Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github

Automatic Spike sorting and robust power line interference cancellation for neural signal processing

Ph.DDOCTOR OF PHILOSOPH

Electric Powered Wheelchair Control with a Variable Compliance Joystick: Improving Control of Mobility Devices for Individuals with Multiple Sclerosis

While technological developments over the past several decades have greatly enhanced the lives of people with mobility impairments, between 10 and 40 percent of clients who desired powered mobility found it very difficult to operate electric powered wheelchairs (EPWs) safely because of sensory impairments, poor motor function, or cognitive deficits [1]. The aim of this research is to improve control of personalized mobility for those with multiple sclerosis (MS) by examining isometric and movement joystick interfaces with customizable algorithms. A variable compliance joystick (VCJ) with tuning software was designed and built to provide a single platform for isometric and movement, or compliant, interfaces with enhanced programming capabilities.The VCJ with three different algorithms (basic, personalized, personalized with fatigue adaptation) was evaluated with four subjects with MS (mean age 58.7±5.0 yrs; years since diagnosis 28.2±16.1 yrs) in a virtual environment. A randomized, two-group, repeated-measures experimental design was used, where two subjects used the VCJ in isometric mode and two in compliant mode.While still too early to draw conclusions about the performance of the joystick interfaces and algorithms, the VCJ was a functional platform for collecting information. Inspection of the data shows that the learning curve may be long for this system. Also, while subjects may have low trial times, low times could be related to more deviation from the target path

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique

An investigation of the utility of monaural sound source separation via nonnegative matrix factorization applied to acoustic echo and reverberation mitigation for hands-free telephony

In this thesis we investigate the applicability and utility of Monaural Sound Source Separation (MSSS) via Nonnegative Matrix Factorization (NMF) for various problems related to audio for hands-free telephony. We first investigate MSSS via NMF as an alternative acoustic echo reduction approach to existing approaches such as Acoustic Echo Cancellation (AEC). To this end, we present the single-channel acoustic echo problem as an MSSS problem, in which the objective is to extract the users signal from a mixture also containing acoustic echo and noise. To perform separation, NMF is used to decompose the near-end microphone signal onto the union of two nonnegative bases in the magnitude Short Time Fourier Transform domain. One of these bases is for the spectral energy of the acoustic echo signal, and is formed from the in- coming far-end user’s speech, while the other basis is for the spectral energy of the near-end speaker, and is trained with speech data a priori. In comparison to AEC, the speaker extraction approach obviates Double-Talk Detection (DTD), and is demonstrated to attain its maximal echo mitigation performance immediately upon initiation and to maintain that performance during and after room changes for similar computational requirements. Speaker extraction is also shown to introduce distortion of the near-end speech signal during double-talk, which is quantified by means of a speech distortion measure and compared to that of AEC. Subsequently, we address Double-Talk Detection (DTD) for block-based AEC algorithms. We propose a novel block-based DTD algorithm that uses the available signals and the estimate of the echo signal that is produced by NMF-based speaker extraction to compute a suitably normalized correlation-based decision variable, which is compared to a fixed threshold to decide on doubletalk. Using a standard evaluation technique, the proposed algorithm is shown to have comparable detection performance to an existing conventional block-based DTD algorithm. It is also demonstrated to inherit the room change insensitivity of speaker extraction, with the proposed DTD algorithm generating minimal false doubletalk indications upon initiation and in response to room changes in comparison to the existing conventional DTD. We also show that this property allows its paired AEC to converge at a rate close to the optimum. Another focus of this thesis is the problem of inverting a single measurement of a non- minimum phase Room Impulse Response (RIR). We describe the process by which percep- tually detrimental all-pass phase distortion arises in reverberant speech filtered by the inverse of the minimum phase component of the RIR; in short, such distortion arises from inverting the magnitude response of the high-Q maximum phase zeros of the RIR. We then propose two novel partial inversion schemes that precisely mitigate this distortion. One of these schemes employs NMF-based MSSS to separate the all-pass phase distortion from the target speech in the magnitude STFT domain, while the other approach modifies the inverse minimum phase filter such that the magnitude response of the maximum phase zeros of the RIR is not fully compensated. Subjective listening tests reveal that the proposed schemes generally produce better quality output speech than a comparable inversion technique

Analysis, modeling and wide-area spatiotemporal control of low-frequency sound reproduction

This research aims to develop a low-frequency response control methodology capable of delivering a consistent spectral and temporal response over a wide listening area. Low-frequency room acoustics are naturally plagued by room-modes, a result of standing waves at frequencies with wavelengths that are integer multiples of one or more room dimension. The standing wave pattern is different for each modal frequency, causing a complicated sound field exhibiting a highly position-dependent frequency response. Enhanced systems are investigated with multiple degrees of freedom (independently-controllable sound radiating sources) to provide adequate low-frequency response control. The proposed solution, termed a chameleon subwoofer array or CSA, adopts the most advantageous aspects of existing room-mode correction methodologies while emphasizing efficiency and practicality. Multiple degrees of freedom are ideally achieved by employing what is designated a hybrid subwoofer, which provides four orthogonal degrees of freedom configured within a modest-sized enclosure. The CSA software algorithm integrates both objective and subjective measures to address listener preferences including the possibility of individual real-time control. CSAs and existing techniques are evaluated within a novel acoustical modeling system (FDTD simulation toolbox) developed to meet the requirements of this research. Extensive virtual development of CSAs has led to experimentation using a prototype hybrid subwoofer. The resulting performance is in line with the simulations, whereby variance across a wide listening area is reduced by over 50% with only four degrees of freedom. A supplemental novel correction algorithm addresses correction issues at select narrow frequency bands. These frequencies are filtered from the signal and replaced using virtual bass to maintain all aural information, a psychoacoustical effect giving the impression of low-frequency. Virtual bass is synthesized using an original hybrid approach combining two mainstream synthesis procedures while suppressing each method‟s inherent weaknesses. This algorithm is demonstrated to improve CSA output efficiency while maintaining acceptable subjective performance

Machine Learning for Understanding Focal Epilepsy

The study of neural dysfunctions requires strong prior knowledge on brain physiology combined with expertise on data analysis, signal processing, and machine learning. One of the unsolved issues regarding epilepsy consists in the localization of pathological brain areas causing seizures. Nowadays the analysis of neural activity conducted with this goal still relies on visual inspection by clinicians and is therefore subjected to human error, possibly leading to negative surgical outcome. In absence of any evidence from standard clinical tests, medical experts resort to invasive electrophysiological recordings, such as stereoelectroencephalography to assess the pathological areas. This data is high dimensional, it could suffer from spatial and temporal correlation, as well as be affected by high variability across the population. These aspects make the automatization attempt extremely challenging. In this context, this thesis tackles the problem of characterizing drug resistant focal epilepsy. This work proposes methods to analyze the intracranial electrophysiological recordings during the interictal state, leveraging on the presurgical assessment of the pathological areas. The first contribution of the thesis consists in the design of a support tool for the identification of epileptic zones. This method relies on the multi-decomposition of the signal and similarity metrics. We built personalized models which share common usage of features across patients. The second main contribution aims at understanding if there are particular frequency bands related to the epileptic areas and if it is worthy to focus on shorter periods of time. Here we leverage on the post-surgical outcome deriving from the Engel classification. The last contribution focuses on the characterization of short patterns of activity at specific frequencies. We argue that this effort could be helpful in the clinical routine and at the same time provides useful insight for the understanding of focal epilepsy

Modelling and practical set-up to investigate the performance of permanent magnet synchronous motor through rotor position estimation at zero and low speeds

This thesis provides a study for the rotor position estimation in SM-PMSMs, particularly at zero and low speeds. The method for zero rotor speed is based on injection of three high frequency voltage pulses in the motor stator windings. Then, the voltage responses at the motor terminals are exploited to extract the rotor position. Two approaches, modelling and practical implementations, are presented. The obtained results have showed a verification of a high-resolution position estimation (a position estimation of 1 degree angle), a simplicity and cost effective implementation and a no need for current sensors is required to achieve the estimation process. It should be noticed that the implementation of rotor position estimation at zero speed is only attended when the rotor is at standstill or very low speed. Therefore, the motor driver is not expected to be active at this condition. Thereby, the zero speed estimation does not provide a robust torque control. In future, this should be taking into consideration to overcome this drawback and to make the estimator more reliable. At low speed running, the primary goal is to start spinning the under test motors, and then the rotor position estimation is achieved. The motor spinning is based on adopting a virtual injected signal to generate the voltage components, Vα and Vβ, of the space vector pulse width modulation technique. Then, generating the eight space vectors is conducted through storing the standard patterns of the six space vector sectors in a memory structure together with the timing sequences of each sector. The presented strategy of motor running includes a proposed motor speed control scheme, which is based on controlling the frequency of the power signal, at the inverter output, through controlling the timing period of execution the power delivery program. The thesis presents a proposed method to achieve the estimation goal depends on tracking the magnetic saliency on one motor line voltage. Thereby, the rotor position estimation The introduced proposed method, for rotor position estimation at zero speed, verifies the following contributions: - Presents a simple and cost effective zero speed rotor position estimator for the motor under test. - The aimed resolution in this thesis is an angle 1 degree. IV - Adopting solely the measuring of motor terminal voltages. Eliminating the detection of the rotor magnet polarity as a necessary technique for completing the position estimation. At low speed running, the following contributions are verified: - Rather than a real frequency signal, a virtual injected signal is adopted to generate the voltage components, Vα and Vβ of the space vector pulse width modulation technique. - The proposed method for generating the eight space vectors is based on storing the standard patterns of the six sectors in a memory structure together with the timing sequence. - The strategy of motor speed control is based on controlling the period of execution the power delivery program. - The strategy of low speed rotor position employs one motor line voltage from which the low speed estimation is achieved