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- 1. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 Design of IIR Notch Filters and Narrow and Wide-Band Filters Institute of Electrical and Electronics Engineering Abstract: In this thesis, a direct IIR design method for real WDFs based on Gazsi's work is summarized in detail, and the cascade realization of first- and second-order all pass sections is generalized to any IIR transfer function, and then a simple design method for bi-reciprocal lattice WDFs is given. A design and realization method for IIR multiple notch filters based on the phase of an all pass filter approximation is described. A design and realization method for high speed narrow-band and wide-band WDFs based on the IFIR technique is given, both nonlinear and approximately linear phase filters are considered; the narrow band filter is composed of a model filter and one or several masking filters in cascade. In the case of nonlinear phase, conventional lattice and bi-reciprocal lattice WDFs are used for the model and masking filters; the overall narrow-band filter can be designed by separately designing the model and masking filters. The wide-band filter is composed of a narrow- band filter in parallel with a series of all pass filters, to obtain an overall wide-band filter. The narrow-band filter is designed first, and is then connected in parallel with one of the all pass filters of the narrow-band filter. In the case of approximately linear phase, the linear phase IIR filter is used for the model filter, and a maximum flat linear phase FIR filter is used for the masking filter. Several advantages of these filters over directly designed filters are that they have a substantially higher maximal sample frequency, lower round off noise and lower finite word length. Several design examples are given to demonstrate the properties of these filters.
- 2. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (a) Single-flow Diagram of Lattice Structure (b) Simplified Wave-flow Diagram
- 3. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (c) Direct Connection of Two Ports (d) Wave-flow Diagrams of i th Second-degree all pass Section
- 4. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (e) Block Diagram of the Lattice WDF with Cascaded all pass Sections for order N1 (as the top structure) and N2 (as the bottom Structure), Order of Filter, N = N1 + N2
- 5. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (f) Realization Structure of bi-reciprocal Filter of Order N. (g) Notch Filter
- 6. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (a) Lattice Realization of Real Coefficients of All pass Filter (b) Details of the Building Blocks (h) Block Diagram of Narrow-band Filter (i) First Order all pass Section
- 7. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (j) Second Order all pass Section (k) Structure of IIR Narrow-band Filter (l) Structure of IIR Wide-band Filter
- 8. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (m) Simplified Structure of IIR Wide-band Filter (n) Structure of IIR Wide-band High-pass Filter
- 9. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 A: - Multiple Notch Filter Designs (a) Phase Response of All pass IIR Multiple Notch Filter
- 10. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (b) Unit Sample of IIR Multiple Notch Filter
- 11. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (c) Magnitude Response of IIR Multiple Notch Filter
- 12. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (d) Phase Response of IIR Multiple Notch Filter
- 13. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 B: - Wide-Band Filter Designs (a) Impulse Response of Wide-Band Filter
- 14. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (b) Magnitude Response of Overall Wide-Band Filter
- 15. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (c) Attenuation Reponses of Overall Wide-band Filter
- 16. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 (d) Attenuation of Overall Wide-Band Filter (After zooming)
- 17. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 Conclusion: In this thesis, a method to design IIR multiple notch filters for a prescribed notch frequencies and 3 dB reflection bandwidths is discussed. This notch filter can be realized by a computationally efficient lattice structure with very low sensitivity. An example has been given IO demonstrate the design procedure. In the second part of this thesis, the design and realization methods for high speed narrow-band and wide- band filters have been given, the narrow-band filters are imposed of a model filter and one or several masking filters in cascade. In the case of nonlinear phase, Lattice and bi-reciprocal lattice WDFs are used for the model and masking fitters; a conventional lattice WDF design method is given, a design method for bi-reciprocal WDFs is also given in detail. The wide-band filters consist of a narrow-band filter in parallel with one of the all pass filters. The overall narrow-band filters can be designed by separately designing the model filter and masking filters. The overall wide-band filters can be designed by first designing a narrow- band filter, then, by connecting is filter in parallel with an all pass filter consisting of a cascade of branches one from each sub filter of the narrow-band filter. Estimations were given for the pass band and stop band ripples of the individual 6iters in the narrow-band filter in order to meet the requirements for the overall wide-band filter. This offers simple design procedures for both narrow-band and wide-band filters since a conventional lattice WDF design method can be used. However, for many wide-band cases, these designs imply an unnecessarily high computational complexity, because the derived estimations are based on a worst case assumption. For the case of approximately linear phase, an approximately linear phase IR filter is used for the mode1 filter, and MF linear phase FIR filters are used for the masking filters. Because both cases (hem and nonlinear phase) are based on the interpolated technique, ail recursive loops contain a number of delay elements, resulting in filters with higher maximal sample sequences compared to the directly designed filters. We gave several examples to demonstrate the effects of quantization; the resulting filters have lower word-lengths compared with directly designed filters. We also discussed the round off noise and concluded that these filters are likely to be in favour.
- 18. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 References: [1] A. B. Smolders and M. P van Haarlem, Perspective on Radio Astronomy, Proceedings of Technology for Large Antenna arrays, 1999, Netherlands foundation for Research in Astronomy. [2] A. Van Ardenne, P. N. Wilkinson, P. D. Patel and J. G. Bij De Vaate, Electronic Multi-beam radio astronomy concept, Experimental Astronomy, 2004, pp.65-77. [3] P. E. Dewdney, P. J. Hall, R. T. Schilizzi and T. J. L. W. Lazio, The Square Kilometre Array. Proceedings of the IEEE, Vol. 97, No. 8, pp. 1482-1496, 2009. [4] H. Arslan and Z. N. Chen and M. -G. Di Benedetto, Ultra Wideband Wireless Communication, Wiley Interscience, 2006. [5] S. V. Hum, H. L. P. A. Madanayake and L. T. Bruton, UWB Beamforming using 2D Beam Digital Filters, IEEE Trans. on Antennas and Propagation (TAP), Vol. 57, No. 3, 2009, pp. 804-807. [6] M. A. Fischman and C. Le and P. A. Rosen, A Digital Beamforming Processor for the Joint DoD/NASA Space based Radar Mission, IEEE Radar Conference, July 2004, pp. 9-14. [7] H. L. P. A. Madanayake and L. T. Bruton, A Speed-optimized Systolic Array Processor Architecture for Spatio-temporal 2-D IIR Broadband Beam Filters, IEEE Trans. on Circuits and Systems-I: Regular Papers, Vol. 55, No. 7, 2008, pp. 1953-1966. [8] Y. Zhang and L. T. Bruton. Applications of 3D LCR Networks in the Design of 3D Recursive Filters for Processing Image Sequences. IEEE Transactions on Circuits and Systems for Video Technology, Vol. 4, 1994, pp. 369-382. [9] P. Agathoklis and L.T. Bruton, Practical-BIBO Stability of N-dimensional Discrete Systems, Proc. IEE., Vol. 130, pt. G, No. 6, Dec. 1983, pp. 236-242. [10] Craig Marven, Gillian Ewers, "A simple approach to digital signal processing" John wiley & sons, 1996. [11] C.-C. Tseng, S.-C. Pei, "IIR Multiple Notch Filter Design Based on Allpass Filter," IEEE Trans. Circuit and Systems-II: Analog and Digital Signal Processing, vol. 44 no. 2, pp. 133-136, February 1997. [12] C.-C. Tseng, S.-C. Pei, "Stable IIR Notch Filter Design with Optimal Pole Placement," IEEE Trans. Signal Processing, vol. 49, no. 11, pp. 2673-2681, November 2001. [13] S. Yimman, W. Hinjit, S. Sriboonsong, M. Puangpool, K. Dejhan "IIR Notch Filter Design with Modified Pole-zero Placement Algorithm," The IEEE International Symposium.on Signal Processing and Information Technology (ISSPIT 2003), Darmstadt, Germany, December 2003.
- 19. Base papers: http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=5548677 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4141559 http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=752914 [14] S. Yimman, W. Hinjit, W. Ussawongaraya, P. Thoopluang, K. Dejhan "Design and Implementation of IIR Multiple Notch Filter with Modified Pole-zero Placemen t Algorithm" International Conference on Control, Automation and Systems (ICCAS 2003), Gyeongju, Korea, October 2003. [15] J. G. Proakis, D. G. Manolakis, "Digital Signal Processing Principle, Algorithms, and Applications," Prentice Hall, 1996. [16] S. K. Mitra, "Digital Signal Processing, A Computer-Based Approach," McGraw-Hill, 2001. [17] S. J. Orfanidis, "Introduction to Signal Processing," Prentice Hall, 1995. [18] R. Carney, "Design of digital notch filter with tracking requirements", IEEE Trans. Space, Electron., Telem., vol. SET-9, pp.109 -114 1963 [19] K. Hirano, S. Nishimura, and S. K. Mitra, "Design of digital notch filters", IEEE Trans. Circuits Syst., vol. CAS-21, pp.540 -546 1974 [20] H. Yu, S. K. Mitra, and H. Babic, "Linear phase FIR notch filter design", Sadhana, vol. 15, pp.133 - 155 1990 [21] P. A. Regalia, S. K. Mitra, and P. P. Vaidyanathan, "The digital all-pass filter: A versatile signal processing building block", Proc. IEEE, vol. 76, pp.19 -37 1988 [22] S. C. Pei and C. C. Tseng, "IIR multiple notch filter design based on all-pass filter", IEEE Trans. Circuits Syst. II, vol. 44, pp.133 -136 1997

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