Automatic Transcription of Polyphonic Musical Signals with Linear Matching Pursuit Open Access

McLeod, Andrew Philip (2013)

Permanent URL: https://etd.library.emory.edu/concern/etds/fn106z159?locale=en
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Abstract

The Harmonic Matching Pursuit (HMP) algorithm has offered promising results in the automatic transcription of audio signals. It works by decomposing the given signal into a set of harmonic atoms, and then grouping those atoms into individual notes. HMP has shown very promising results, but more research has been needed for one case: when multiple notes with rational frequency relation are played simultaneously. This situation is called the overlapping partial problem, and it is very common in music, occurring in intervals such as major thirds, perfect fourths, and perfect fifths. A few solutions have been proposed to handle this overlapping partial problem by performing post-processing on the output of HMP (notably HMP with Spectral Smoothness (HMP SS)). In this paper, I propose an algorithm called Linear Matching Pursuit (LMP) to solve the overlapping partial problem of automatic note detection, which uses new heuristics to solve the problem with no post-processing required. LMP's runtime is independent of the number of notes present in a given audio signal, unlike HMP. My experiments show that LMP offers an improvement upon the accuracy of the HMP algorithm, though not to the extent of HMP SS, and is very robust in runtime with respect to polyphony.

Table of Contents

Contents

1 Introduction 1 2 Background and Related Works 2 2.1 Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.1 Matching Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2.2.2 Harmonic Matching Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.3 HMP with Spectral Smoothness . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Proposed Solution 9 3.1 Linear Matching Pursuit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 4 Experiments 13 4.1 Metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 4.2 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.3 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 4.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 5 Conclusion 19 6 Appendix 20 List of Figures 1 Harmonics Vibrating on a String . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Note-set Search Tree . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Accuracy Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 4 Error Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 5 Speed Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 List of Tables 1 Symbol Table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 2 Interval Ratios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3 Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 4 Piano Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

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