Theory and design of uniform DFT, parallel, quadrature mirror filter banks

In this paper, the theory of uniform DFT, parallel, quadrature mirror filter (QMF) banks is developed. The QMF equations, i.e., equations that need to be satisfied for exact reconstruction of the input signal, are derived. The concept of decimated filters is introduced, and structures for both analysis and synthesis banks are derived using this concept. The QMF equations, as well as closed-form expressions for the synthesis filters needed for exact reconstruction of the input signalx(n), are also derived using this concept. In general, the reconstructed. signalhat{x}(n)suffers from three errors: aliasing, amplitude distortion, and phase distortion. Conditions for exact reconstruction (i.e., all three distortions are zero, andhat{x}(n)is equal to a delayed version ofx(n))of the input signal are derived in terms of the decimated filters. Aliasing distortion can always be completely canceled. Once aliasing is canceled, it is possible to completely eliminate amplitude distortion (if suitable IIR filters are employed) and completely eliminate phase distortion (if suitable FIR filters are employed). However, complete elimination of all three errors is possible only with some simple, pathalogical stable filter transfer functions. In general, once aliasing is canceled, the other distortions can be minimized rather than completely eliminated. Algorithms for this are presented. The properties of FIR filter banks are then investigated. Several aspects of IIR filter banks are also studied using the same framework

Digital filter design using root moments for sum-of-all-pass structures from complete and partial specifications

Published versio

Theory and design of perfect reconstruction transmultiplexers and their relation to perfect reconstruction QMF banks

The theory of transmultiplexers involves the design of filters for interconversion between Time Domain Multiplexing (TDM) and Frequency Division Multiplexing (FDM), such that the undesirable Crosstalk is minimized. In TDM → FDM → TDM conversion, the perfect reconstruction trans-multiplexer (PR-TMUX) achieves complete Crosstalk Cancellation (CC) and is distortion-free. In this paper, we present an analysis of the PR-TMUX based on the polyphase component matrices of the filter banks used in TDM → FDM and FDM → TDM conversion respectively. Using that, a necessary and sufficient condition for complete CC is obtained. The close relation between PR-TMUX filters and PR-QMF banks is used to obtain a direct design procedure for PR-TMUX filters

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

Vector space framework for unification of one- and multidimensional filter bank theory

A number of results in filter bank theory can be viewed using vector space notations. This simplifies the proofs of many important results. In this paper, we first introduce the framework of vector space, and then use this framework to derive some known and some new filter bank results as well. For example, the relation among the Hermitian image property, orthonormality, and the perfect reconstruction (PR) property is well-known for the case of one-dimensional (1-D) analysis/synthesis filter banks. We can prove the same result in a more general vector space setting. This vector space framework has the advantage that even the most general filter banks, namely, multidimensional nonuniform filter banks with rational decimation matrices, become a special case. Many results in 1-D filter bank theory are hence extended to the multidimensional case, with some algebraic manipulations of integer matrices. Some examples are: the equivalence of biorthonormality and the PR property, the interchangeability of analysis and synthesis filters, the connection between analysis/synthesis filter banks and synthesis/analysis transmultiplexers, etc. Furthermore, we obtain the subband convolution scheme by starting from the generalized Parseval's relation in vector space. Several theoretical results of wavelet transform can also be derived using this framework. In particular, we derive the wavelet convolution theorem

FPGA IMPLEMENTATION OF LOW COMPLEXITY LINEAR PERIODICALLY TIME VARYING FILTER

ABSTRACT This paper presents a low complexity architecture for a linear periodically time varying (LPTV) filter. This architecture is based on multi-input multi-output(MIMO) representation of LPTV filters. The input signal is divided into blocks and parallel processing is incorporated, there by considerably reducing the effective input sampling rate. A single multiplier can be shared for each linear time invariant (LTI) filter in the representation. Each LTI filter is realized in the transposed direct form filter using multiplier less multiplication structures based on Binary common bit patterns (BCS). The proposed structure is simulated, synthesized and implemented on Virtex v50efg256-7 Field Programmable Gate Array (FPGA). LPTV systems can be expressed as generalization of Linear time invariant (LTI) systems. If the input for a M-period LPTV system is delayed by M samples, output is also delayed by the same number of samples. An LPTV system with a period of '1' is nothing but an LTI syste

Multi-dimensional filter design in digital television systems

Imperial Users onl

A Novel Iterative Structure for Online Calibration of M-Channel Time-Interleaved ADCs

published_or_final_versio

OFDM techniques for multimedia data transmission

Orthogonal Frequency Division Multiplexing (OFDM) is an efficient parallel data transmission scheme that has relatively recently become popular in both wired and wireless communication systems for the transmission of multimedia data. OFDM can be found at the core of well known systems such as digital television/radio broadcasting, ADSL internet and wireless LANs. Research into the OFDM field continually looks at different techniques to attempt to make this type of transmission more efficient. More recent works in this area have considered the benefits of using wavelet transforms in place of the Fourier transforms traditionally used in OFDM systems and other works have looked at data compression as a method of increasing throughput in these types of transmission systems. The work presented in this thesis considers the transmission of image and video data in traditional OFDM transmission and discusses the strengths and weaknesses of this method. This thesis also proposes a new type of OFDM system that combines transmission and data compression into one block. By merging these two processes into one the complexity of the system is reduced, therefore promising to increase system efficiency. The results presented in this thesis show the novel compressive OFDM method performs well in channels with a low signal-to-noise ratio. Comparisons with traditional OFDM with lossy compression show a large improvement in the quality of the data received with the new system when used in these noisy channel environments. The results also show superior results are obtained when transmitting image and video data using the new method, the high correlative properties of images are ideal for effective transmission using the new technique. The new transmission technique proposed in this thesis also gives good results when considering computation time. When compared to MATLAB simulations of a traditional DFT-based OFDM system with a separate compression block, the proposed transmission method was able to reduce the computation time by between a half to three-quarters. This decrease in computational complexity also contributes to transmission efficiency when considering the new method