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Filter Design

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Conceptual Digital Signal Processing with MATLAB

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Abstract

We designed the primitive filters based on the time and frequency domain. The convolution sum operation is used to derive the time domain filter and DTFT (or DFT) is utilized to figure out the FIR filter. The IIR filter is devised from the Z-transform in the previous chapter. We already knew the simple methods to design the basic filter structures. Are these all? Did we miss something? Why we have filter design chapter after all? In general, the filter design is the part of system construction to realize the specific purpose. The target performance is achieved by the dedicated filter operation specified by the sophisticated numbers known as specifications. The previous filter designs only follow personal intuition and ambiguous number for filter implementation; hence, the constructed filter likely shows the unstable performance in overall.

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References

  1. Hewitt, E., Hewitt, R.E.: The Gibbs-Wilbraham phenomenon: an episode in fourier analysis. Arch. Hist. Exact Sci. 21(2), 129–160 (1979). https://doi.org/10.1007/BF00330404

    Article  MathSciNet  MATH  Google Scholar 

  2. Hazewinkel, M.: Encyclopaedia of Mathematics: Orbit—Rayleigh Equation. Springer, Netherlands (2012)

    Google Scholar 

  3. Oppenheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing. Prentice Hall, (1989)

    Google Scholar 

  4. Kaise, J.F.: Nonrecursive digital filter design using the I0-Sinh window function. In: IEEE International Symposium on Circuits and Systems, San Francisco, California, USA, 22–25 April 1974. IEEE

    Google Scholar 

  5. Marple, S.L.: Computing the discrete-time ‘analytic’ signal via FFT. In: Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136), 2–5 November 1997, vol.1322, pp. 1322–1325 (1997)

    Google Scholar 

  6. Rabiner, L.R., McClellan, J.H., Parks, T.W.: FIR digital filter design techniques using weighted Chebyshev approximation. Proc. IEEE 63(4), 595–610 (1975). https://doi.org/10.1109/PROC.1975.9794

    Article  Google Scholar 

  7. Parks, T.W., Burrus, C.S.: Digital Filter Design. Wiley, (1987)

    Google Scholar 

  8. Jackson, L.B.: Digital Filters and Signal Processing, 3rd edn. Kluwer Academic Publishers, Boston (1996)

    Book  Google Scholar 

  9. Wikipedia: Unitary matrix (2020). https://en.wikipedia.org/w/index.php?title=Unitary_matrix&oldid=961644790

  10. Wikipedia: Conjugate transpose (2020). https://en.wikipedia.org/w/index.php?title=Conjugate_transpose&oldid=961399224

  11. Wikipedia: Vandermonde matrix (2020). https://en.wikipedia.org/w/index.php?title=Vandermonde_matrix&oldid=965588394

  12. Wikipedia: Moore–Penrose inverse (2020). https://en.wikipedia.org/w/index.php?title=Moore%E2%80%93Penrose_inverse&oldid=961651512

  13. Selesnick, I.W., Lang, M., Burrus, C.S.: Constrained least square design of FIR filters without specified transition bands. IEEE Trans. Signal Process. 44(8), 1879–1892 (1996). https://doi.org/10.1109/78.533710

    Article  Google Scholar 

  14. Wikipedia: Lagrange multiplier (2020). https://en.wikipedia.org/w/index.php?title=Lagrange_multiplier&oldid=964661260

  15. Wikipedia: Karush–Kuhn–Tucker conditions (2020). https://en.wikipedia.org/w/index.php?title=Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions&oldid=966216684

  16. Karam, L.J., McClellan, J.H.: Complex Chebyshev approximation for FIR filter design. IEEE Trans. Circuits Syst. II: Analog. Digit. Signal Process. 42(3), 207–216 (1995). https://doi.org/10.1109/82.372870

    Article  MATH  Google Scholar 

  17. Butterworth, S.: On the theory of filter amplifiers. Exp. Wirel. Wirel. Eng. 7, 536–541 (1930)

    Google Scholar 

  18. Wikipedia: Chebyshev polynomials. https://en.wikipedia.org/w/index.php?title=Chebyshev_polynomials&oldid=962339092 (2020)

  19. Wikipedia: Elliptic rational functions (2020). https://en.wikipedia.org/w/index.php?title=Elliptic_rational_functions&oldid=946797692

  20. Stoica, P., Moses, R.L.: Introduction to Spectral Analysis. Prentice Hall (1997)

    Google Scholar 

  21. Yule, G.U.: On a method of investigating periodicities in disturbed series, with special reference to Wolfer’s sunspot numbers. Philos. Trans. R. Soc. Lond. Ser. A (Containing Papers of a Mathematical or Physical Character) 226, 267–298 (1927)

    Google Scholar 

  22. Walker, G.T.: On periodicity in series of related terms. Proc. R. Soc. Lond. Ser. A (Containing Papers of a Mathematical and Physical Character) 131(818), 518–532 (1931). https://doi.org/10.1098/rspa.1931.0069

  23. Selesnick, I.W., Burrus, C.S.: Generalized digital Butterworth filter design. In: 1996 IEEE International Conference on Acoustics, Speech, and Signal Processing Conference Proceedings, 9–9 May 1996, vol. 1363, pp. 1367–1370 (1996)

    Google Scholar 

  24. Herrmann, O.: On the approximation problem in nonrecursive digital filter design. IEEE Trans. Circuit Theory 18(3), 411–413 (1971). https://doi.org/10.1109/TCT.1971.1083275

    Article  Google Scholar 

  25. Makhoul, J.: Linear prediction: a tutorial review. Proc. IEEE 63(4), 561–580 (1975). https://doi.org/10.1109/PROC.1975.9792

    Article  Google Scholar 

  26. Papoulis, A.: Probability, Random Variables, and Stochastic Processes. McGraw-Hill (1991)

    Google Scholar 

  27. Kay, S.M.: Fundamentals of Statistical Signal Processing. Estimation Theory, vol. 1. Prentice Hall (1993)

    Google Scholar 

  28. Hauer, J.F., Demeure, C.J., Scharf, L.L.: Initial results in Prony analysis of power system response signals. IEEE Trans. Power Syst. 5(1), 80–89 (1990). https://doi.org/10.1109/59.49090

    Article  Google Scholar 

  29. Steiglitz, K., McBride, L.: A technique for the identification of linear systems. IEEE Trans. Autom. Control. 10(4), 461–464 (1965). https://doi.org/10.1109/TAC.1965.1098181

    Article  Google Scholar 

  30. Constantinides, A.G.: Spectral transformations for digital filters. Proc. Inst. Electr. Eng. 117(8), 1585–1590 (1970). https://doi.org/10.1049/piee.1970.0281

    Article  Google Scholar 

  31. Yeong Ho, H., Pearce, J.A.: A new window and comparison to standard windows. IEEE Trans. Acoust. Speech Signal Process. 37(2), 298–301 (1989). https://doi.org/10.1109/29.21693

    Article  Google Scholar 

  32. Harris, F.J.: On the use of windows for harmonic analysis with the discrete Fourier transform. Proc. IEEE 66(1), 51–83 (1978). https://doi.org/10.1109/PROC.1978.10837

    Article  Google Scholar 

  33. Elliott, D.F.: Handbook of Digital Signal Processing. Academic, New York (1987)

    MATH  Google Scholar 

  34. D’Antona, G., Ferrero, A.: Digital Signal Processing for Measurement Systems: Theory and Applications. Springer, US (2006)

    Book  Google Scholar 

  35. Nuttall, A.: Some windows with very good sidelobe behavior. IEEE Trans. Acoust. Speech Signal Process. 29(1), 84–91 (1981). https://doi.org/10.1109/TASSP.1981.1163506

    Article  Google Scholar 

  36. Brookner, E.: Practical Phased-array Antenna Systems. Artech House (1991)

    Google Scholar 

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Kim, K. (2021). Filter Design. In: Conceptual Digital Signal Processing with MATLAB. Signals and Communication Technology. Springer, Singapore. https://doi.org/10.1007/978-981-15-2584-1_6

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  • DOI: https://doi.org/10.1007/978-981-15-2584-1_6

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