein neuartiges Verfahren auf Basis von Harmonic Pattern Match (HPM) entwickelt, welches eine höhere Schätzungsgenauigkeit als bisher verwendete Verfahren bietet. Hierzu wird nach Festlegung einer geeigneten Teilmenge der Spektraldaten die Autokorrelation sowohl im Zeitals auch im Frequenzbereich analysiert, um Kandidaten für die Grundfrequenz des Signals zu bestimmen. Anschließend wird die Übereinstimmung jedes dieser Kandidaten mit dem Profil der Harmonischen des Musiksignals nach einem effizienten Verfahren analysiert. Das vorgeschlagene Verfahren wurde analysiert und im Kontext mit anderen Verfahren zur Grundfrequenzschätzung bewertet. Die praktische Anwendbarkeit des HPM Verfahrens konnte gezeigt werden. Zur Implementierung einer FM Synthese wird ein Verfahren zur Approximation eines Spektrums auf Basis Genetischer Algorithmen (GA) vorgestellt. Die Problemstellung des GA einschließlich eines Verfahrens zur Bestimmung optimaler FMParameter wird beschrieben. Des Weiteren wurden im Hinblick auf eine optimierte FM-Synthese die Anforderungen an das Trägersignal sowie an den Modulator untersucht, mit dem Ziel einer Vorab-Festlegung des Parameterraums für akkurate Syntheseresultate. Mit dem Ziel einer Datenreduktion bei der FM-Synthese wurde eine stückweise lineare Approximation der Einhüllenden des Trägersignals entwickelt. Einen weiteren Aspekt der Optimierung stellt die Verknüpfung von Formanten in der Matching-Prozedur dar, wobei die Harmonischen der Formanten mit entsprechenden Faktoren gewichtet werden. Auf diese Weise wird eine deutlich genauere Approximation des Timbres des zu synthetisierenden Klangs erreicht. Hierzu wurden die Schätzung der spektralen Einhüllenden und die Extraktion der Formanten analysiert und implementiert. Die im Rahmen dieser Arbeit entwickelte Testumgebung ermöglicht die Schätzung der Parameter und die Analyse und Bewertung der so erzeugten FM-Syntheseresultate.Frequency modulation (FM) as an efficient method to synthesize musical sounds is of great importance in the area of computer music. In this thesis, the estimation of fundamental frequency, the FM synthesis procedure of musical instrument tones and the optimization on FM synthesis were analysed, evaluated, improved and implemented. A FM analysis and synthesis environment was developed, in which the presented work in this thesis were implemented. For the estimation of fundamental frequency of music signals, an algorithm based on harmonic pattern match (HPM) was designed to achieve more reliable estimation accuracy. After defining the spectrum subset, the autocorrelation was applied on the spectrum subset to exploiting candidates of fundamental frequency, and an efficient mechanism to evaluate the match between each candidate and the harmonic pattern of the musical signal was designed. Evaluation of the proposed algorithm and several other estimation algorithms was performed. For the implementation of FM synthesis, the matching procedure of spectra using genetic algorithm (GA) was described, including the definition of the task in GA and the searching procedure of optimized FM parameters through GA. For the optimization on FM synthesis, the requirements of carrier and modulator were analysed and the parameter space was examined, based on which a method for the predetermination of parameter space was designed to achieve accurate synthesis results. For data reduction in FM synthesis, the piecewise linear approximation of the carrier amplitude envelope was designed. Further step on the FM synthesis optimization was implemented by the combination of formants in the spectra matching procedure, in which the formant harmonics were emphasized by the weighting coefficients to achieve more accurate timbre of the synthesized sounds. The spectral envelope estimation and the formant extraction were analysed and implemented. For the analysis and implementation of FM synthesis, a testing environment program was developed, offering the functionality of parameter estimation and performance evaluation in FM synthesis