On the theory and design of a class of recombination nonuniform filter banks with low-delay FIR and IIR filters

This paper studies the theory and design of a class of recombination nonuniform FBs (RNFB) with low-delay (LD) FIR and IIR filters. The conditions for suppressing the spurious response and achieving a good frequency characteristic for these LD FIR/IIR RNFBs are developed. The proposed LD FIR RNFBs have a lower system delay than their linear-phase counterparts, at the expense of slight increase in phase distortion of the analysis filters and arithmetic complexity. By model reducing the LD FIR uniform FBs by the modified model reduction method, an IIR RNFB with a similar characteristic can be readily obtained. A design example is given illustrate the effectiveness of the proposed method. © 2006 IEEE.published_or_final_versio

On the theory and design of a class of PR uniform and recombination nonuniform causal-Stable IIR cosine modulated filter banks

This paper studies the theory and design of a class of perfect reconstruction (PR) uniform causal-stable infinite-impulse response (IIR) cosine modulated filter banks (CMFBs). The design approach is also applicable to the design of PR recombination nonuniform (RN) IIR CMFBs. The polyphase components of the prototype filters of these IIR CMFBs are assumed to have the same denominator so as to simplify the PR condition. In designing the proposed IIR CMFB, a PR FIR CMFB with similar specifications is first designed. The finite-impulse response prototype filter is then converted to a nearly PR (NPR) IIR CMFB using a modified model reduction technique. The NPR IIR CMFB so obtained has a reasonably low reconstruction error. Its denominator is designed to be a polynomial in z M, where M is the number of channels, to simplify the PR condition. Finally, it is employed as the initial guess to constrained nonlinear optimization software for the design of the PR IIR CMFB. Design results show that both NPR and PR IIR CMFBs with good frequency characteristics and different system delays can be obtained by the proposed method. By using these IIR CMFBs in the RN CMFBs, new RN NPR and PR IIR CMFBs can be obtained similarly. © 2008 IEEE.published_or_final_versio

On the theory and design of a class of PR causal-stable IIR non-uniform recombination cosine modulated filter banks

This paper studies the theory and design of a class of perfect reconstruction (PR) causal-stable nonuniform recombination cosine modulated filter banks (RN CMFBs) with IIR filters. It is based on the RN CMFB previously proposed by one of the author. A PR FIR RN CMFB of similar specification is first designed. The prototype filters of the CMFBs are then model reduced to obtain a nearly PR (NPR) IIR RN CMFB by modifying a model reduction technique proposed by Brandenstein and Unbehauen. With these NPR IIR RN CMFBs as initial guess, PR IIR RN CMFB with very good frequency characteristics can be obtained readily by solving a constrained nonlinear optimisation problem using for example the function fmincom from MATLAB. Design results show that the proposed method is very effective in designing PR RN IIR CMFBs with good frequency characteristics and different system delays. © 2005 IEEE.published_or_final_versio

Optimal cosine modulated nonuniform linear phase FIR filter bank design via stretching and shifting frequency response of prototype filter

This paper proposes an optimal cosine modulated nonuniform linear phase finite impulse response (FIR) filter bank design. The frequency responses of all the analysis filters and the synthesis filters of the filter bank are derived based on both stretching and shifting the frequency response of the prototype filter. The total aliasing error of the filter bank is minimized subject to a specification on the maximum amplitude distortion of the filter bank as well as specifications on both the maximum passband ripple magnitude and the maximum stopband ripple magnitude of the prototype filter. This filter bank design problem is actually a functional inequality constrained optimization problem. Our recently developed integration approach is employed for solving the problem. Computer numerical simulation results show that our proposed design method outperforms existing design methods

The theory and design of recombination nonuniform filter-banks with linear-phase analysis/synthesis filters

The 47th Midwest Symposium on Circuits and Systems Conference, Salt Lake City, Utah, USA, 25-28 July 2004This paper studies the theory and design of a class of linear-phase (LP) nonuniform filter-banks (FBs) called recombination nonuniform FBs (RNFBs). It is based on a recombination structure, where certain channels of an M-channel uniform FB are merged by synthesis filters of transmultiplexor (TMUX). It is assumed that the numbers of channels of the FB and TMUX are coprime to each other so that it is possible to obtain linear-time invariant (LTI) analysis/synthesis filters, instead of linear periodic time varying (LPTV) filters. The spectral supports of the analysis filters are analyzed, and the existence and matching conditions to obtain LP RNFBs with good frequency characteristics are then derived. The LTI representation of the analysis filters and the use of cosine-roll-off characteristics allow us to design the analysis filters by the REMEZ exchange algorithm. Design examples of LP nearly perfect reconstruction (NPR) RNFBs are given to demonstrate the effectiveness of the proposed method.published_or_final_versio

Channelization for Multi-Standard Software-Defined Radio Base Stations

As the number of radio standards increase and spectrum resources come under more pressure, it becomes ever less efficient to reserve bands of spectrum for exclusive use by a single radio standard. Therefore, this work focuses on channelization structures compatible with spectrum sharing among multiple wireless standards and dynamic spectrum allocation in particular. A channelizer extracts independent communication channels from a wideband signal, and is one of the most computationally expensive components in a communications receiver. This work specifically focuses on non-uniform channelizers suitable for multi-standard Software-Defined Radio (SDR) base stations in general and public mobile radio base stations in particular. A comprehensive evaluation of non-uniform channelizers (existing and developed during the course of this work) shows that parallel and recombined variants of the Generalised Discrete Fourier Transform Modulated Filter Bank (GDFT-FB) represent the best trade-off between computational load and flexibility for dynamic spectrum allocation. Nevertheless, for base station applications (with many channels) very high filter orders may be required, making the channelizers difficult to physically implement. To mitigate this problem, multi-stage filtering techniques are applied to the GDFT-FB. It is shown that these multi-stage designs can significantly reduce the filter orders and number of operations required by the GDFT-FB. An alternative approach, applying frequency response masking techniques to the GDFT-FB prototype filter design, leads to even bigger reductions in the number of coefficients, but computational load is only reduced for oversampled configurations and then not as much as for the multi-stage designs. Both techniques render the implementation of GDFT-FB based non-uniform channelizers more practical. Finally, channelization solutions for some real-world spectrum sharing use cases are developed before some final physical implementation issues are considered

Design of quadrature mirror filter banks with canonical signed digit coefficients using genetic algorithms.

This thesis is about the use of a genetic algorithm to design QMF bank with canonical signed digit coefficients. A filter bank has applications in areas like video and audio coding, data communication, etc. Filter bank design is a multiobjective optimization problem. The performance depends on the reconstruction error of the overall filter bank and the individual performance of the composing lowpass filter. In this thesis we have used reconstruction error of the overall filter bank as our main objective and passband error, stopband error, stopband and passband ripples and transition width of the individual lowpass filter as constraints. Therefore filter bank design can be formulated as single objective multiple constraint optimization problem. A unique genetic algorithm is developed to optimize filer bank coefficients such that the corresponding system\u27s response matches that of an ideal system with an additional constraint that all coefficients are in canonical signed digit (CSD) format. A special restoration technique is used to restore the CSD format of the coefficients after crossover and mutation operators in Genetic algorithm. The proposed restoration technique maintains the specified word length and the maximum number of nonzero digits in filter banks coefficients. Experimental results are presented at the end. It is demonstrated that the designed genetic algorithm is reliable, and efficient for designing QMF banks.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .U67. Source: Masters Abstracts International, Volume: 43-05, page: 1785. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

Architectural Improvements Towards an Efficient 16-18 Bit 100-200 MSPS ADC

As Data conversion systems continue to improve in speed and resolution, increasing demands are placed on the performance of high-speed Analog to Digital Conversion systems. This work makes a survey about all these and proposes a suitable architecture in order to achieve the desired specifications of 100-200MS/s with 16-18 bit of resolution. The main architecture is based on paralleled structures in order to achieve high sampling rate and at the same time high resolution. In order to solve problems related to Time-interleaved architectures, an advanced randomization method was introduced. It combines randomization and spectral shaping of mismatches. With a simple low-pass filter the method can, compared to conventional randomization algorithms, improve the SFDR as well as the SINAD. The main advantage of this technique over previous ones is that, because the algorithm only need that ADCs are ordered basing on their time mismatches, the absolute accuracy of the mismatch identification method does not matter and, therefore, the requirements on the timing mismatch identification are very low. In addition to that, this correction system uses very simple algorithms able to correct not only for time but also for gain and offset mismatches

Wavelets and Subband Coding

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