A novel technique for high-resolution frequency discriminators and their application to pitch and onset detection in empirical musicology

Milligan, Keziah (2020) A novel technique for high-resolution frequency discriminators and their application to pitch and onset detection in empirical musicology. PhD thesis, University of Glasgow.

Abstract

This thesis presents and evaluates software for simultaneous, high-resolution time-frequency
discrimination. Whilst this is a problem that arises in many areas of engineering, the software here is developed to assist musicological investigations. In order to analyse musical performances, we must first know what is happening and when; that is, at what time each note begins to sound (the note onset) and what frequencies are present (the pitch). The work presented here focusses on onset detection, although the representation of data used for this task could also be used to track the pitch. A potential method of determining pitch on a sample-to-sample basis is given in the final chapter.

Extant software for onset detection uses standard signal processing techniques to search for changes in features like the spectrum or phase. These methods struggle somewhat, as they are constrained by the uncertainty principle, which states that, as time resolution is increased, frequency resolution must decrease and vice versa.

However, we can hear changes in frequency to a far greater time resolution than the uncertainty principle would suggest is possible. There is an active process in the inner ear which adds energy and enables this perceptual acuity. The mathematical expression which describes this system is known as the Hopf bifurcation.

By building a bank of tuned resonators in software, each of which operates at a Hopf bifurcation, and driving it with audio, changes in frequency can be detected in times that defy the uncertainty relation, as we are not seeking to directly measure the time-frequency features of a system, rather it is used to drive a system. Time and frequency information is then available from the internal state variables of the system.

The characteristics of this bank of resonators - called a 'DetectorBank' - are investigated thoroughly. The bandwidth of each resonator ('detector') can be as narrow as 0.922Hz and the system bandwidth is extended to the Nyquist frequency. A nonlinear system may be expected to respond poorly when presented with multiple simultaneous input frequencies; however, the DetectorBank performs well under these circumstances.

The data generated by the DetectorBank is then analysed by an OnsetDetector. Both the development and testing of this OnsetDetector are detailed. It is tested using a repository of recordings of individual notes played on a variety of instruments, with promising results. These results are discussed, problems with the current implementation are identified and potential solutions presented.

This OnsetDetector can then be combined with a PitchTracker to create a NoteDetector, capable of detecting not only a single note onset time and pitch, but information about changes that occur within a note.

Musical notes are not static entities: they contain much variation. Both the performer's intonation and the characteristics of the instrument itself have an effect on the frequency present, as well as features like vibrato. Knowledge of these frequency components, and how they appear or disappear over the course of the note, is valuable information and the software presented here enables the collection of this data.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: Digital signal processing, Filters, Band-pass filters, Digital filters, Filtering theory, Nonlinear filters, Signal analysis, Spectral analysis, Signal detection, Music information retrieval, Music, Open source software.
• Subjects: Q Science > Q Science (General); T Technology > TA Engineering (General). Civil engineering (General)
• Colleges/Schools: College of Science and Engineering > School of Engineering > Systems Power and Energy
• Funder's Name: EPSRC
• Supervisor's Name: Bailey, Dr. Nicholas
• Date of Award: 2020
• Depositing User: Dr Keziah Milligan
• Unique ID: glathesis:2020-81344
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 21 May 2020 11:10
• Last Modified: 21 May 2020 11:15
• URI: https://theses.gla.ac.uk/id/eprint/81344

Related URLs

• https://github.com/keziah55/DetectorBank
• https://github.com/keziah55/ExtraThesisM...