# April 2001, Volume 10, Number 1

**R. Lukac, S. Marchevsky**
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Design of Boolean LUM Smoothers through Permutation Coloring Concept

Rank-order based LUM (lower-upper-middle) smoothers distinguishes by wide range of smoothing characteristics given by filter parameter. Thus, for the capability to achieve the best balance between noise suppression and signal details preservation, the LUM smoothers are preferred in smoothing applications. Thanks to threshold decomposition and stacking properties, the LUM smoothers belong to the class of stack filters. This paper is focused to the derivation of minimal positive Boolean function for LUM smoothers through permutation groups and a coloring concept.

- BARNER, K. E., ARCE, G. R. Permutation Filters: A Class of Nonlinear Filters Based on Set Permutations. IEEE Transac-tion on Signal Processing, vol. 42, no. 4, pp. 782-798, April 1994.
- BARNER, K. E., ARCE, G. R. Design of Permutation Filters Through Group Colorings. IEEE Transaction on Circuits and Systems - II, vol. 44, no. 7, pp. 531-548, July 1997.
- HARDIE, R. C., BONCELET, C. G. LUM Filters: A Class of Rank-Order-Based Filters for Smoothing and Sharpening. IEEE Transactions on Signal Processing, vol. 41, no. 3, pp. 1061-1076, March 1993.
- LEE, K.D., LEE, Y.H. Threshold Boolean Filters. IEEE Trans-actions on Signal Processing, vol. 42, no. 8, pp. 2022-2036, August 1994.
- LUKAC, R. An Adaptive Control of LUM Smoother. Radioen-gineering, vol. 9, no. 1, pp. 9-12, April 2000.
- LUKAC, R. Boolean LUM Smoother. Journal of Electrical Engineering, submitted.
- LUKAC, R., MARCHEVSKY, S. Digital Image Processing Based on LUM Filters. In Proceedings of the 3rd International Scientific Conference ELEKTRO '99, Zilina (Slovakia), pp. 84-89, May 1999.
- LUKAC, R., MARCHEVSKY, S. Adaptive LUM Smoother Controlled by Adaptive Threshold System. Journal of Electrical Engineering, no. 3-4, vol. 51, 2000, pp.100-104.
- LUKAC, R., MARCHEVSKY, S. A Neural LUM Smoother. Radioengineering, submitted.
- LUKAC, R., MARCHEVSKY, S. Reduced Permutation Group by Mean-Based Coloring. Journal of Electrical Engineering, submitted.
- MARCHEVSKY, S. Stack Filters for image processing. In Proceedings of Conference Digital Signal Processing. Tatran-ska Lomnica (Slovakia), pp. 61-64, November 1993.
- MARCHEVSKY, S. Stack Filters of Images Using Neural Networks. In Proceedings of First International Conference on Applied Mathematics, Oradea (Romania), pp. 87-96, 1993.
- PRASAD, M. K., LEE, Y. H. Stack Filters and Selection Probabilities. IEEE Transaction on Signal Processing, vol. 42, no. 10, pp. 2628-2643, October 1994.
- STUPAK, C. Searching the Optimal Training Set for Neural Stack Filters. In Proceedings of 5th International Scientific Conference of the Fund of Jozef Murgas for Telecommunication Joined with Competition, Bratislava, pp. 35-38, 1999.
- YU, P. T., LIAO, W. H. Weighted Order Statistics Filters - Their Classification, Some Properties, and Conversion Algorithm. IEEE Transaction on Signal Processing, vol. 42, no. 10, pp. 2678-2691, October 1994.

**K. Zaplatilek, M. Lares**
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Efficient Algorithms of Direct and Inverse First-Order S-Z
Transformations

In the article, we describe principles of numerical algorithms by means of which coefficients of continuous-time and discrete-time frequency filters are possible to transform each other for several s-z trans-formations. The basis of algorithms is so-called Pascal matrix for calculation of which an original procedure is used. We discuss problems of numerical conditionality of Pascal matrix and possibility of its practical usage. Illustrative examples of numerical calculations programmed in Matlab 5.1 are the constituent part of the article.

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- BIOLEK, D., BIOLKOVA, V. FIR-BL Analog Filters. In: Proc. of MWSCAS '99, Las Cruces, New Mexico (USA), 1999, pp. 259-262.
- BIOLKOVA, V., BIOLEK, D. LDI Matrix and its Utilization for the Circuit Analysis and Design. In: Proc. of Radioelektroni-ka '99, FEI VUT Brno (Czech Rep.), 1999, pp. 38-41.
- DOSTAL, T. Analyza a synteza obvodu se spinanymi kapacitory. VUT Publishing, Brno, 1988.
- FEISTEL, K. H., UNBEHAUEN, R. Tiefpasse mit Tschebyscheff-Charakter der Betriebsdampfung im Sperrbereich und Maximal Geebneter Laufzeit. Frequenz 19, 1965, pp. 265-282.
- KLEIN, W. Finite Systemtheorie. Teuner Studienbucher, Stuttgart, 1976.
- Matlab User's Giude. The Mathworks, Natick, 1996.
- POWER, H. M. The mechanics of the bilinear transformation. IEEE Trans. on CAS, vol. 10, no. 5, 1967, pp. 114-116.
- PSENICKA, B., PHAM KHAC, Di. Vypocet prenosove funkce cislicoveho filtru pomoci Pascalovy matice. Slaboproudy obzor, vol. 46, no. 7., 1985, pp. 348-350.
- RABINER, L. R., GOLD, B. Theory and Application of Digital Signal Processing. Prentice-Hall, Englewood Cliffs, 1975.
- RALSTON, A. A first course in numerical analysis. McGraw Hill, New York, 1965.
- VICH, R. Transformace Z a nektera jeji pouziti. SNTL, Praha, 1983.
- ZAPLATILEK, K. Synthesis of transfer functions of analogue filters by means of bilinear transformation In: Proc. of XXVIth General Assembly of URSI. Toronto (Canada), 1999, pp. 230.
- BIOLKOVA, V., BIOLEK, D. Generalized Pascal Matrix of First Order s-z Transforms. In: Proc. of the ICECS'99, Pafos, (Cyprus), 1999, pp. 929-931.
- BIOLEK, D.: Computer design of IIR filters using signal inva-riance approach. BIOSIGNAL'94, VUT Brno, 1994.

**R. Hudec, S. Marchevsky**
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Extension of Impulse Detectors to Spatial Dimension and their
Utilization as Switch in the LMS L-SD Filter

In this paper, one kind of adaptive LMS filters based on order statistics is used for two-dimensional filtration of noisy greyscale images degraded by mixed noise. The signal-dependent adaptive LMS L-filter (L-SD) consists of two normalized constrained adaptive LMS L-filters, because they have better convergence properties than simple LMS algorithm. Moreover, first filter suppresses the noise in homogeneous regions and second filter preserves the high components of filtered image. Some versions of spatial order statistic detectors were developed from the impulse detectors and were employed as switch between output these filters.

- KONTROPOULOS, C., PITAS, I. Adaptive LMS L-Filters for Noise Suppression in Image. IEEE Transaction on Image Processing, vol. 5, no. 12, pp. 1596-1609, December 1996.
- KONTROPOULOS, C. PITAS, I. Constrained adaptive LMS L-Filters. IEEE Transactions on Signal Processing, vol. 26, no. 3, pp. 335-358, March 1992.
- HUDEC, R., MARCHEVSKY, S. Reduction of mixed noise by using adaptive LMS L-Filters. In: Proceedings of the 4th International Conference on Digital Signal Processing, Herzany (Slovakia), pp. 88-92, September 1999.
- KOCUR, D. , HUDEC, R., MARCHEVSKY, S. Suppression of mixed noise in the similar images by using adaptive LMS L-filters. Radioengineering, submitted.
- KOCUR, D. Adaptation algorithms for the digital adaptive Voltera filters. Habilitation Thesis, FEI TU Kosice, Decem-ber 1994. (in Slovak)
- KOCUR, D. Non-linear adaptive digital filtration. In Proceedings of the Conference Digital signal processing '92, Kosice (Slovakia), pp. 60-65, 1992. (in Slovak)
- LUKAC, R., STUPAK , Cs. A Class of Impulse Detectors Controlled By a Threshold. In: Proceedings of the 3rd International Scientific Conference Information and Algorithms '99, Kosice (Slovakia), pp. 178-181, 1999.

**A. Rudiakova, V. Krizhanovski**
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Maximally Flat Waveforms Operation of Class-F Power Amplifiers

The requirements to output network's impedance on higher harmonic components and appropriate input driving for formation maximally flat waveforms of drain current and voltage were presented. Using such waveforms allows obtaining maximal efficiency and output power capability of class-F power amplifiers.

- TYLER, V. A new high efficiency high power amplifier, Marconi Rev., vol. 21, pp. 96 - 109, 1958.
- SNIDER, D. A theoretical analysis and experimental confirmation of the optimally loaded and overdriven RF power amplifier, IEEE Trans. Electron Devices, vol. ED-14, pp. 851-857, June 1967.
- KRAUSS, H., BOSTIAN, C., RAAB, F. Solid State Radio Engineering, New -York: Wiley, 1980.
- RAAB, F. Introduction to Class-F Power Amplifiers, R.F. Des., vol. 19, no.5 pp. 79-84, July 1996.
- RAAB, F. Class F Power Amplifiers with maximally Flat Waveforms, IEEE Trans. on Microwave Theory and Tech-niques, vol.45, pp. 2007 - 2013, 1997.
- RUDIAKOVA, A., KRIZHANOVSKI V. The theory of Power Amplifiers with a polyharmonic operating, XIII International Conference on Microwaves, Radar and Wireless Communications, Wroclaw, Poland, p.p 105 - 108, 2000.
- INGRUBER, B., PRITZL, W., SMELY, D., WACHUTKA, M., MAGERL, G. High-Efficiency Harmonic-Control Amplifier, IEEE Trans. on Microwave Theory and Techniques, vol.46, pp. 857 - 862, 1998.
- INGRUBER, B., BAUMGARTNER, J., SMELY, D., WACHUTKA, M., MAGERL, G., PETZ, F. Rectangularly Driven Class A Harmonic-Control Amplifier, IEEE Trans. on Microwave Theory and Techniques, vol.46, pp. 1667 - 1672, 1998.
- SHUR, M. GaAs Devices and Circuits, Plenum Press - New York and London, 1987.

**R. Hudec, S. Marchevsky**
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Adaptive Order-Statistic LMS Filters

The LMS-based adaptive order-statistic filters are presented in this paper. The adaptive Ll-filters as extension of the adaptive L-filter for two-dimensional filtering of noisy greyscale images is studied too. Their adaptation properties are studied by three types of noise, the additive white Gaussian noise, the impulsive noise or both, respectively. Moreover, the impulsive noise has the fixed noise value (Salt & Pepper noise). The problem of pixel value multiplicity and determination its position in the ordered input vector for adaptive Ll-filter is shown in this article. The two types of images with different of image complexity are used to demonstration of the power of time-spatial ordering.

- KONTROPOULOS, C., PITAS, I. Adaptive LMS L-Filters for Noise Suppression in Image. IEEE Transaction on Image Processing, vol. 5, no. 12, pp. 1596-1609, December 1996.
- KOCUR, D., HUDEC, R., MARCHEVSKY, S. Suppression of mixed noise in the similar images by using adaptive LMS L-filters. Radioengineering, submitted.
- HUDEC, R.: Multidimensional digital filtration of the noisy images degraded by mixed noise by the adaptive LMS Wiener, L and IIR filters. Minima Work, Technical University of Kosice, 2000. (In Slovak)
- PALMIERI, F., BONCELET, C.G. Ll-filters - A new class of order statistic filters. IEEE Transaction on Acoustics, Speech and Signal Processing, vol. 37, no. 5, pp. 691-701, May 1989.
- TSEKERIDOU, S., KOTROPOULOS, C., PITAS, I. Adaptive Order Statistic Filters for the Removal of Noise from Corrupted Images. SPIE Optical Engineering, vol. 37, no. 10, pp. 2798-2816, October 1998.
- MARCHEVSKY, S., MARTINEC, P. Fast Ll-filters for image processing. In: proceedings of the Statewide seminary "New trends in signal processing", Rackova dolina, pp. 65-69, May 1990. (In Slovak)
- KOCUR, D., DRUTAROVSKY, M., MARCHEVSKY, S. A new class of nonlinear filters: Microstatistic Volterra filters. Radioengineering, vol. 5, no. 1, pp. 19-24, April 1996.
- KOCUR, D. Convergence in the Mean of Adaptive LMS Volterra Filters. Proceedings of The Technical University of Oradea (Romania), 1994.
- KOCUR, D., DRUTAROVSKY, M., MARCHEVSKY, S. Microstatistic Volterra filters. In: Proceedings of the 40. Internationales Wissenschaftliches Kolloquium, Ilmenau, Band 1, September 1995, pp. 376-381.
- KOCUR, D., HENDEL, I.: Adaptive Microstatistic Volterra Filters. Journal of Electrical Engineering, vol. 49, no. 9-10, pp. 225-231, 1998.

**J. Turan, P. Farkas**
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Line Fitting Using Hough-Like Procedure

The Hough Transform is an image processing algorithm which is used to extract geometric primitives from digital images. It has a number of desirable properties, typically robustness to noise and data occlusion. In this paper a new approach to line fitting problem based on Hough Transform is presented. A critical comparison is made with the more traditional least squares method and potential benefits arising from the application of the proposed HT method is illustrated by examples.

- DAVIES, E. R. Machine Vision: Theory, Algorithms, Practicalities. Academic Press, London, 1990.
- HOUGH, P. V. C. Method and Means for Recognizing Complex Patterns. U. S. Patent 3069654, 1962.
- DUDA, R. D., HART, P. E.: Use of the Hough Transform to Detect Lines and Curves in Pictures. Comm. ACM, vol. 15, no. 1, 1972, pp. 11-15.
- ILLINGWORTH, J., KITTLER, J. A Survey of the Hough Transform. Computer Vision, Graphics, and Image Processing, vol. 44, 1988, pp. 87-116.
- DEANS, S. R. The Radon Transform and Some of Its Applications. John Wiley and Sons, New York, 1983.
- LEAVERS, V.F., BENTZVI, D., SANDLER, M.B. A dynamic combinational Hough transform for straight lines and circles. Proceedings of the Fifth Alvey Vision Conference, Reading, UK, September 1989, pp. 163-167.
- KIRYATI, N., ELDAR, Y., BRUCKSTEIN, A. M. A probabilistic Hough transform. Pattern Recognition, vol. 24, no. 4, 1991, pp. 303-316.
- LEAVERS, V. F. The dynamic generalized Hough transform. Proceedings of the SPIE - The International Society for Optical Engineering, vol. 1251, 1990, pp. 281-292.
- KALVIAINEN, H., HIRVONEN, P. Connective randomized Hough transform (CRHT). Theory and Applications of Image Analysis II. Selected Paper from the 9th Scandinavian Conference on Image Analysis, Uppsala (Sweden), 1995, pp. 15-26.
- XU, L., OJA, E. Randomized Hough transform (RHT): basic mechanisms, algorithms, and computational complexities. CVGIP: Image Understanding, vol. 57, no. 2, 93, pp. 131-154.
- MAITRE, H. Un panorama de la transformation de Hough. Traitement du Signal, vol. 2, no. 4, 1985, pp. 305-317.
- HAN, J. H., KOCZY, L. T., POSTON, T. Fuzzy Hough transform. Pattern Recognition Letters, vol. 15, no. 7, 1994, pp. 649-658.

**K. Hanousek**
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Measuring of Track Velocity and Drift Angle

The fundamental problem of air navigation in real meteorological conditions is the fact that the aircraft is all the flight time under the action of wind causing its drifting and changing its velocity. Detailed exploration of possibilities of drifting and velocity changes measuring is not the intention of this article. The article is just pointing out the possible use of a space filtration method for this purpose.

- HANOUSEK, K. Radiolokace a radionavigace. Textbook of TU Brno. Brno, 1999. ISBN 80-214-1319-0.
- PODOLAK, S. Speed Velocity Measurement by CCD Sensors. PhD theses. CTU Praha. Praha, 1992.
- AMARI,Y., MASUDA, I. Velocity Sense Detection Based on the Spatial Filter Method. IEEE Transactions on Instrumentation and Measurement. Vol. 39. No. 4. August 1990, p. 649-652.

**M. Candik**
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Trigonometric Approximation in Fractal Image Coding

In this paper is presented a new approach in fractal image coding based on trigonometric approximation. The least square approximation method is used for approximation of blocks in standard fractal image compression algorithm. In the paper is shown that it is possible to use also trigonometric approximation for describing of blocks in fractal image coding. This approximation was implemented and analyzed from point of view of quality of reconstructed images. The experimental results of this method were tested on static grayscale images.

- FISHER, Y. Fractal Image Compression, Theory and Application. Springer - Verlag, New York, 1995.
- LU, N. Fractal Imaging. Academic Press, San Diego, 1997.
- CERNA, R., MACHLICKY, M., VOGEL, J., ZLATNIK, C. Zaklady numerickej matematiky a programovani. SNTL/ALFA, Praha, 1987.
- PIRC, V., BUSA, J. Numericke metody. ELFA, Kosice, 1998.