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

Multirate digital filters, filter banks, polyphase networks, and applications: a tutorial

Multirate digital filters and filter banks find application in communications, speech processing, image compression, antenna systems, analog voice privacy systems, and in the digital audio industry. During the last several years there has been substantial progress in multirate system research. This includes design of decimation and interpolation filters, analysis/synthesis filter banks (also called quadrature mirror filters, or QMFJ, and the development of new sampling theorems. First, the basic concepts and building blocks in multirate digital signal processing (DSPJ, including the digital polyphase representation, are reviewed. Next, recent progress as reported by several authors in this area is discussed. Several applications are described, including the following: subband coding of waveforms, voice privacy systems, integral and fractional sampling rate conversion (such as in digital audio), digital crossover networks, and multirate coding of narrow-band filter coefficients. The M-band QMF bank is discussed in considerable detail, including an analysis of various errors and imperfections. Recent techniques for perfect signal reconstruction in such systems are reviewed. The connection between QMF banks and other related topics, such as block digital filtering and periodically time-varying systems, based on a pseudo-circulant matrix framework, is covered. Unconventional applications of the polyphase concept are discussed

Design of near-perfect-reconstructed transmultiplexer using different modulation techniques: A comparative study

AbstractIn this paper, an efficient iterative method for design of near-perfect reconstructed transmultiplexer (NPR TMUX) is proposed for the prescribed roll-off factor (RF) and stop band attenuation (As). In this method, windowing technique has been used for the design of prototype filter, and different modulation techniques have been exploited for designing multi-channel transmultiplexer (TMUX). In this method, inter-channel interference (ICI) is iteratively minimized so that it approximately reduces to ideal value zero. Design example is given to illustrate the superiority of the proposed method over earlier reported work. A comparative study of the performance of different modulation techniques for designing TMUX is also presented

On optimal design and applications of linear transforms

Linear transforms are encountered in many fields of applied science and engineering. In the past, conventional block transforms provided acceptable answers to different practical problems. But now, under increasing competitive pressures, with the growing reservoir of theory and a corresponding development of computing facilities, a real demand has been created for methods that systematically improve performance. As a result the past two decades have seen the explosive growth of a class of linear transform theory known as multiresolution signal decomposition. The goal of this work is to design and apply these advanced signal processing techniques to several different problems. The optimal design of subband filter banks is considered first. Several design examples are presented for M-band filter banks. Conventional design approaches are found to present problems when the number of constraints increases. A novel optimization method is proposed using a step-by-step design of a hierarchical subband tree. This method is shown to possess performance improvements in applications such as subband image coding. The subband tree structuring is then discussed and generalized algorithms are presented. Next, the attention is focused on the interference excision problem in direct sequence spread spectrum (DSSS) communications. The analytical and experimental performance of the DSSS receiver employing excision are presented. Different excision techniques are evaluated and ranked along with the proposed adaptive subband transform-based excises. The robustness of the considered methods is investigated for either time-localized or frequency-localized interferers. A domain switchable excision algorithm is also presented. Finally, sonic of the ideas associated with the interference excision problem are utilized in the spectral shaping of a particular biological signal, namely heart rate variability. The improvements for the spectral shaping process are shown for time-frequency analysis. In general, this dissertation demonstrates the proliferation of new tools for digital signal processing

Filter Bank Multicarrier Modulation for Spectrally Agile Waveform Design

In recent years the demand for spectrum has been steadily growing. With the limited amount of spectrum available, Spectrum Pooling has gained immense popularity. As a result of various studies, it has been established that most of the licensed spectrum remains underutilized. Spectrum Pooling or spectrum sharing concentrates on making the most of these whitespaces in the licensed spectrum. These unused parts of the spectrum are usually available in chunks. A secondary user looking to utilize these chunks needs a device capable of transmitting over distributed frequencies, while not interfering with the primary user. Such a process is known as Dynamic Spectrum Access (DSA) and a device capable of it is known as Cognitive Radio. In such a scenario, multicarrier communication that transmits data across the channel in several frequency subcarriers at a lower data rate has gained prominence. Its appeal lies in the fact that it combats frequency selective fading. Two methods for implementing multicarrier modulation are non-contiguous orthogonal frequency division multiplexing (NCOFDM)and filter bank multicarrier modulation (FBMC). This thesis aims to implement a novel FBMC transmitter using software defined radio (SDR) with modulated filters based on a lowpass prototype. FBMCs employ two sets of bandpass filters called analysis and synthesis filters, one at the transmitter and the other at the receiver, in order to filter the collection of subcarriers being transmitted simultaneously in parallel frequencies. The novel aspect of this research is that a wireless transmitter based on non-contiguous FBMC is being used to design spectrally agile waveforms for dynamic spectrum access as opposed to the more popular NC-OFDM. Better spectral containment and bandwidth efficiency, combined with lack of cyclic prefix processing, makes it a viable alternative for NC-OFDM. The main aim of this thesis is to prove that FBMC can be practically implemented for wireless communications. The practicality of the method is tested by transmitting the FBMC signals real time by using the Simulink environment and USRP2 hardware modules

Locally Adaptive Wavelet-Based Image Interpolation

We describe a spatially adaptive algorithm for image interpolation. The algorithm uses a wavelet transform to extract information about sharp variations in the low-resolution image and then implicitly applies interpolation which adapts to the image local smoothness/singularity characteristics. The proposed algorithm yields images that are sharper compared to several other methods that we have considered in this paper. Better performance comes at the expense of higher complexity

Xampling: Signal Acquisition and Processing in Union of Subspaces

We introduce Xampling, a unified framework for signal acquisition and processing of signals in a union of subspaces. The main functions of this framework are two. Analog compression that narrows down the input bandwidth prior to sampling with commercial devices. A nonlinear algorithm then detects the input subspace prior to conventional signal processing. A representative union model of spectrally-sparse signals serves as a test-case to study these Xampling functions. We adopt three metrics for the choice of analog compression: robustness to model mismatch, required hardware accuracy and software complexities. We conduct a comprehensive comparison between two sub-Nyquist acquisition strategies for spectrally-sparse signals, the random demodulator and the modulated wideband converter (MWC), in terms of these metrics and draw operative conclusions regarding the choice of analog compression. We then address lowrate signal processing and develop an algorithm for that purpose that enables convenient signal processing at sub-Nyquist rates from samples obtained by the MWC. We conclude by showing that a variety of other sampling approaches for different union classes fit nicely into our framework.Comment: 16 pages, 9 figures, submitted to IEEE for possible publicatio

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide