A Statistical Perspective of the Empirical Mode Decomposition

This research focuses on non-stationary basis decompositions methods in time-frequency analysis. Classical methodologies in this field such as Fourier Analysis and Wavelet Transforms rely on strong assumptions of the underlying moment generating process, which, may not be valid in real data scenarios or modern applications of machine learning. The literature on non-stationary methods is still in its infancy, and the research contained in this thesis aims to address challenges arising in this area. Among several alternatives, this work is based on the method known as the Empirical Mode Decomposition (EMD). The EMD is a non-parametric time-series decomposition technique that produces a set of time-series functions denoted as Intrinsic Mode Functions (IMFs), which carry specific statistical properties. The main focus is providing a general and flexible family of basis extraction methods with minimal requirements compared to those within the Fourier or Wavelet techniques. This is highly important for two main reasons: first, more universal applications can be taken into account; secondly, the EMD has very little a priori knowledge of the process required to apply it, and as such, it can have greater generalisation properties in statistical applications across a wide array of applications and data types. The contributions of this work deal with several aspects of the decomposition. The first set regards the construction of an IMF from several perspectives: (1) achieving a semi-parametric representation of each basis; (2) extracting such semi-parametric functional forms in a computationally efficient and statistically robust framework. The EMD belongs to the class of path-based decompositions and, therefore, they are often not treated as a stochastic representation. (3) A major contribution involves the embedding of the deterministic pathwise decomposition framework into a formal stochastic process setting. One of the assumptions proper of the EMD construction is the requirement for a continuous function to apply the decomposition. In general, this may not be the case within many applications. (4) Various multi-kernel Gaussian Process formulations of the EMD will be proposed through the introduced stochastic embedding. Particularly, two different models will be proposed: one modelling the temporal mode of oscillations of the EMD and the other one capturing instantaneous frequencies location in specific frequency regions or bandwidths. (5) The construction of the second stochastic embedding will be achieved with an optimisation method called the cross-entropy method. Two formulations will be provided and explored in this regard. Application on speech time-series are explored to study such methodological extensions given that they are non-stationary

Noise-Robust Voice Conversion

A persistent challenge in speech processing is the presence of noise that reduces the quality of speech signals. Whether natural speech is used as input or speech is the desirable output to be synthesized, noise degrades the performance of these systems and causes output speech to be unnatural. Speech enhancement deals with such a problem, typically seeking to improve the input speech or post-processes the (re)synthesized speech. An intriguing complement to post-processing speech signals is voice conversion, in which speech by one person (source speaker) is made to sound as if spoken by a different person (target speaker). Traditionally, the majority of speech enhancement and voice conversion methods rely on parametric modeling of speech. A promising complement to parametric models is an inventory-based approach, which is the focus of this work. In inventory-based speech systems, one records an inventory of clean speech signals as a reference. Noisy speech (in the case of enhancement) or target speech (in the case of conversion) can then be replaced by the best-matching clean speech in the inventory, which is found via a correlation search method. Such an approach has the potential to alleviate intelligibility and unnaturalness issues often encountered by parametric modeling speech processing systems. This work investigates and compares inventory-based speech enhancement methods with conventional ones. In addition, the inventory search method is applied to estimate source speaker characteristics for voice conversion in noisy environments. Two noisy-environment voice conversion systems were constructed for a comparative study: a direct voice conversion system and an inventory-based voice conversion system, both with limited noise filtering at the front end. Results from this work suggest that the inventory method offers encouraging improvements over the direct conversion method

IMPROVING THE AUTOMATIC RECOGNITION OF DISTORTED SPEECH

Automatic speech recognition has a wide variety of uses in this technological age, yet speech distortions present many difficulties for accurate recognition. The research presented provides solutions that counter the detrimental effects that some distortions have on the accuracy of automatic speech recognition. Two types of speech distortions are focused on independently. They are distortions due to speech coding and distortions due to additive noise. Compensations for both types of distortion resulted in decreased recognition error.Distortions due to the speech coding process are countered through recognition of the speech directly from the bitstream, thus eliminating the need for reconstruction of the speech signal and eliminating the distortion caused by it. There is a relative difference of 6.7% between the recognition error rate of uncoded speech and that of speech reconstructed from MELP encoded parameters. The relative difference between the recognition error rate for uncoded speech and that of encoded speech recognized directly from the MELP bitstream is 3.5%. This 3.2 percentage point difference is equivalent to the accurate recognition of an additional 334 words from the 12,863 words spoken.Distortions due to noise are offset through appropriate modification of an existing noise reduction technique called minimum mean-square error log spectral amplitude enhancement. A relative difference of 28% exists between the recognition error rate of clean speech and that of speech with additive noise. Applying a speech enhancement front-end reduced this difference to 22.2%. This 5.8 percentage point difference is equivalent to the accurate recognition of an additional 540 words from the 12,863 words spoken

Computation of the one-dimensional unwrapped phase

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2006.Includes bibliographical references (p. 101-102). "Cepstrum bibliography" (p. 67-100).In this thesis, the computation of the unwrapped phase of the discrete-time Fourier transform (DTFT) of a one-dimensional finite-length signal is explored. The phase of the DTFT is not unique, and may contain integer multiple of 27r discontinuities. The unwrapped phase is the instance of the phase function chosen to ensure continuity. This thesis presents existing algorithms for computing the unwrapped phase, discussing their weaknesses and strengths. Then two composite algorithms are proposed that use the existing ones, combining their strengths while avoiding their weaknesses. The core of the proposed methods is based on recent advances in polynomial factoring. The proposed methods are implemented and compared to the existing ones.by Zahi Nadim Karam.S.M

Studies on noise robust automatic speech recognition

Noise in everyday acoustic environments such as cars, traffic environments, and cafeterias remains one of the main challenges in automatic speech recognition (ASR). As a research theme, it has received wide attention in conferences and scientific journals focused on speech technology. This article collection reviews both the classic and novel approaches suggested for noise robust ASR. The articles are literature reviews written for the spring 2009 seminar course on noise robust automatic speech recognition (course code T-61.6060) held at TKK

Increasing Accuracy Performance through Optimal Feature Extraction Algorithms

This research developed models and techniques to improve the three key modules of popular recognition systems: preprocessing, feature extraction, and classification. Improvements were made in four key areas: processing speed, algorithm complexity, storage space, and accuracy. The focus was on the application areas of the face, traffic sign, and speaker recognition. In the preprocessing module of facial and traffic sign recognition, improvements were made through the utilization of grayscaling and anisotropic diffusion. In the feature extraction module, improvements were made in two different ways; first, through the use of mixed transforms and second through a convolutional neural network (CNN) that best fits specific datasets. The mixed transform system consists of various combinations of the Discrete Wavelet Transform (DWT) and Discrete Cosine Transform (DCT), which have a reliable track record for image feature extraction. In terms of the proposed CNN, a neuroevolution system was used to determine the characteristics and layout of a CNN to best extract image features for particular datasets. In the speaker recognition system, the improvement to the feature extraction module comprised of a quantized spectral covariance matrix and a two-dimensional Principal Component Analysis (2DPCA) function. In the classification module, enhancements were made in visual recognition through the use of two neural networks: the multilayer sigmoid and convolutional neural network. Results show that the proposed improvements in the three modules led to an increase in accuracy as well as reduced algorithmic complexity, with corresponding reductions in storage space and processing time