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Detection and analysis of musical events using model-based signal processing

Citation

Owen, Randall Lee (1999) Detection and analysis of musical events using model-based signal processing. Engineer's thesis, California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-12182007-111636

Abstract

The present work is directed to the detection and analysis of notes, chords and other musical events produced by a stringed musical instrument, specifically the guitar. The chords generated by a guitar are polyphonic, meaning that they comprise multiple notes sounded simultaneously. Each note is also spectrally complex, in that it comprises a fundamental tone and several harmonics. Despite this complexity, the statistics of the signal containing the notes and chords are expected to be similar to those of human speech. This similarity will allow the signal to be characterized as a parametric random process so that established mathematical and speech recognition techniques can be used to extract the events from the signal. The analysis of musical signals is an important application since it is a logical extension to the problem of speech recognition. Moreover, a robust computer-based solution to this problem could have both research and commercial applications.

A system for automated detection and analysis of musical events, such as notes and chords, has been designed. The system is comprised of two main elements: the event library and a set of match measures. The event library contains a hierarchy of event models each corresponding to a distinct musical note or chord. Each event model is structured as a hidden Markov model (HMM), λ = (A, B, π), having the four distinct states labeled attack, sustain, decay or silence, that correspond to the specific physical states of the musical event. Associated with each model state Q={q1, ••• , q4} are a set of M observation symbols V={ v1,v2, ••• , vM} and a set of three probability distributions: a transition probability distribution A={aij} , an observable probability distribution B={bj(k)} and an initial probability distribution π=π{i}. Three match measures are developed for solving the recognition problem: one for estimating the HMM parameters, one for determining the optimal state sequence of the HMM and one for evaluating the probability that a given observation sequence was produced by a specific HMM. The observation sequence is derived from the input signal by sampling, converting to a spectral representation, and digitally coding using standard speech recognition techniques. The three match measures correspond, respectively, to training the model, refining the model and matching an event to a model, each of which is performed using conventional speech processing algorithms.

Item Type:Thesis (Engineer's thesis)
Subject Keywords:detection ; analysis ; musical events ; signal processing
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Mechanical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Culick, Fred E. C.
Thesis Committee:
  • Culick, Fred E. C. (chair)
  • Vaidyanathan, P. P.
  • Murray, Richard M.
Defense Date:1 May 1999
Record Number:CaltechETD:etd-12182007-111636
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-12182007-111636
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:5051
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:08 Jan 2008
Last Modified:24 Apr 2014 18:13

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