Tree-structured complementary filter banks using all-pass sections

Tree-structured complementary filter banks are developed with transfer functions that are simultaneously all-pass complementary and power complementary. Using a formulation based on unitary transforms and all-pass functions, we obtain analysis and synthesis filter banks which are related through a transposition operation, such that the cascade of analysis and synthesis filter banks achieves an all-pass function. The simplest structure is obtained using a Hadamard transform, which is shown to correspond to a binary tree structure. Tree structures can be generated for a variety of other unitary transforms as well. In addition, given a tree-structured filter bank where the number of bands is a power of two, simple methods are developed to generate complementary filter banks with an arbitrary number of channels, which retain the transpose relationship between analysis and synthesis banks, and allow for any combination of bandwidths. The structural properties of the filter banks are illustrated with design examples, and multirate applications are outlined

Role of anticausal inverses in multirate filter-banks. I. System-theoretic fundamentals

In a maximally decimated filter bank with identical decimation ratios for all channels, the perfect reconstructibility property and the nature of reconstruction filters (causality, stability, FIR property, and so on) depend on the properties of the polyphase matrix. Various properties and capabilities of the filter bank depend on the properties of the polyphase matrix as well as the nature of its inverse. In this paper we undertake a study of the types of inverses and characterize them according to their system theoretic properties (i.e., properties of state-space descriptions, McMillan degree, degree of determinant, and so forth). We find in particular that causal polyphase matrices with anticausal inverses have an important role in filter bank theory. We study their properties both for the FIR and IIR cases. Techniques for implementing anticausal IIR inverses based on state space descriptions are outlined. It is found that causal FIR matrices with anticausal FIR inverses (cafacafi) have a key role in the characterization of FIR filter banks. In a companion paper, these results are applied for the factorization of biorthogonal FIR filter banks, and a generalization of the lapped orthogonal transform called the biorthogonal lapped transform (BOLT) developed

Construction of M - Band bandlimited wavelets for orthogonal decomposition

While bandlimited wavelets and associated IIR filters have shown serious potential in areas of pattern recognition and communications, the dyadic Meyer wavelet is the only known approach to construct bandlimited orthogonal decomposition. The sine scaling function and wavelet are a special case of the Meyer. Previous works have proposed a M - Band extension of the Meyer wavelet without solving the problem. One key contribution of this thesis is the derivation of the correct bandlimits for the scaling function and wavelets to guarantee an orthogonal basis. In addition, the actual construction of the wavelets based upon these bandlimits is developed. A composite wavelet will be derived based on the M scale relationships from which we will extract the wavelet functions. A proper solution to this task is proposed which will generate associated filters with the knowledge of the scaling function and the constraints for Mband orthogonality

Iterative greedy algorithm for solving the FIR paraunitary approximation problem

In this paper, a method for approximating a multi-input multi-output (MIMO) transfer function by a causal finite-impulse response (FIR) paraunitary (PU) system in a weighted least-squares sense is presented. Using a complete parameterization of FIR PU systems in terms of Householder-like building blocks, an iterative algorithm is proposed that is greedy in the sense that the observed mean-squared error at each iteration is guaranteed to not increase. For certain design problems in which there is a phase-type ambiguity in the desired response, which is formally defined in the paper, a phase feedback modification is proposed in which the phase of the FIR approximant is fed back to the desired response. With this modification in effect, it is shown that the resulting iterative algorithm not only still remains greedy, but also offers a better magnitude-type fit to the desired response. Simulation results show the usefulness and versatility of the proposed algorithm with respect to the design of principal component filter bank (PCFB)-like filter banks and the FIR PU interpolation problem. Concerning the PCFB design problem, it is shown that as the McMillan degree of the FIR PU approximant increases, the resulting filter bank behaves more and more like the infinite-order PCFB, consistent with intuition. In particular, this PCFB-like behavior is shown in terms of filter response shape, multiresolution, coding gain, noise reduction with zeroth-order Wiener filtering in the subbands, and power minimization for discrete multitone (DMT)-type transmultiplexers

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

Image Registration Using Redundant Wavelet Transforms

Imagery is collected much faster and in significantly greater quantities today compared to a few years ago. Accurate registration of this imagery is vital for comparing the similarities and differences between multiple images. Since human analysis is tedious and error prone for large data sets, we require an automatic, efficient, robust, and accurate method to register images. Wavelet transforms have proven useful for a variety of signal and image processing tasks, including image registration. In our research, we present a fundamentally new wavelet-based registration algorithm utilizing redundant transforms and a masking process to suppress the adverse effects of noise and improve processing efficiency. The shift-invariant wavelet transform is applied in translation estimation and a new rotation-invariant polar wavelet transform is effectively utilized in rotation estimation. We demonstrate the robustness of these redundant wavelet transforms for the registration of two images (i.e., translating or rotating an input image to a reference image), but extensions to larger data sets are certainly feasible. We compare the registration accuracy of our redundant wavelet transforms to the \u27critically sampled\u27 discrete wavelet transform using the Daubechies (7,9) wavelet to illustrate the power of our algorithm in the presence of significant additive white Gaussian noise and strongly translated or rotated images

Use of frequency response masking technique in designing A/D converter for SDR.

Thesis (M.Sc.Eng.)-University of KwaZulu-Natal, Durban, 2005.Analog-to-digital converters (ADCs) are required in almost all signal processing and communication systems. They are often the most critical components, since they tend to determine the overall system performance. Hence, it is important to determine their performance limitations and develop improved realizations. One of the most challenging tasks for realizing software defined radio (SDR) is to move ND conversion as close to the antenna as possible, this implies that the ADC has to sample the incoming signal with a very high sample rate (over 100 MSample/s) and with a very high resolution (14 -to -16 bits). To design and implement AID converters with such high performance, it is necessary to investigate new designing techniques. The focus in this work is on a particular type of potentially high-performance (high-resolution and highspeed) analog-to-digital conversion technique, utilizing filter banks, where two or more ADCs are used in the converter array in parallel together with asymmetric filter banks. The hybrid filter bank analog-todigital converter (HFB ADC) utilizes analog filters (analysis filters) to allocate a frequency band to each ADC in a converter array and digital synthesis filters to reconstruct the digitized signal. The HFB improves the speed and resolution of the conversion, in comparison to the standard time-interleaving technique by attenuating the effect of gain and phase mismatches between the ADCs. Many of the designs available in the literature are compromising between some metrics: design complexity, order of the filter bank (computation time) and the sharpness of the frequency response rolloff (the transition from the pass band to the stop band). In this dissertation, five different classes of near perfect magnitude reconstruction (NPMR) continuoustime hybrid filter banks (CT HFBs) are proposed. In each of the five cases, two filter banks are designed; analysis filter bank and synthesis filter bank. Since the systems are hybrid, continuous time IlR filter are used to implement the analysis filter bank and digital filters are used for the synthesis filter bank. To optimize the system, we used a new technique, known in the literature as frequency response masking (FRM), to design the synthesis filter bank. In this technique, the sharp roll-off characteristics can be achieved while keeping the complexity of the filter within practical range, this is done by splitting the filter into two filters in cascade; model filter with relaxed roll-off characteristics followed by a masking filter. One of the main factors controlling the overall complexity of the filter is the way of designing the model filter and that of designing the masking filter. The dissertation proposes three combinations: use of HR model filter and IlR masking filter, HR model filter/FIR masking filter and FIR model filter/FIR masking filter. To show the advantages of our designs, we considered the cases of designing the synthesis filter as one filter, either FIR or IlR. These two filters are used as base for comparison with our proposed designs (the use of masking response filter). The results showed the following: 1. Asymmetric hybrid filter banks alone are not sufficient for filters with sharp frequency response roll-off especially for HR/FIR class. 2. All classes that utilize FRM in their synthesis filter banks gave a good performance in general in comparison to conventional classes, such as the reduction of the order of filters 3. HR/HR FRM gave better performance than HR/FIR FRM. 4. Comparing HR/HR FRM using FIR masking filters and HR/IIR FRM using IIR masking filters, the latter gave better performance (the performance is generally measured in terms of reduced filter order). 5. All classes that use the FRM approach have a very low complexity, in terms of reduced filter order. Our target was to design a system with the following overall characteristics: pass band ripple of -0.01 dB, stop band minimum attenuation of - 40 dB and of response roll-off of 0.002. Our calculations showed that the order of the conventional IIR/FIR filter that achieves such characteristics is aboutN =2000. Using the FRM technique, the order N reduced to aboutN = 244, N = 179 for IIRJFIR and IIR/IIR classes, respectively. This shows that the technique is very effective in reducing the filter complexity. 6. The magnitude distortion and the aliasing noise are calculated for each design proposal and compared with the theoretical values. The comparisons show that all our proposals result in approximately perfect magnitude reconstruction (NPMR). In conclusion, our proposal of using frequency-response masking technique to design the synthesis filter bank can, to large extent, reduce the complexity of the system. The design of the system as a whole is simplified by designing the synthesis filter bank separately from the design of the analysis filter bank. In this case each bank is optimized separately. This implies that for SDR applications we are proposing the use of the continuous-time HFB ADC (CT HFB ADC) structure utilizing FRM for digital filters

Cognitive Radio Systems

Cognitive radio is a hot research area for future wireless communications in the recent years. In order to increase the spectrum utilization, cognitive radio makes it possible for unlicensed users to access the spectrum unoccupied by licensed users. Cognitive radio let the equipments more intelligent to communicate with each other in a spectrum-aware manner and provide a new approach for the co-existence of multiple wireless systems. The goal of this book is to provide highlights of the current research topics in the field of cognitive radio systems. The book consists of 17 chapters, addressing various problems in cognitive radio systems