264 research outputs found

    Wavelets and Subband Coding

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    First published in 1995, Wavelets and Subband Coding offered a unified view of the exciting field of wavelets and their discrete-time cousins, filter banks, or subband coding. The book developed the theory in both continuous and discrete time, and presented important applications. During the past decade, it filled a useful need in explaining a new view of signal processing based on flexible time-frequency analysis and its applications. Since 2007, the authors now retain the copyright and allow open access to the book

    Introduction to frames

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    This survey gives an introduction to redundant signal representations called frames. These representations have recently emerged as yet another powerful tool in the signal processing toolbox and have become popular through use in numerous applications. Our aim is to familiarize a general audience with the area, while at the same time giving a snapshot of the current state-of-the-art

    Unified Theory for Biorthogonal Modulated Filter Banks

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    Modulated filter banks (MFBs) are practical signal decomposition tools for M -channel multirate systems. They combine high subfilter selectivity with efficient realization based on polyphase filters and block transforms. Consequently, the O(M 2 ) burden of computations in a general filter bank (FB) is reduced to O(M log2 M ) - the latter being a complexity order comparable with the FFT-like transforms.Often hiding from the plain sight, these versatile digital signal processing tools have important role in various professional and everyday life applications of information and communications technology, including audiovisual communications and media storage (e.g., audio codecs for low-energy music playback in portable devices, as well as communication waveform processing and channelization). The algorithmic efficiency implies low cost, small size, and extended battery life, bringing the devices close to our skins.The main objective of this thesis is to formulate a generalized and unified approach to the MFBs, which includes, in addition to the deep theoretical background behind these banks, both their design by using appropriate optimization techniques and efficient algorithmic realizations. The FBs discussed in this thesis are discrete-time time-frequency decomposition/reconstruction, or equivalently, analysis-synthesis systems, where the subfilters are generated through modulation from either a single or two prototype filters. The perfect reconstruction (PR) property is a particularly important characteristics of the MFBs and this is the core theme of this thesis. In the presented biorthogonal arbitrary-delay exponentially modulated filter bank (EMFB), the PR property can be maintained also for complex-valued signals.The EMFB concept is quite flexible, since it may respond to the various requirements given to a subband processing system: low-delay PR prototype design, subfilters having symmetric impulse responses, efficient algorithms, and the definition covers odd and even-stacked cosine-modulated FBs as special cases. Oversampling schemes for the subsignals prove out to be advantageous in subband processing problems requiring phase information about the localized frequency components. In addition, the MFBs have strong connections with the lapped transform (LT) theory, especially with the class of LTs grounded in parametric window functions.<br/

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

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    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

    Discrete Wavelet Transforms

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    The discrete wavelet transform (DWT) algorithms have a firm position in processing of signals in several areas of research and industry. As DWT provides both octave-scale frequency and spatial timing of the analyzed signal, it is constantly used to solve and treat more and more advanced problems. The present book: Discrete Wavelet Transforms: Algorithms and Applications reviews the recent progress in discrete wavelet transform algorithms and applications. The book covers a wide range of methods (e.g. lifting, shift invariance, multi-scale analysis) for constructing DWTs. The book chapters are organized into four major parts. Part I describes the progress in hardware implementations of the DWT algorithms. Applications include multitone modulation for ADSL and equalization techniques, a scalable architecture for FPGA-implementation, lifting based algorithm for VLSI implementation, comparison between DWT and FFT based OFDM and modified SPIHT codec. Part II addresses image processing algorithms such as multiresolution approach for edge detection, low bit rate image compression, low complexity implementation of CQF wavelets and compression of multi-component images. Part III focuses watermaking DWT algorithms. Finally, Part IV describes shift invariant DWTs, DC lossless property, DWT based analysis and estimation of colored noise and an application of the wavelet Galerkin method. The chapters of the present book consist of both tutorial and highly advanced material. Therefore, the book is intended to be a reference text for graduate students and researchers to obtain state-of-the-art knowledge on specific applications

    The Telecommunications and Data Acquisition Report

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    This quarterly publication provides archival reports on developments in programs in space communications, radio navigation, radio science, and ground-based radio and radar astronomy. It reports on activities of the Deep Space Network (DSN) in planning, supporting research and technology, implementation, and operations. Also included are standardization activities at the Jet Propulsion Laboratory for space data and information systems

    Signal Processing in Space and Time:A Multidimensional Fourier Approach

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    Sound waves propagate through space and time by transference of energy between the particles in the medium, which vibrate according to the oscillation patterns of the waves. These vibrations can be captured by a microphone and translated into a digital signal, representing the amplitude of the sound pressure as a function of time. The signal obtained by the microphone characterizes the time-domain behavior of the acoustic wave field, but has no information related to the spatial domain. The spatial information can be obtained by measuring the vibrations with an array of microphones distributed at multiple locations in space. This allows the amplitude of the sound pressure to be represented not only as a function of time but also as a function of space. The use of microphone arrays creates a new class of signals that is somewhat unfamiliar to Fourier analysis. Current paradigms try to circumvent the problem by treating the microphone signals as multiple "cooperating" signals, and applying the Fourier analysis to each signal individually. Conceptually, however, this is not faithful to the mathematics of the wave equation, which expresses the acoustic wave field as a single function of space and time, and not as multiple functions of time. The goal of this thesis is to provide a formulation of Fourier theory that treats the wave field as a single function of space and time, and allows it to be processed as a multidimensional signal using the theory of digital signal processing (DSP). We base this on a physical principle known as the Huygens principle, which essentially says that the wave field can be sampled at the surface of a given region in space and subsequently reconstructed in the same region, using only the samples obtained at the surface. To translate this into DSP language, we show that the Huygens principle can be expressed as a linear system that is both space- and time-invariant, and can be formulated as a convolution operation. If the input signal is transformed into the spatio-temporal Fourier domain, the system can also be analyzed according to its frequency response. In the first half of the thesis, we derive theoretical results that express the 4-D Fourier transform of the wave field as a function of the parameters of the scene, such as the number of sources and their locations, the source signals, and the geometry of the microphone array. We also show that the wave field can be effectively analyzed on a small scale using what we call the space/time-frequency representation space, consisting of a Gabor representation across the spatio-temporal manifold defined by the microphone array. These results are obtained by treating the signals as continuous functions of space and time. The second half of the thesis is dedicated to processing the wave field in discrete space and time, using Nyquist sampling theory and multidimensional filter banks theory. In particular, we show examples of orthogonal filter banks that effectively represent the wave field in terms of its elementary components while satisfying the requirements of critical sampling and perfect reconstruction of the input. We discuss the architecture of such filter banks, and demonstrate their applicability in the context of real applications, such as spatial filtering and wave field coding
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