Circulant and skew-circulant matrices as new normal-form realization of IIR digital filters

Normal-form fixed-point state-space realization of IIR (infinite-impulse response) filters are known to be free from both overflow oscillations and roundoff limit cycles, provided magnitude truncation arithmetic is used together with two's-complement overflow features. Two normal-form realizations are derived that utilize circulant and skew-circulant matrices as their state transition matrices. The advantage of these realizations is that the A-matrix has only N (rather than N2) distinct elements and is amenable to efficient memory-oriented implementation. The problem of scaling the internal signals in these structures is addressed, and it is shown that an approximate solution can be obtained through a numerical optimization method. Several numerical examples are included

COMPLEX DIGITAL SIGNAL PROCESSING USING QUADRATIC RESIDUE NUMBER SYSTEMS.

This work presents the development of complex digital signal processing algorithms using number theoretic techniques. Residue number principles and techniques are applied to process complex signal information in Finite Impulse Response (FIR) and Infinite Impulse Response (IIR) digital filters. Residue coding of complex samples and arithmetic for processing complex data have been presented using principles of quadratic residues in the Residue Number System (RNS). In this work, we have presented modifications to the Quadratic Residue Number System (QRNS), which we have termed the Modified Quadratic Residue Number System (MQRNS), to process complex integers. New results and theorems have been obtained for the selection of operators to code complex integers into the new MQRNS representation. A novel scheme for residue to binary conversion has been presented for implementation using both the QRNS and MQRNS. Hardware implementations of multiplication intensive complex nonrecursive and recursive digital filters have been presented where the QRNS and MQRNS structures are realized using a bit-slice architectural approach. The computation of Complex Number Theoretic Transforms (CNTTs) and the hardware implementation of a radix-2 NTT butterfly structure, using high density ROM arrays, are presented in both the QRNS and MQRNS systems. As an illustration, the computation of the CNTT developed in this work, is used to compute Cyclic Convolution for complex sequences. These results are verified by computer programs. The recursive FIR filter structure for uniformly spaced frequency samples on the unit circle developed by adapting the Complex Number Theoretic z-transform, has been implemented using the QRNS and MQRNS. In this work, the filter structure is extended for non-uniformly spaced frequency samples and has been termed the generalized number theoretic filter structure. It is shown that for the implementation of this generalized structure, the MQRNS is more efficient than the conventional RNS; the QRNS does not support appropriate fields for the generalized structure.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis1985 .K757. Source: Dissertation Abstracts International, Volume: 46-08, Section: B, page: 2757. Thesis (Ph.D.)--University of Windsor (Canada), 1985

Components for oversampled signal processors

Oversampled converters trade transmission bandwidth for resolution. An idealized model gives an insight into the way in which signals are encoded and thus how they can be manipulated. Oversampling offers a form of signal processing that requires simple processing elements capable of exploiting the growing clock speeds available in integrated solutions. Simultaneously avoids the need for analog circuitry. This paper reviews common operations that can be performed on oversampled signals

Improved roundoff noise performance in a direct-form IIR filter using a modified delta operator

Among various direct-form delta operator filters, the delta direct-form II transposed (δDFIIt) has been shown to produce the lowest roundoff noise in finite-word-length implementations. Recent analyses focus on the optimization of the free parameter Δ of the delta operator, with scaling of the structure to prevent arithmetic overflow. This paper proposes a modified δDFIIt second-order section in which the Δs at different branches are separately optimized to further suppress roundoff noise gain. Noise variance plots against pole locations are presented. Closed-form expressions for the optimal filter coefficients are derived and reduction of noise gain is confirmed by numerical examples.published_or_final_versio

A study on adaptive filtering for noise and echo cancellation.

The objective of this thesis is to investigate the adaptive filtering technique on the application of noise and echo cancellation. As a relatively new area in Digital Signal Processing (DSP), adaptive filters have gained a lot of popularity in the past several decades due to the advantages that they can deal with time-varying digital system and they do not require a priori knowledge of the statistics of the information to be processed. Adaptive filters have been successfully applied in a great many areas such as communications, speech processing, image processing, and noise/echo cancellation. Since Bernard Widrow and his colleagues introduced adaptive filter in the 1960s, many researchers have been working on noise/echo cancellation by using adaptive filters with different algorithms. Among these algorithms, normalized least mean square (NLMS) provides an efficient and robust approach, in which the model parameters are obtained on the base of mean square error (MSE). The choice of a structure for the adaptive filters also plays an important role on the performance of the algorithm as a whole. For this purpose, two different filter structures: finite impulse response (FIR) filter and infinite impulse response (IIR) filter have been studied. The adaptive processes with two kinds of filter structures and the aforementioned algorithm have been implemented and simulated using Matlab.Dept. of Electrical and Computer Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2005 .J53. Source: Masters Abstracts International, Volume: 44-01, page: 0472. Thesis (M.A.Sc.)--University of Windsor (Canada), 2005

An Introduction to Digital Signal Processing

An Introduction to Digital Signal Processing aims at undergraduate students who have basic knowledge in C programming, Circuit Theory, Systems and Simulations, and Spectral Analysis. The book is focused on basic concepts of digital signal processing, MATLAB simulation and implementation on selected DSP hardware in which the candidate is introduced to the basic concepts first before embarking to the practical part which comes in the later chapters. Initially Digital Signal Processing evolved as a postgraduate course which slowly filtered into the undergraduate curriculum as a simplified version of the latter. The goal was to study DSP concepts and to provide a foundation for further research where new and more efficient concepts and algorithms can be developed. Though this was very useful it did not arm the student with all the necessary tools that many industries using DSP technology would require to develop applications. This book is an attempt to bridge the gap. It is focused on basic concepts of digital signal processing, MATLAB simulation and implementation on selected DSP hardware. The objective is to win the student to use a variety of development tools to develop applications. Contents• Introduction to Digital Signal processing.• The transform domain analysis: the Discrete-Time Fourier Transform• The transform domain analysis: the Discrete Fourier Transform• The transform domain analysis: the z-transform• Review of Analogue Filter• Digital filter design.• Digital Signal Processing Implementation Issues• Digital Signal Processing Hardware and Software• Examples of DSK Filter Implementatio

A computer-aided design for digital filter implementation

Imperial Users onl

Implementing IIR filters via residue number systems.

by Tai Leong Charn.Bibliography: leaves R-i-iiiThesis (M.Phil.)--Chinese University of Hong Kong, 198

Two-dimensional block processors - structures and implementations

Includes bibliographical references.Two-dimensional (2-D) block processing technique for linear filtering of digital images is introduced. New 2-D block structures are derived for 2-D recursive digital filters realized by difference equations and state-space formulations. Several special cases have also been considered and the relevant 2-D block structures are given. The computational costs of different implementation techniques employing high-speed convolution algorithms such as fast Fourier transform, number theoretic transform and polynomial transform have been studied. A comparison among the relative efficiencies of these implementation schemes is made and a suitable method is then proposed using short convolution algorithm which results in a minimized computational time

An Introduction to Digital Signal Processing

An Introduction to Digital Signal Processing aims at undergraduate students who have basic knowledge in C programming, Circuit Theory, Systems and Simulations, and Spectral Analysis. The book is focused on basic concepts of digital signal processing, MATLAB simulation and implementation on selected DSP hardware in which the candidate is introduced to the basic concepts first before embarking to the practical part which comes in the later chapters. Initially Digital Signal Processing evolved as a postgraduate course which slowly filtered into the undergraduate curriculum as a simplified version of the latter. The goal was to study DSP concepts and to provide a foundation for further research where new and more efficient concepts and algorithms can be developed. Though this was very useful it did not arm the student with all the necessary tools that many industries using DSP technology would require to develop applications. This book is an attempt to bridge the gap. It is focused on basic concepts of digital signal processing, MATLAB simulation and implementation on selected DSP hardware. The objective is to win the student to use a variety of development tools to develop applications. Contents• Introduction to Digital Signal processing.• The transform domain analysis: the Discrete-Time Fourier Transform• The transform domain analysis: the Discrete Fourier Transform• The transform domain analysis: the z-transform• Review of Analogue Filter• Digital filter design.• Digital Signal Processing Implementation Issues• Digital Signal Processing Hardware and Software• Examples of DSK Filter Implementatio