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Frequency, phase and amplitude estimation of overlapping partials in monaural musical signals
KTH, School of Computer Science and Communication (CSC), Speech, Music and Hearing, TMH, Music Acoustics.
2010 (English)In: 13th International Conference on Digital Audio Effects, DAFx 2010 Proceedings, 2010, 1-8 p.Conference paper (Refereed)
Abstract [en]

A method is described that simultaneously estimates the frequency, phase and amplitude of two overlapping partials in a monaural musical signal from the amplitudes and phases in three frequency bins of the signal's Odd Discrete Fourier Transform (ODFT). From the transform of the analysis window in its analytical form, and given the frequencies of the two partials, an analytical solution for the amplitude and phase of the two overlapping partials was obtained. Furthermore, the frequencies are estimated numerically solving a system of two equations and two unknowns, since no analytical solution could be found. Although the estimation is done independently frame by frame, particular situations (e.g. extremely close frequencies, same phase in the time window) lead to errors, which can be partly corrected with a moving average filter over several time frames. Results are presented for artificial sinusoids with time varying frequencies and amplitudes, and with different levels of noise added. The system still performs well with a Signalto- Noise ratio of down to 30 dB, with moderately modulated frequencies, and time varying amplitudes.

Place, publisher, year, edition, pages
2010. 1-8 p.
Keyword [en]
Amplitude estimation, Analysis windows, Frequency bins, Moving average filter, Musical signals, Noise ratio, Odd discrete fourier transforms, Time frame, Time varying, Time windows, Time-varying frequency, Two equation
National Category
Fluid Mechanics and Acoustics
URN: urn:nbn:se:kth:diva-34083ScopusID: 2-s2.0-84872727032ISBN: 978-320001940-9OAI: diva2:419075
13th International Conference on Digital Audio Effects, DAFx 2010; Graz; Austria; 6 September 2010 through 10 September 2010

QC 20110708

Available from: 2011-07-08 Created: 2011-05-25 Last updated: 2014-08-14Bibliographically approved
In thesis
1. Interactive computer-aided expressive music performance: Analysis, control, modification and synthesis
Open this publication in new window or tab >>Interactive computer-aided expressive music performance: Analysis, control, modification and synthesis
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis describes the design and implementation process of two applications (PerMORFer and MoodifierLive) for the interactive manipulation of music performance. Such applications aim at closing the gap between the musicians, who play the music, and the listeners, who passively listen to it. The goal was to create computer programs that allow the user to actively control how the music is performed. This is achieved by modifying such parameters as tempo, dynamics, and articulation, much like a musician does when playing an instrument. An overview of similar systems and the problems related to their development is given in the first of the included papers.

Four requirements were defined for the applications: (1) to produce a natural, high quality sound; (2) to allow for realistic modifications of the performance parameters; (3) to be easy to control, even for non-musicians; (4) to be portable. Although there are many similarities between PerMORFer and MoodifierLive, the two applications fulfill different requirements. The first two were addressed in PerMORFer, with which the user can manipulate pre-recorded audio performance. The last two were addressed in MoodifierLive, a mobile phone application for gesture-based control of a MIDI score file. The tone-by tone modifications in both applications are based on the KTH rule system for music performance. The included papers describe studies, methods, and algorithms used in the development of the two applications.

Audio recordings of real performance have been used in PerMORFer toachieve a natural sound. The tone-by-tone manipulations defined by the KTH rules first require an analysis of the original performance to separate the tones and estimate their parameters (IOI, duration, dynamics). Available methods were combined with novel solutions, such as an approach to the separation of two overlapping sinusoidal components. On the topic of performance analysis, ad-hoc algorithms were also developed to analyze DJ scratching recordings.

A particularly complex problem is the estimation of a tone’s dynamic level. A study was conducted to identify the perceptual cues that listeners use to determinethe dynamics of a tone. The results showed that timbre is as important as loudness. These findings were applied in a partly unsuccessful attempt to estimate dynamics from spectral features.

The manipulation of tempo is a relatively simple problem, as is that of articulation (i.e. legato-staccato) as long as the tone can be separated. The modification of dynamics on the other hand is more difficult, as was its estimation. Following the findings of the previously mentioned perceptual study, a method to modify both loudness and timbre using a database of spectral models was implemented.

MoodifierLive was used to experiment with performance control interfaces. In particular, the mobile phone’s built-in accelerometer was used to track, analyze, and interpret the movements of the user. Expressive gestures were then mapped to corresponding expressive music performances. Evaluation showed that modes based on natural gestures were easier to use than those created witha top-down approach.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. 69 p.
Trita-CSC-A, ISSN 1653-5723 ; 2011:12
National Category
Fluid Mechanics and Acoustics
urn:nbn:se:kth:diva-34099 (URN)978-91-7501-031-1 (ISBN)
Public defence
2011-06-15, F3, Lindstedtsvägen 26, KTH, Stockholm, 10:00 (English)
QC 20110607Available from: 2011-06-07 Created: 2011-05-25 Last updated: 2012-03-22Bibliographically approved

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