Non-stationary sinusoidal parameter estimation

Brian Hamilton

Research output: ThesisMaster's Thesis

Abstract / Description of output

Parameter estimation is an essential step in sinusoidal modelling for additive sound synthesis, speech synthesis, and digital audio effects. This thesis investigates parameter estimation for a non-stationary sinusoidal signal model with a polynomial log-amplitude and a polynomial phase up to a given order. Two existing parameter estimation methods are investigated (the Reassignment Method and the Derivative Method) for the non-stationary sinusoidal model up to second-order. These methods are related to time-frequency reassignment for the spectrogram and they are shown to be biased by the effect of second-order log-amplitude and second-order phase modulations on spectrogram reassignment. Three generalized parameter estimations methods (the Distribution Derivative Method, the Generalized Reassignment Method, and the Generalized Derivative Method) that provide unbiased estimators for the non-stationary sinusoidal model up to any order are presented and formulated in a new, unified framework. These generalized methods are also related to spectrogram reassignment and it is shown that they correct the bias present in the second-order methods. Practical comparisons of the generalized methods and the theoretical lower limits of estimator performance, the Cramér-Rao bounds, are carried out in experimental tests with synthetic signals. For the sake of completeness, another state of the art method (the Quadratic Interpolated Fast Fourier Transform method) based the Fourier transform of a Gaussian windowed signal, is extended to second-order log-amplitude modulation and tested along with the generalized methods.
Original languageEnglish
Awarding Institution
  • McGill University
Supervisors/Advisors
  • Depalle, Philippe, Supervisor, External person
  • Clark, James J, Supervisor, External person
Publication statusPublished - 2012

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