A generalized, parametric PR-QMF/wavelet transform design approach for multiresolution signal decomposition

This dissertation aims to emphasize the interrelations and the linkages of the theories of discrete-time filter banks and wavelet transforms. It is shown that the Binomial-QMF banks are identical to the interscale coefficients or filters of the compactly supported orthonormal wavelet transform bases proposed by Daubechies. A generalized, parametric, smooth 2-band PR-QMF design approach based on Bernstein polynomial approximation is developed. It is found that the most regular compact support orthonormal wavelet filters, coiflet filters are only the special cases of the proposed filter bank design technique. A new objective performance measure called Non-aliasing Energy Ratio(NER) is developed. Its merits are proven with the comparative performance studies of the well known orthonormal signal decomposition techniques. This dissertation also addresses the optimal 2-band PR-QMF design problem. The variables of practical significance in image processing and coding are included in the optimization problem. The upper performance bounds of 2-band PR-QMF and their corresponding filter coefficients are derived. It is objectively shown that there are superior filter bank solutions available over the standard block transform, DCT. It is expected that the theoretical contributions of this dissertation will find its applications particularly in Visual Signal Processing and Coding

Scattered Pilot-Based Channel Estimation for Channel Adaptive FBMC-OQAM Systems

Shaping the pulse of FilterBank MultiCarrier with Offset Quadrature Amplitude Modulation subcarrier modulation (FBMC-OQAM) systems offers a new degree of freedom for the design of mobile communication systems. In previous studies, we evaluated the gains arising from the application of Prototype Filter Functions (PFFs) and subcarrier spacing matched to the delay and Doppler spreads of doubly dispersive channels. In this paper, we investigate the impact of having imperfect channel knowledge at the receiver on the performance of Channel Adaptive Modulation (CAM) in terms of channel estimation errors and Bit Error Rate (BER). To this end, the channel estimation error for two different interference mitigation schemes proposed in the literature is derived analytically and its influence on the BER performance is analyzed for practical channel scenarios. The results show that FBMC-OQAM systems utilizing CAM and scattered pilot-based channel estimation provide a significant performance gain compared with the current one system design for a variety of channel scenarios ("one-fits-all") approach. Additionally, we verified that the often used assumption of a flat channel in the direct neighborhood of a pilot symbol is not valid for practical scenarios. © 2017 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works

An Adaptive Hilbert-Huang Transform System

This thesis presents a system which can be used to generate Intrinsic Mode Functions and the associated Hilbert spectrum resulting from techniques based on the Empirical Mode Decomposition as pioneered by N. E. Huang at the end of the 20th century. Later dubbed the Hilbert-Huang Transform by NASA, the process of decomposing data manually through repetitive detrending and subtraction followed by applying the Hilbert transform to the results was presented as a viable alternative to the wavelet transform which was gaining traction at the time but had shown significant limitations. In the last 20 years, the Hilbert-Huang Transform has received a lot of attention, but that attention has been miniscule relative to the amount of attention received by wavelet transformation. This is, in part, due to the limitations of the Empirical Mode Decomposition and also in part due to the difficulty in developing a theoretical basis for the manner in which the Empirical Mode Decomposition works. While the question of theoretical foundations is an important and tricky one, this thesis presents a system that breaks many of the previously known limits on band-width resolution, mode mixing, and viable decomposable frequency range relative to sampling frequency of the Empirical Mode Decomposition. Many recent innovations do not simply improve on N. E. Huang’s algorithm, but rather provide new approaches with different decompositional properties. By choosing the best technique at each step, a superior total decomposition can be arrived at. Using the Hilbert-Huang Transform itself during the decomposition as a guide as suggested by R. Deering in 2005, the final HHT can show distinct improvements. The AHHT System utilizes many of the properties of various Empirical Mode Decomposition techniques from literature, includes some novel innovations on those techniques, and then manages the total decomposition in an adaptive manner. The Adaptive Hilbert-Huang Transform System (AHHT) is demonstrated successfully on many different artificial signals, many with varying levels of noise down to -5dB SNR, as well as on an electrocardiogram and for comparison with a surface electromyographic study which found biopotential frequency-shifting associated with the fatigue of fast-twitch muscle fibers

Multidimensional Wave Digital Filters and Wavelets (Mehrdimensionale Wellendigitalfilter und Wavelets)

Das Kernziel dieser Dissertation ist der Entwurf von orthogonalen, mehrdimensionalen Wellendigitalfiltern für nichtseparierbare Abtastmatritzen (z.B. Quincunx-, Hexagonal-, BCCS-Matrix). Damit der Leser einen einfacheren Einstieg in den Filterentwurf hat, sind einige Grundlagen elektrischer Netzwerke und Filter vom analogen als auch vom digitalen Typ in Kapitel 2 angegeben. Wichtiges Beiwerk, welches digitale Filter mit der Wavelettransformation verknüpft, ist zusammengefaßt. Es wird weiterführende Literatur angegeben, die diesen Stoff ausführlicher behandelt. Weiterhin werden wichtige Abtastsätze präsentiert und ein angegebener Vergleich über die minimale Abtastrate zeigt einen interessanten Aspekt. Kapitel 3 zeigt Verbindungen von Wellendigitalfiltern zu ihren analogen Referenzfiltern. Desweiteren wird gezeigt, wie man eine perfekte Rekonstruktion mit Filterbänken erreicht ohne eine spektrale Faktorisierung durchführen zu müssen. Bekannte Wavelets, wie z.B. Meyer Wavelets, Sinc-Wavelet (Littlewood-Paley Wavelet), Haar Wavelet, Daubechies Wavelets und Butterworth Wavelets, sind in Kapitel 4 präsentiert. Weiterhin werden bekannte Filter gezeigt, die (sofern einige Einschränkungen eingehalten werden) benutzt werden können um neue orthonormale Wavelets, nämlich Cosinus-Rolloff Wavelets und Chebyshev Wavelets zu generieren. Es wird auch ein Filter präsentiert mit welchem eine Verschiebung der Abtastwerte um einen beliebigen reellen Wert effizient erfolgen kann. In den Kapiteln 5, 6 und 7 werden Entwurfsmethoden für mehrdimensionale Filter angegeben mit denen nichtseparierbare, orthogonale Wavelets (zwei- und dreidimensional) erzeugt werden können

Radar Technology

In this book “Radar Technology”, the chapters are divided into four main topic areas: Topic area 1: “Radar Systems” consists of chapters which treat whole radar systems, environment and target functional chain. Topic area 2: “Radar Applications” shows various applications of radar systems, including meteorological radars, ground penetrating radars and glaciology. Topic area 3: “Radar Functional Chain and Signal Processing” describes several aspects of the radar signal processing. From parameter extraction, target detection over tracking and classification technologies. Topic area 4: “Radar Subsystems and Components” consists of design technology of radar subsystem components like antenna design or waveform design

Planck early results. VI. The High Frequency Instrument data processing

We describe the processing of the 336 billion raw data samples from the High Frequency Instrument (HFI) which we performed to produce six temperature maps from the first 295 days of Planck-HFI survey data. These maps provide an accurate rendition of the sky emission at 100, 143, 217, 353, 545 and 857 GHz with an angular resolution ranging from 9.9 to 4.4^2. The white noise level is around 1.5 {\mu}K degree or less in the 3 main CMB channels (100--217GHz). The photometric accuracy is better than 2% at frequencies between 100 and 353 GHz and around 7% at the two highest frequencies. The maps created by the HFI Data Processing Centre reach our goals in terms of sensitivity, resolution, and photometric accuracy. They are already sufficiently accurate and well-characterised to allow scientific analyses which are presented in an accompanying series of early papers. At this stage, HFI data appears to be of high quality and we expect that with further refinements of the data processing we should be able to achieve, or exceed, the science goals of the Planck project.Comment: Replaced by the accepted version for publication, as part of a package of papers describing first results of the Planck mission The paper with figures at full resolution and full color tables can also be downloaded from the ESA site http://www.rssd.esa.int/Planc