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
About this Master's Thesis
Rights statement
- Permission granted by the author to include this thesis or dissertation in this repository. All rights reserved by the author. Please contact the author for information regarding the reproduction and use of this thesis or dissertation.
| School |
|
|---|
| Department |
|
|---|
| Degree |
|
|---|
| Submission |
|
|---|
| Language |
|
|---|
| Research Field |
|
|---|
| 关键词 |
|
|---|
| Committee Chair / Thesis Advisor |
|
|---|
| Committee Members |
|
|---|