Digital Signal Processing Problems Research Articles

Triple-Base Hybrid Joint Sparse Form and its Applications

Multi-scalar multiplication and multi-exponentiation are the major problems in digital signal processing(DSP) and in public-key cryptography. In DSP, multiplication of the filter coefficients, which is used in different signal processing algorithms, is a time consuming operation. Also in elliptic curve cryptography(ECC), this multiplication process takes a lot of time. Though there are several algorithms to speed up this multiplication process, but they are not up to the satisfactory limit. The algorithms are based on the minimization of the multipliers or adders required, i.e. the minimization of the numbers of „one‟ appear in the binary representation of the signal and the coefficients in DSP or of the number of general multiplications and points addition in ECC. Different existing algorithms in this context are Joint Sparse Form(JSF), w-NAF, Double Base Chain(DBC), Hybrid Binery-Ternary Joint Sparse Form(HBTJSF) etc. In this paper, a novel algorithm has been proposed which is the modified HBTJSF, known as Triple-Base Hybrid Joint Sparse Form(TBHJSF). The proposed method is based on the decomposition of an integer or fraction that mixes the power of the base 2,3 and 5. The experimental results show that it requires less numbers of multiplier and adder and hence show its novelty over other algorithms.

Hardware Approach of a Multipurpose Finite Impulse Response Filter for Real-Time Filtering Applications

Problem statement: Finite Impulse Response (FIR) filters are widely u sed in various DSP applications. The design of digital FIR filters is a very basic problem in digital signal processing. A FIR filter with multiple operation capability is ce rtainly very useful for any real-time filtering applications. This article presents a multipurpose FIR filter design modeled by the hardware description language VHDL for real-time filtering a pplication. Approach: The VHDL has its concept of concurrency to cope with the parallelism of digi tal hardware. The novel feature is the capability o f the design to accomplish up to 127variable filter o rder and an arbitrary filter frequency response. Th e coefficients are calculated by Hamming windowing technique. Basing on selection embedded in the design, the model is able to execute highpass, lowp ass, bandstop and bandpass filtering operations. It is set at 8-bit signed data processing. To filter t he input data in time domain, Linear Constant Coefficient Difference Equation (LCCDE) is used by the filter. Results: The design outputs are validated through simulation and compilation. The o utput results are also compared with the MATLAB implemented calculated output results to test the correctness that proves the effectiveness of the design. Conclusion: With the capability of filtering signal in real ti me mode utilizing arbitrary filter shape, the multipurpose filter proves to be versatile.

Genetic algorithm and M-estimator based robust sequential estimation of parameters of nonlinear sinusoidal signals

Estimation of parameters of nonlinear superimposed sinusoidal signals is an important problem in digital signal processing. In this paper, we consider the problem of estimation of parameters of real valued sinusoidal signals. We propose a real-coded genetic algorithm based robust sequential estimation procedure for estimation of signal parameters. The proposed sequential method is based on elitist generational genetic algorithm and robust M-estimation techniques. The method is particularly useful when there is a large number of superimposed sinusoidal components present in the observed signal and is robust with respect to presence of outliers in the data and impulsive heavy tail noise distributions. Simulations studies and real life signal analysis are performed to ascertain the performance of the proposed sequential procedure. It is observed that the proposed methods perform better than the usual non-robust methods of estimation.

Piecewise‐quadratic Harmut basis functions and their application to problems in digital signal processing

AbstractIn this work, the well‐known system of orthogonal piecewise‐constant Harmut basis functions is investigated. As a result of research, their shortcomings are revealed such as weak convergence, discontinuity and others. To eliminate these problems, a new basis of piecewise‐quadratic Harmut functions is proposed and a fast spectral transformation algorithm is developed in this basis. For examples of analytically set and experimentally verified dependencies, the advantages of the algorithm for spectral transformations in a basis of piecewise‐quadratic Harmut functions are demonstrated. The proposed system and algorithm could find wide application in such areas as computer graphics, image processing and restoration, machine vision and multimedia, animation and programming of computer games. Copyright © 2010 John Wiley & Sons, Ltd.

Parameter estimation for exponential sums by approximate Prony method

The recovery of signal parameters from noisy sampled data is a fundamental problem in digital signal processing. In this paper, we consider the following spectral analysis problem: Let f be a real-valued sum of complex exponentials. Determine all parameters of f, i.e., all different frequencies, all coefficients, and the number of exponentials from finitely many equispaced sampled data of f. This is a nonlinear inverse problem. In this paper, we present new results on an approximate Prony method (APM) which is based on [1]. In contrast to [1], we apply matrix perturbation theory such that we can describe the properties and the numerical behavior of the APM in detail. The number of sampled data acts as regularization parameter. The first part of APM estimates the frequencies and the second part solves an overdetermined linear Vandermonde-type system in a stable way. We compare the first part of APM also with the known ESPRIT method. The second part is related to the nonequispaced fast Fourier transform (NFFT). Numerical experiments show the performance of our method.

Digital Model of Blood Circulation Analysis System

Digital signal processing is one of the most powerful technologies, developed by achievements in science and electronics engineering. Achievements of this technology significantly influenced communications, medicine technique, radiolocation and other. Digital signal processors are usually used for effective solution of digital signal processing problems class. Today digital signal processors are widely used practically in all fields, in which information processing in real-time is needed. Creation of diagnostic medicine systems is one of perspective fields using digital signal processors. The aim of this work was to create digital mathematical model of blood circulation analysis system using digital signal processing instead of analogical nodes of device. In first stage - work algorithm of blood circulation analysis system and mathematical model of blood circulation analysis system in Matlab-Simulink environment was created. In second stage - mathematical model was tested experimentally. Mathematically imitated Doppler signal was sent to tissue and was reflected. The signal was processed in digitally, blood flow direction was marked and blood speed was evaluated. Experimentation was done with real signals that were recorded while investigating patients in eye clinics. Gained results confirmed adequacy of created mathematical model to real analogical blood circulation analysis system (Lizi et al., 2003).

A statistical analysis of the “internal linear combination” method in problems of signal separation as in cosmic microwave background observations

Aims. The separation of foreground contamination from cosmic microwave background (CMB) observations is one of the most challenging and important problems of digital signal processing in Cosmology. In the literature, various techniques have been presented but no general consensus about their real performance and properties has been reached. This is due to the characteristics of these techniques that have been studied essentially through numerical simulations based on semi-empirical models of the CMB and the Galactic foreground. Such models often have different levels of sophistication and/or are based on different physical assumptions (e.g. the number of Galactic components and level of the noise). Hence, a reliable comparison is difficult. What is missing is a statistical analysis of the properties of the proposed methodologies. Here, we consider the Internal Linear Combination method (ILC) which, among the separation techniques, requires the smallest number of a priori assumptions. This feature is of particular interest in the context of CMB polarization measurements at small angular scales where the lack of knowledge of the polarized backgrounds represents a serious limit.

Algorithm and architecture for a high density, low power scalar product macrocell

The authors present a design approach for an arithmetic macrocell that computes the scalar product of two vectors, an operation ubiquitously present in the solution of many communications and digital signal processing problems. The core of the proposed architecture is a full combinational design containing a partial product generator, a partial product accumulator and a vector accumulator. The design addresses the competing optimisation goals of VLSI area, power dissipation and latency in the deep submicron regime. Compared with conventional merged arithmetic architectures, the proposed macrocell design represents a substantial improvement in the VLSI layout with little area wastage, a high degree of regularity and a good scalability for different vector lengths and operand widths. A theoretical analysis shows that the design of a 16-bit scalar product multiplier for input vectors with 16 elements, in comparison with traditionally designed architecture, achieves a saving of 38.6% in the silicon area, an up to 73% increase in the area usage efficiency and a 29.4% saving in the interconnect delay. Post-layout simulations of the proposed circuit, based on a 0.18 /spl mu/m CMOS process, show an average power dissipation of 64.96 mW and a latency of 6.92 ns at a standard supply voltage of 1.8 V, a superior performance for a single cycle instruction in a high-speed, low voltage 16-bit digital signal processor operating at 144 MHz. The use of shorter interconnects and more equalised interconnect delays, leads to the power dissipation and delay incurred by the interconnects being substantially reduced. Post-layout simulation of our proposed circuit at supply voltages ranging from 0.7 to 3.3 V shows a significant power reduction of 6 to 13% over the pre-layout simulation results of the conventional design.

Symbolic computation and signal processing

Many problems in digital signal processing can be converted to algebraic problems over polynomial and Laurent polynomial rings, and can be solved using the existing methods of algebraic and symbolic computation. This paper aims to establish this connection in a systematic manner, and demonstrate how it can be used to solve various problems arising from multidimensional signal processing. The method of Gröbner bases is used as a main computational tool.

Systolic SVD and QR Decomposition by Householder Reflections

SVD and QR Decomposition have attracted much attention recently for solving linear algebra and digital signal processing problems. The House-holder QR Decomposition requires a smaller number of operations then the Givens QR Decomposition and therefore is strongly recommended for sequential computer implementations (as found in nearly all known libraries like NAG, LINPACK, EISPACK etc.) However for parallel implementation it has not been widely used, because the Givens Rotations possess inherent parallelism and the Householder Reflections do not. This is true if one analyzes the original algorithm. Four independent loops and three bottlenecks between the loops are constraint for pipelining the computations. This leads to an inefficient solution, i.e. 4n time moments for each iteration and since there are n iterations then the total time to execute the algorithm is O(4n 2 ). Compared to 3n m 2 time steps for the Givens QR Decomposition it is uneconomic. In this paper we have used some recent results for the elimination of the computational and data broadcast, and data synchronization to derive a fully localized form of the Householder QR Decomposition algorithm. We have succeeded in reorganizing and transforming the algorithm from three bottlenecks to one and four loops to one. A linear and a double pipeline array of n+1 processors are presented to solve the problem in O ( n 2 /2) time steps. It is also shown that the bottlenecks for the bidiagonalization and SVD computation cannot be eliminated.

PARALLEL SOLUTION OF SYMMETRIC POSITIVE DEFINITE TOEPLITZ SYSTEMS

Initially, parallel algorithms were designed by parallelising the existing sequential algorithms for frequently occurring problems on available parallel architectures. More recently, parallel strategies have been identified and utilised resulting in many new parallel algorithms. However, the analysis of such techniques reveals that further strategies can be applied to increase the parallelism. One of these strategies, i.e., increasing the computational work in each processing node, can reduce the memory accesses and hence congestion in a shared memory multiprocessor system. Similarly, when network message passing is minimised in a distributed memory processor system, dramatic improvements in the performance of the algorithm ensue. A frequently occurring computational problem in digital signal processing (DSP) is the solution of symmetric positive definite Toeplilz linear systems. The Levinson algorithm for solving such linear equations is where the Toeplitz matrix property is utilised in the elimination process of each element to advantage. However, it can be shown that in the Parallel Implicit Elimination (PIE) method where more than one element is eliminated simultaneously, the Toeplitz structure can again be utilised to advantage. This relatively simple strategy yields a reduction in accesses to shared memory or network message passing, resulting in a significant improvement in the performance of the algorithm [2],

Discrete Equivalents of a Continuous Integral in Problems of Digital Signal Processing, Modeling, and Control

Discrete Equivalents of a Continuous Integral in Problems of Digital Signal Processing, Modeling, and Control

Z-transform theory and the FDTD method

In implementing the finite-difference time-domain (FDTD) method on materials which are dispersive or nonlinear, the relationship between the flux density and the electric field can be the most complicated part of the problem. Because the FDTD method is a sampled time-domain method, this relationship can be can be looked upon as a digital filtering problem. The Z transform is typically used in digital filtering and signal processing problems. The paper illustrates the use of the Z transform in implementing the FDTD method where complicated dispersive or nonlinear materials are involved.

Implementing the Viterbi algorithm

The Viterbi algorithm, an application of dynamic programming, is widely used for estimation and detection problems in digital communications and signal processing. It is used to detect signals in communication channels with memory, and to decode sequential error-control codes that are used to enhance the performance of digital communication systems. The Viterbi algorithm is also used in speech and character recognition tasks where the speech signals or characters are modeled by hidden Markov models. The article explains the basics of the Viterbi algorithm as applied to systems in digital communication systems, and speech and character recognition. It also focuses on the operations and the practical memory requirements to implement the Viterbi algorithm in real-time.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A sparse preconditioner for symmetric positive definite banded circulant and toeplitz linear systems

A tridiagonal circulant preconditioner for banded symmetric circulant linear systems which occur in digital signal processing (DSP) problems is studied. It is shown, that for banded symmetric positive definite (SPD) circulant matrices with bandwidth p and elements satisfying an efficient tridiagonal circulant preconditioner can be designed. The influence of a preconditioning parameter w on the condition number of the preconditioned linear system is studied and a formula for estimating is proposed.

The use of noise properties in set theoretic estimation

In most digital signal processing problems, the goal is to estimate an object from noise corrupted observations of a physical system. The authors describe how a wide range of probabilistic information pertaining to the noise process can be used in a general set theoretic estimation framework. The basic principle is to constrain the sample statistics of the estimation residual to be consistent with those probabilistic properties of the noise which are available and to construct sets accordingly in the solution space. Adding these sets to the collection of sets describing the solution will yield a smaller feasibility set and, hence, more reliable estimates. Pieces of information relative to quantities such as range, moments, absolute moments, and second and higher order probabilistic attributes are considered, and properties of the corresponding sets are established. Simulations are provided to illustrate the theoretical developments. >

Parameter estimation and spectral analysis of the discrete nonlinear secondorder Wiener filter (NSWF)

In many problems of digital signal processing, it is required to determine a model matching the statistics of a given observation of a generally non-Gaussian random process. Because of the wide range of systems that can be represented by Volterra series and Wiener expansions, the discrete nonlinear second-order Wiener filter (NSWF) driven by white Gaussian noise has been used in this study to match the statistics of a discrete zero-mean stationary non-Gaussian random process. First, we derive the autocorrelation function and show that it does not provide sufficient information necessary for estimating the parameters of the proposed model. Next, we derive the third-order moment sequence and show that it provides additional information that can be used in conjunction with the autocorrelation function to solve the problem. The power spectrum and bispectrum of the discrete NSWF have been also derived.

SU I (2, F [ z,1/z ]) for F A Subfield of C

Let F be a subfield of C closed under complex conjugation, and denote by U(2, F[z, 1/z]) the multiplicative group of two-by-two unitary matrices over the ring F[z, 1/z] where lzl = 1. Let SU1(2, F[z, 1/z]) be the subgroup of such unitary matrices with determinant equal to the constant polynomial 1 and which are equal to the identity matrix upon evaluation at z = 1. The main result is the Unique Factorization Theorem for S U1 (2, F[z, 1 /z]), which expresses each element as an unique product of a minimal number of simple factors in SU1(2, F[z, 1/z]). Since these factors are free of relations, it follows that SU1(2, F[z, 1/z]) is a (nonabelian) free group generated by the factors. Besides having interesting algebraic and topological properties from the standpoint of pure mathematics, these unitary groups have application to the theory of Quadrature Mirror Filter banks and to the theory of with compact support especially in parameterizing various classes of QMF banks and wavelet families. After this manuscript was completed, the author's attention was drawn to reference [V], which derives (nonunique) factorizations of the groups U(d, R[z, 1/z]) and U(d, C[z, 1/z]) for d > 2. Reference [V], part of the extensive QMF literature, concentrates mainly on the application of these factorizations to design QMF banks for particular digital signal processing problems. The theory of wavelets with compact support provides both a generalization of and an analytical viewpoint of QMF theory. Wavelets with compact support were recently discovered by Ingrid Daubechies as described in [DI] and [D2].

General purpose video processor for high speed filtering applications

A video processor that allows the implementation of high-speed finite impulse response (FIR) video filters is described. This is made possible by using a parallel architecture implemented on 1.2 mu m CMOS EPROM technology. This solution makes it possible to overcome classical DSP (digital signal processing) problems such as processing speed, number of taps, flexibility, and volatility. The maximum achievable throughput in a single-chip configuration is 30 Mwords/s; such a processing speed allows comfortable use of the chip in the field of Rec. 601 (13.5 MHz sampling rate) while, in the case of HDTV (high-definition television), multiple-chip architectures may be configured to obtain a higher sampling rate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

30-Msamples/s programmable filter processor

A 30-MHz finite impulse response (FIR) programmable filter processor that has been developed using a 1.2- mu m CMOS EPROM technology with single metal is discussed. Its 30-MHz worst-case operating frequency meets most video filtering requirements and demonstrates the potential of nonvolatile memory technologies in embedded applications. The processor has been designed with a high level of parallelism and pipelining by using a transposed FIR structure. In this approach, the multipliers are implemented with an EPROM-based look-up table containing the results of the products between video samples and filter coefficients, according to the user's application. The chap can implement every kind of FIR filter with a maximum complexity of 59 taps in a half-band filter configuration, 32 taps for a symmetric filter, and 167 taps for an asymmetric one. The equivalent coefficient precision is 12 b, assuming 8 b of input data precision. Multiprocessor configurations are allowed for more demanding performances such as longer filters, input signal precision extension, two-dimensional processing, and increased throughput.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>