Modern Methods of Time-Frequency Warping of Sound Signals

Tato práce se zabývá reprezentací nestacionárních harmonických signálů s časově proměnnými komponentami. Primárně je zaměřena na Harmonickou transformaci a jeji variantu se subkvadratickou výpočetní složitostí, Rychlou harmonickou transformaci. V této práci jsou prezentovány dva algoritmy využívající Rychlou harmonickou transformaci. Prvni používá jako metodu odhadu změny základního kmitočtu sbírané logaritmické spektrum a druhá používá metodu analýzy syntézou. Oba algoritmy jsou použity k analýze řečového segmentu pro porovnání vystupů. Nakonec je algoritmus využívající metody analýzy syntézou použit na reálné zvukové signály, aby bylo možné změřit zlepšení reprezentace kmitočtově modulovaných signálů za použití Harmonické transformace.This thesis deals with representation of non-stationary harmonic signals with time-varying components. Its main focus is aimed at Harmonic Transform and its variant with subquadratic computational complexity, the Fast Harmonic Transform. Two algorithms using the Fast Harmonic Transform are presented. The first uses the gathered log-spectrum as fundamental frequency change estimation method, the second uses analysis-by-synthesis approach. Both algorithms are used on a speech segment to compare its output. Further the analysis-by-synthesis algorithm is applied on several real sound signals to measure the increase in the ability to represent real frequency-modulated signals using the Harmonic Transform.

Estimation de l'enveloppe et de la fréquence locales par les opérateurs de Teager-Kaiser en interférométrie en lumière blanche.

In this work, a new method for surface extraction in white light scanning interferometry (WLSI) is introduced. The proposed extraction scheme is based on the Teager-Kaiser energy operator and its extended versions. This non-linear class of operators is helpful to extract the local instantaneous envelope and frequency of any narrow band AM-FM signal. Namely, the combination of the envelope and frequency information, allows effective surface extraction by an iterative re-estimation of the phase in association with a new correlation technique, based on a recent TK crossenergy operator. Through the experiments, it is shown that the proposed method produces substantially effective results in term of surface extraction compared to the peak fringe scanning technique, the five step phase shifting algorithm and the continuous wavelet transform based method. In addition, the results obtained show the robustness of the proposed method to noise and to the fluctuations of the carrier frequency

Multiple multidimensional morse wavelets

This paper defines a set of operators that localize a radial image in space and radial frequency simultaneously. The eigenfunctions of the operator are determined and a nonseparable orthogonal set of radial wavelet functions are found. The eigenfunctions are optimally concentrated over a given region of radial space and scale space, defined via a triplet of parameters. Analytic forms for the energy concentration of the functions over the region are given. The radial function localization operator can be generalised to an operator localizing any L-2(R-2) function. It is demonstrated that the latter operator, given an appropriate choice of localization region, approximately has the same radial eigenfunctions as the radial operator. Based on a given radial wavelet function a quaternionic wavelet is defined that can extract the local orientation of discontinuous signals as well as amplitude, orientation and phase structure of locally oscillatory signals. The full set of quaternionic wavelet functions are component by component orthogonal; their statistical properties are tractable, and forms for the variability of the estimators of the local phase and orientation are given, as well as the local energy of the image. By averaging estimators across wavelets, a substantial reduction in the variance is achieved