各種の性質を改善した直交DTCWTの設計に関する研究

The Dual tree complex wavelet transforms (DTCWTs) have been found to be successful in many applications of signal and image processing. DTCWTs employ two real wavelet transforms, where one wavelet corresponds to the real part of complex wavelet and the other is the imaginary part. Two wavelet bases are required to be a Hilbert transform pair. Thus, DTCWTs are nearly shift invariant and have a good directional selectivity in two or higher dimensions with limited redundancies. In this dissertation, we propose two new classes of DTCWTs with improved properties. In Chapter 2, we review the Fourier transform at first and then introduce the fundamentals of dual tree complex wavelet transform. The wavelet transform has been proved to be a successful tool to express the signal in time and frequency domain simultaneously. To obtain the wavelet coefficients efficiently, the discrete wavelet transform has been introduced since it can be achieved by a tree of two-channel filter banks. Then, we discuss the design conditions of two-channel filter banks, i.e., the perfect reconstruction and orthonormality. Additionally, some properties of scaling and wavelet functions including orthonormality, symmetry and vanishing moments are also given. Moreover, the structure of DTCWT is introduced, where two wavelet bases are required to form a Hilbert transform pair. Thus, the corresponding scaling lowpass filters must satisfy the half-sample delay condition. Finally, the objective measures of quality are given to evaluate the performance of the complex wavelet. In Chapter 3, we propose a new class of DTCWTs with improved analyticity and frequency selectivity by using general IIR filters with numerator and denominator of different degree. In the common-factor technique proposed by Selesnick, the maximally at allpass filter was used to satisfy the halfsample delay condition, resulting in poor analyticity of complex wavelets. Thus, to improve the analyticity of complex wavelets, we present a method for designing allpass filters with the specified degree of flatness and equiripple phase response in the approximation band. Moreover, to improve the frequency selectivity of scaling lowpass filters, we locate the specified number of zeros at z = -1 and minimize the stopband error. The well-known Remez exchange algorithm has been applied to approximate the equiripple response. Therefore, a set of filter coefficients can be easily obtained by solving the eigenvalue problem. Furthermore, we investigate the performance on the proposed DTCWTs and dedicate how to choose the approximation band and stopband properly. It is shown that the conventional DTCWTs proposed by Selesnick are only the special cases of DTCWTs proposed in this dissertation. In Chapter 4, we propose another class of almost symmetric DTCWTs with arbitrary center of symmetry. We specify the degree of flatness of group delay, and the number of vanishing moments, then apply the Remez exchange algorithm to minimize the difference between two scaling lowpass filters in the frequency domain, in order to improve the analyticity of complex wavelets. Therefore, the equiripple behaviour of the error function can be obtained through a few iterations. Moreover, two scaling lowpass filters can be obtained simultaneously. As a result, the complex wavelets are orthogonal and almost symmetric, and have the improved analyticity. Since the group delay of scaling lowpass filters can be arbitrarily specified, the scaling functions have the arbitrary center of symmetry. Finally, several experiments of signal denoising are carried out to demonstrate the efficiency of the proposed DTCWTs. It is clear that the proposed DTCWTs can achieve better performance on noise reduction.電気通信大学201

NOVEL OFDM SYSTEM BASED ON DUAL-TREE COMPLEX WAVELET TRANSFORM

The demand for higher and higher capacity in wireless networks, such as cellular, mobile and local area network etc, is driving the development of new signaling techniques with improved spectral and power efficiencies. At all stages of a transceiver, from the bandwidth efficiency of the modulation schemes through highly nonlinear power amplifier of the transmitters to the channel sharing between different users, the problems relating to power usage and spectrum are aplenty. In the coming future, orthogonal frequency division multiplexing (OFDM) technology promises to be a ready solution to achieving the high data capacity and better spectral efficiency in wireless communication systems by virtue of its well-known and desirable characteristics. Towards these ends, this dissertation investigates a novel OFDM system based on dual-tree complex wavelet transform (D

The development of the quaternion wavelet transform

The purpose of this article is to review what has been written on what other authors have called quaternion wavelet transforms (QWTs): there is no consensus about what these should look like and what their properties should be. We briefly explain what real continuous and discrete wavelet transforms and multiresolution analysis are and why complex wavelet transforms were introduced; we then go on to detail published approaches to QWTs and to analyse them. We conclude with our own analysis of what it is that should define a QWT as being truly quaternionic and why all but a few of the “QWTs” we have described do not fit our definition

H^∞-Optimal Fractional Delay Filters

Fractional delay filters are digital filters to delay discrete-time signals by a fraction of the sampling period. Since the delay is fractional, the intersample behavior of the original analog signal becomes crucial. In contrast to the conventional designs based on the Shannon sampling theorem with the band-limiting hypothesis, the present paper proposes a new approach based on the modern sampled-data $H^{infty}$ optimization that aims at restoring the intersample behavior beyond the Nyquist frequency. By using the lifting transform or continuous-time blocking the design problem is equivalently reduced to a discrete-time $H^{infty}$ optimization, which can be effectively solved by numerical computation softwares. Moreover, a closed-form solution is obtained under an assumption on the original analog signals. Design examples are given to illustrate the advantage of the proposed method

Model-based Filtering of Interfering Signals in Ultrasonic Time Delay Estimations

In dieser Arbeit werden modellbasierte algorithmische Ansätze zur Interferenz-invarianten Zeitverschiebungsschätzung vorgestellt, die speziell für die Schätzung kleiner Zeitverschiebungsdifferenzen mit einer notwendigen Auflösung, die deutlich unterhalb der Abtastzeit liegt, geeignet sind. Daher lassen sich die Verfahren besonders gut auf die Laufzeit-basierte Ultraschalldurchflussmessung anwenden, da hier das Problem der Interferenzsignale besonders ausgeprägt ist. Das Hauptaugenmerk liegt auf der Frage, wie mehrere Messungen mit unterschiedlichen Zeitverschiebungen oder Prozessparametern zur Unterdrückung der Interferenzsignale in Ultraschalldurchflussmessungen verwendet werden können, wobei eine gute Robustheit gegenüber additivem weißen Gauß\u27schen Rauschen und eine hohe Auflösung erhalten bleiben sollen. Zu diesem Zweck wird ein Signalmodell angenommen, welches aus stationären Interferenzsignalen, die nicht von wechselnden Zeitverschiebungen abhängig sind, und aus Zielsignalen, die den Messeffekt enthalten, besteht. Zunächst wird das Signalmodell einer Ultraschalldurchflussmessung und sein dynamisches Verhalten bei Temperatur- oder Zeitverschiebungsschwankungen untersucht. Ziel ist es, valide Simulationsdatensätze zu erzeugen, mit denen die entwickelten Methoden sowohl unter der Prämisse, dass die Daten perfekt zum Signalmodell passen, als auch unter der Prämisse, dass Modellfehler vorliegen, getestet werden können. Dabei werden die Eigenschaften der Signalmodellkomponenten, wie Bandbreite, Stationarität und Temperaturabhängigkeit, identifiziert. Zu diesem Zweck wird eine neue Methode zur Modellierung der Temperaturabhängigkeit der Interferenzsignale vorgestellt. Nach der Charakterisierung des gesamten Messsystems wird das Signalmodell -- angepasst an die Ultraschalldurchflussmessung -- als Grundlage für zwei neue Methoden verwendet, deren Ziel es ist, die Auswirkungen der Interferenzsignale zu reduzieren. Die erste vorgeschlagene Technik erweitert die auf der Signaldynamik basierenden Ansätze in der Literatur, indem sie die Voraussetzungen für die erforderliche Varianz der Zeitverschiebungen abschwächt. Zu diesem Zweck wird eine neue Darstellung von mehreren Messsignalen als Punktwolken eingeführt. Die Punktwolken werden dann mithilfe der Hauptkomponentenanalyse und B-Splines verarbeitet, was entweder zu Interferenz-invarianten Zeitverschiebungsschätzungen oder geschätzten Interferenzsignalen führt. In diesem Zusammenhang wird eine neuartige gemeinsame B-Spline- und Registrierungsschätzung entwickelt, um die Robustheit zu erhöhen. Der zweite Ansatz besteht in einer regressionsbasierten Schätzung der Zeitverschiebungsdifferenzen durch das Erlernen angepasster Signalunterräume. Diese Unterräume werden effizient durch die Analytische Wavelet Packet Transformation berechnet, bevor die resultierenden Koeffizienten in Merkmale transformiert werden, die gut mit den Zeitverschiebungssdifferenzen korrelieren. Darüber hinaus wird ein neuartiger, unbeaufsichtigter Unterraum-Trainingsansatz vorgeschlagen und mit den konventionellen Filter- und Wrapper-basierten Merkmalsauswahlmethoden verglichen. Schließlich werden beide Methoden in einem experimentellen Ultraschalldurchflussmesssystem mit einem hohen Maß an vorhandenen Interferenzsignalen getestet, wobei sich zeigt, dass sie in den meisten Fällen den Methoden aus der Literatur überlegen sind. Die Qualität der Methoden wird anhand der Genauigkeit der Zeitverschiebungsschätzung bewertet, da die Grundwahrheit für die Interferenzsignale nicht zuverlässig bestimmt werden kann. Anhand verschiedener Datensätze werden die Abhängigkeiten von den Hyperparametern, den Prozessbedingungen und, im Falle der regressionsbasierten Methode, dem Trainingsdatensatz analysiert

Model-based Filtering of Interfering Signals in Ultrasonic Time Delay Estimations

This work presents model-based algorithmic approaches for interference-invariant time delay estimation, which are specifically suited for the estimation of small time delay differences with a necessary resolution well below the sampling time. Therefore, the methods can be applied particularly well for transit-time ultrasonic flow measurements, since the problem of interfering signals is especially prominent in this application

Wavelet Theory

The wavelet is a powerful mathematical tool that plays an important role in science and technology. This book looks at some of the most creative and popular applications of wavelets including biomedical signal processing, image processing, communication signal processing, Internet of Things (IoT), acoustical signal processing, financial market data analysis, energy and power management, and COVID-19 pandemic measurements and calculations. The editor’s personal interest is the application of wavelet transform to identify time domain changes on signals and corresponding frequency components and in improving power amplifier behavior