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Abstract

Many studies have been developed aiming to improve digital filters realizations, recurring to intricate structures and analyzing probabilistically the error's behavior. The work presented in this paper analyzes the feasibility of fixed-point implementation of classical infinite impulse response notch filters: Butterworth, Chebyshev I and II, and elliptic. To scrutinize the deformations suffered for distinct design specifications, it is assessed: the effect of the quality factor and normalized cut-off frequency, in the number of significant bits necessary to represent the filter's coefficients. The implications brought to FPGA implementation are also verified. The work focuses especially on the implementation of power line notch filters used to improve the signal-to-noise ratio in biomedical signals. The results obtained, when quantizing the digital notch filters, show that by applying second-order sections decomposition, low-order digital filters may be designed using only part of double precision capabilities. High-order notch filters with harsh design constraints are implementable using double precision, but only in second-order sections. Thus, it is revealed that to optimize computation time in real-time applications, an optimal digital notch filter implementation platform should have variable arithmetic precision. Considering these implementation constraints, utmost operation performance is finally estimated when implementing digital notch filters in Xilinx Virtex-5 field-programmable gate arrays. The influence of several design specifications, e.g. type, and order, in the filter's behavior was evaluated, namely in regard to order, type, input and coefficient number of bits, quality factor and cut-off frequency. Finally the implications and potential applications of such results are discussed.
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Abstract

Various components of surface texture are identified, namely form, waviness and roughness. Separation of these components is done by digital filtering. Several problems exist during analysis of two-process surfaces. Therefore the Gaussian robust profile filtering technique was established and has been studied here. The computer generated 2D profiles and 3D surface topographies having triangular scratches as well as measured stratified surfaces were subjected to filtration. However even robust filter applications cause distortion of profiles having valleys wider than 100 μm. In order to minimize the distortion associated with wide and deep valleys, the robust filter should be modified. A special procedure was elaborated for minimizing distortion of roughness profiles caused by filtration. Application of this method to analyses of several profiles was presented. The difference between 1-D and 2-D filtering of surface topography using the same kind of filter was discussed. As a result we found that modification of a 2-D surface topography filter was not necessary.
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Abstract

The paper presents the equalization problem of non-linear phase response of digital IIR type filters. An improved analytical method of designing a low-order equalizer is presented. The proposed approach is compared with the original method. The genetic algorithm is presented as an iterative method of optimization. The vector and matrix representation of the all-pass equalizer are shown and introduced to the algorithm. The results are compared with the analytical method. In this paper we have also proposed the use of an aging factor and setting the initial population of the genetic algorithm around the solution provided by the analytical methodology
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