19,233 research outputs found

    A study of the effects of the coefficients of generalized bilinear transformations in design of two-dimensional variable recursive digital filters

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    Two-dimensional variable recursive digital filters are applied in signal processing and communication systems where the frequency-domain characteristics of digital filters are required to be adjustable. The main objective of this thesis is to propose a new technique of designing 2-D recursive digital filters with variable characteristics. From a 1-D second order Butterworth low-pass analog ladder structure, 2-D low-pass and high-pass digital filters can be obtained through the application of double generalized bilinear transformations when the coefficients of the transformations are chosen in their specified ranges. And when one or more these coefficients are changing, the resulting 2-D low-pass and high-pass filters possess variable magnitude responses. Another two important types of 2-D digital filters, 2-D band-pass and band-elimination filters, can also be obtained by properly combining a 2-D low-pass filter and a 2-D high-pass filter. When the coefficients used to obtain the 2-D low-pass and high-pass filters are changeable, the resulting 2-D band-pass and band-elimination filters also possess variable magnitude characteristics. The manner how each coefficient of generalized bilinear transformation affects each type of desiring 2-D recursive digital filters is investigated in detail. Stability is always an important issue in 2-D recursive digital filter design. The stability conditions of generalized bilinear transformation and the stability conditions of the 2-D digital filters having a denominator with single degree of each variable are discussed in detail here

    Design of Two-Dimensional Digital Filters Having Variable Monotonic Amplitude-Frequency Responses Using Darlington-type Gyrator Networks

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    This paper develops a design of two-dimensional (2D) digital filter with monotonic amplitude-frequency responses using Darlington-type gyrator networks by the application of Generalized Bilinear Transformation (GBT). The proposed design provides the stable monotonic amplitude-frequency responses and the desired cutoff frequency of the 2D digital filters. This 2D recursive digital filter design includes 2D digital low-pass, high-pass, band-pass and band-elimination filters. Design examples are given to illustrate the usefulness of the proposed technique. Index Terms— Stability, monotonic response, GBT, gyrator network. 1. Introduction Because of recent growth in the 2D signal processing activities, a significant amount of research work has been done on the 2D filter design [1] and it is seen that monotonic characteristics in frequency response of a filter is getting more popular. The filters with the monotonic characteristics are one of the best filters for the digital image, video and audio (enhancement and restoration) [2]. The filters are widely accepted in the applications of medical science, geographical science and environment, space and robotic engineering [1]. For example, medical applications are concerned with processing of chest X-Ray, cine angiogram, projection of frame axial tomography and other medical images that occurs in radiology, nuclear magnetic resonance (NMR), ultrasonic scanning and magnetic resonance imaging (MRI) etc. and the restoration and enhancement of these images are done by the 2D digital filters [3]. The design of 2D recursive filters is difficult due to the non-existence of the fundamental theorem of algebra in that the factorization of 2D polynomials into lower order polynomials and the testing for stability of a 2D transfer function (recursive) requires a large number of 54 Digital Filters computations. But, the major drawbacks of the recursive filters are their lower-order realizations and computational intensive design techniques. Several design techniques of 2D recursive filter have been reported in the literature [2], [4] – [9] and most of these designs have problems of computational complexity, stability and unable to provide variable magnitude monotonic characteristic. A design technique of 2D recursive filters have been shown which met simultaneously magnitude and group delay specifications [4], although the technique has the advantage of always ensuring the filter stability, the difficulties to be encountered are computational complexity and convergence [5]. In [6], 2D filter design as a linear programming problem has been proposed, but, this tends to require relatively long computation time. In [7], a filter design has been shown using the two specifications as the problem of minimizing the total length of modified complex errors and minimized it by an iterative procedure. Difficulties of the design obtain for two-dimensional stability testing at each iteration during the minimization procedure. One way to ensure a 2D transfer function is stable is if the denominator of the transfer function is satisfied to be a Very Strict Hurwitz Polynomial (VSHP) [8] and that can ensure a transfer function that there is no singularity in the right half of the biplane, which can make a system unstable. In [9]-[11], stable 2D recursive filters have been designed by generation of Very Strict Hurwitz Polynomial (VSHP), but it is not guaranteed to provide the stable monotonic amplitude-frequency responses. Several filter designs with monotonic amplitude frequency response has been reported [12] – [16], but to the best of our knowledge, filter design with variable monotonic amplitude frequency response is not proposed yet. In this paper, 2-D digital filters with variable monotonic amplitude frequency responses are designed starting from Darlington-type networks containing gyrators and doublyterminated RLC-networks. The extension of Darlington-synthesis to two-variable positive real functions is given in [17], [18]; but they do not contain gyrators. From the 2-D stable transfer functions so obtained, the GBT [19] is applied to obtain 2-D digital functions and their properties are studied. The designed filters are used in the image processing application. 2. THE TWO BASIC STRUCTURES CONSIDERED Two filter structures are considered for 2D digital recursive filters design and both structures are taken from Darlington-synthesis [20]. Figures 1(a) and (b) show the two structures considered in this paper. The impedances of the filters are replaced by doubly-terminated RLC filters and the overall transfer function will be of the form H ( s1 , s 2 , g )   N ï²ï® ( g )s ï² sï® ï²ï® 0 0 1 M n Nn 2 ï« ï€½0 ï¬ ï€½0   Dï« ( g )s ï¬ M d Nd (1

    All-Pole Recursive Digital Filters Design Based on Ultraspherical Polynomials

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    A simple method for approximation of all-pole recursive digital filters, directly in digital domain, is described. Transfer function of these filters, referred to as Ultraspherical filters, is controlled by order of the Ultraspherical polynomial, nu. Parameter nu, restricted to be a nonnegative real number (nu ≥ 0), controls ripple peaks in the passband of the magnitude response and enables a trade-off between the passband loss and the group delay response of the resulting filter. Chebyshev filters of the first and of the second kind, and also Legendre and Butterworth filters are shown to be special cases of these allpole recursive digital filters. Closed form equations for the computation of the filter coefficients are provided. The design technique is illustrated with examples

    On the Active Compensation of Operational Amplifier Based VCVS

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    A unified treatment of the active compensation for VCVS realized by operational amplifiers is presented. It is a summary of low-sensitivity circuit structures which can be either magnitude or phase compensated. The performance of such a circuits is discussed in detail. Experimental data for some of them are also included

    Adaptive identification and control of structural dynamics systems using recursive lattice filters

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    A new approach for adaptive identification and control of structural dynamic systems by using least squares lattice filters thar are widely used in the signal processing area is presented. Testing procedures for interfacing the lattice filter identification methods and modal control method for stable closed loop adaptive control are presented. The methods are illustrated for a free-free beam and for a complex flexible grid, with the basic control objective being vibration suppression. The approach is validated by using both simulations and experimental facilities available at the Langley Research Center

    Two dimensional recursive digital filters for near real time image processing

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    A program was designed toward the demonstration of the feasibility of using two dimensional recursive digital filters for subjective image processing applications that require rapid turn around. The concept of the use of a dedicated minicomputer for the processor for this application was demonstrated. The minicomputer used was the HP1000 series E with a RTE 2 disc operating system and 32K words of memory. A Grinnel 256 x 512 x 8 bit display system was used to display the images. Sample images were provided by NASA Goddard on a 800 BPI, 9 track tape. Four 512 x 512 images representing 4 spectral regions of the same scene were provided. These images were filtered with enhancement filters developed during this effort

    Underdetermined-order recursive least-squares adaptive filtering: The concept and algorithms

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    Design of recursive digital filters having specified phase and magnitude characteristics

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    A method for a computer-aided design of a class of optimum filters, having specifications in the frequency domain of both magnitude and phase, is described. The method, an extension to the work of Steiglitz, uses the Fletcher-Powell algorithm to minimize a weighted squared magnitude and phase criterion. Results using the algorithm for the design of filters having specified phase as well as specified magnitude and phase compromise are presented

    Adaptive control of large space structures using recursive lattice filters

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    The use of recursive lattice filters for identification and adaptive control of large space structures is studied. Lattice filters were used to identify the structural dynamics model of the flexible structures. This identification model is then used for adaptive control. Before the identified model and control laws are integrated, the identified model is passed through a series of validation procedures and only when the model passes these validation procedures is control engaged. This type of validation scheme prevents instability when the overall loop is closed. Another important area of research, namely that of robust controller synthesis, was investigated using frequency domain multivariable controller synthesis methods. The method uses the Linear Quadratic Guassian/Loop Transfer Recovery (LQG/LTR) approach to ensure stability against unmodeled higher frequency modes and achieves the desired performance
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