One- and two-level filter-bank convolvers

In a recent paper, it was shown in detail that in the case of orthonormal and biorthogonal filter banks we can convolve two signals by directly convolving the subband signals and combining the results. In this paper, we further generalize the result. We also derive the statistical coding gain for the generalized subband convolver. As an application, we derive a novel low sensitivity structure for FIR filters from the convolution theorem. We define and derive a deterministic coding gain of the subband convolver over direct convolution for a fixed wordlength implementation. This gain serves as a figure of merit for the low sensitivity structure. Several numerical examples are included to demonstrate the usefulness of these ideas. By using the generalized polyphase representation, we show that the subband convolvers, linear periodically time varying systems, and digital block filtering can be viewed in a unified manner. Furthermore, the scheme called IFIR filtering is shown to be a special case of the convolver

A new class of two-channel biorthogonal filter banks and wavelet bases

We propose a novel framework for a new class of two-channel biorthogonal filter banks. The framework covers two useful subclasses: i) causal stable IIR filter banks. ii) linear phase FIR filter banks. There exists a very efficient structurally perfect reconstruction implementation for such a class. Filter banks of high frequency selectivity can be achieved by using the proposed framework with low complexity. The properties of such a class are discussed in detail. The design of the analysis/synthesis systems reduces to the design of a single transfer function. Very simple design methods are given both for FIR and IIR cases. Zeros of arbitrary multiplicity at aliasing frequency can be easily imposed, for the purpose of generating wavelets with regularity property. In the IIR case, two new classes of IIR maximally flat filters different from Butterworth filters are introduced. The filter coefficients are given in closed form. The wavelet bases corresponding to the biorthogonal systems are generated. the authors also provide a novel mapping of the proposed 1-D framework into 2-D. The mapping preserves the following: i) perfect reconstruction; ii) stability in the IIR case; iii) linear phase in the FIR case; iv) zeros at aliasing frequency; v) frequency characteristic of the filters

Hybrid Wavelet-Support Vector Classifiers

The Support Vector Machine (SVM) represents a new and very promising technique for machine learning tasks involving classification, regression or novelty detection. Improvements of its generalization ability can be achieved by incorporating prior knowledge of the task at hand. We propose a new hybrid algorithm consisting of signal-adapted wavelet decompositions and SVMs for waveform classification. The adaptation of the wavelet decompositions is tailormade for SVMs with radial basis functions as kernels. It allows the optimization Of the representation of the data before training the SVM and does not suffer from computationally expensive validation techniques. We assess the performance of our algorithm against the background of current concerns in medical diagnostics, namely the classification of endocardial electrograms and the detection of otoacoustic emissions. Here the performance of SVMs can significantly be improved by our adapted preprocessing step

Lattice factorization and design of Perfect Reconstruction Filter Banks with any Length yielding linear phase

Publication in the conference proceedings of EUSIPCO, Florence, Italy, 200

The Design of Equal Complexity FIR Perfect Reconstruction Filter Banks Incorporating Symmetries

In this report, we present a new approach to the design of perfect reconstruction filter banks (PRFB’s) which have equal length FIR analysis and synthesis filters. To achieve perfect reconstruction, necessary and sufficient conditions are incorporated directly in a numerical design procedure as a set of quadratic equality constraints among the impulse response coefficients of the filters. Any symmetry inherent in a particular application, such as quadrature mirror symmetry, linear phase, or symmetry between analysis and synthesis filters, may be exploited to reduce the number of variables and constraints in the design problem. A novel feature of our new approach is that it allows the design of filter banks that perform functions other than flat passband band-splitting

A Novel Method for Designing M-Band Linear-Phase Perfrect-Reconstruction filter Banks

This paper studies the design of M-channel perfect-reconstruction (PR) linear-phase (LP) filter banks (FBs) with M=2k using a tree-structured FB. It is based on a observation of Fliege(1995) that the length of the analysis filters is decreased by a factor of two when the depth of the tree is increased by one, while its transition bandwidth is increased by the same factor. A lattice-based 2-channel LP FB is chosen because the frequency responses of the lowpass and highpass analysis (synthesis) filters can be designed to be closely symmetric to the other around π/2. By properly selecting the filter length, transition bandwidth. and stopband attenuation of the 2-channel PR LP FBs at each level of the tree structure, it is possible to design uniform PR LP FB with excellent frequency characteristic and much lower system delay.published_or_final_versio

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

Wavelets and multirate filter banks : theory, structure, design, and applications

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2004.Includes bibliographical references (p. 219-230) and index.Wavelets and filter banks have revolutionized signal processing with their ability to process data at multiple temporal and spatial resolutions. Fundamentally, continuous-time wavelets are governed by discrete-time filter banks with properties such as perfect reconstruction, linear phase and regularity. In this thesis, we study multi-channel filter bank factorization and parameterization strategies, which facilitate designs with specified properties that are enforced by the actual factorization structure. For M-channel filter banks (M =/> 2), we develop a complete factorization, M-channel lifting factorization, using simple ladder-like structures as predictions between channels to provide robust and efficient implementation; perfect reconstruction is structurally enforced, even under finite precision arithmetic and quantization of lifting coefficients. With lifting, optimal low-complexity integer wavelet transforms can thus be designed using a simple and fast algorithm that incorporates prescribed limits on hardware operations for power-constrained environments. As filter bank regularity is important for a variety of reasons, an aspect of particular interest is the structural imposition of regularity onto factorizations based on the dyadic form uvt. We derive the corresponding structural conditions for regularity, for which M-channel lifting factorization provides an essential parameterization. As a result, we are able to design filter banks that are exactly regular and amenable to fast implementations with perfect reconstruction, regardless of the choice of free parameters and possible finite precision effects. Further constraining u = v ensures regular orthogonal filter banks,(cont.) whereas a special dyadic form is developed that guarantees linear phase. We achieve superior coding gains within 0.1% of the optimum, and benchmarks conducted on image compression applications show clear improvements in perceptual and objective performance. We also consider the problem of completing an M-channel filter bank, given only its scaling filter. M-channel lifting factorization can efficiently complete such biorthogonal filter banks. On the other hand, an improved scheme for completing paraunitary filter banks is made possible by a novel order-one factorization which allows greater design flexibility, resulting in improved frequency selectivity and energy compaction over existing state of the art methods. In a dual setting, the technique can be applied to transmultiplexer design to achieve higher-rate data transmissions.by Ying-Jui Chen.Ph.D

Unified Theory for Biorthogonal Modulated Filter Banks

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/

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