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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
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
Hazewinkel, M.: Encyclopaedia of Mathematics: Orbit—Rayleigh Equation. Springer, Netherlands (2012)
Oppenheim, A.V., Schafer, R.W.: Discrete-Time Signal Processing. Prentice Hall, (1989)
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
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)
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
Parks, T.W., Burrus, C.S.: Digital Filter Design. Wiley, (1987)
Jackson, L.B.: Digital Filters and Signal Processing, 3rd edn. Kluwer Academic Publishers, Boston (1996)
Wikipedia: Unitary matrix (2020). https://en.wikipedia.org/w/index.php?title=Unitary_matrix&oldid=961644790
Wikipedia: Conjugate transpose (2020). https://en.wikipedia.org/w/index.php?title=Conjugate_transpose&oldid=961399224
Wikipedia: Vandermonde matrix (2020). https://en.wikipedia.org/w/index.php?title=Vandermonde_matrix&oldid=965588394
Wikipedia: Moore–Penrose inverse (2020). https://en.wikipedia.org/w/index.php?title=Moore%E2%80%93Penrose_inverse&oldid=961651512
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
Wikipedia: Lagrange multiplier (2020). https://en.wikipedia.org/w/index.php?title=Lagrange_multiplier&oldid=964661260
Wikipedia: Karush–Kuhn–Tucker conditions (2020). https://en.wikipedia.org/w/index.php?title=Karush%E2%80%93Kuhn%E2%80%93Tucker_conditions&oldid=966216684
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
Butterworth, S.: On the theory of filter amplifiers. Exp. Wirel. Wirel. Eng. 7, 536–541 (1930)
Wikipedia: Chebyshev polynomials. https://en.wikipedia.org/w/index.php?title=Chebyshev_polynomials&oldid=962339092 (2020)
Wikipedia: Elliptic rational functions (2020). https://en.wikipedia.org/w/index.php?title=Elliptic_rational_functions&oldid=946797692
Stoica, P., Moses, R.L.: Introduction to Spectral Analysis. Prentice Hall (1997)
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)
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
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)
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
Makhoul, J.: Linear prediction: a tutorial review. Proc. IEEE 63(4), 561–580 (1975). https://doi.org/10.1109/PROC.1975.9792
Papoulis, A.: Probability, Random Variables, and Stochastic Processes. McGraw-Hill (1991)
Kay, S.M.: Fundamentals of Statistical Signal Processing. Estimation Theory, vol. 1. Prentice Hall (1993)
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
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
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
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
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
Elliott, D.F.: Handbook of Digital Signal Processing. Academic, New York (1987)
D’Antona, G., Ferrero, A.: Digital Signal Processing for Measurement Systems: Theory and Applications. Springer, US (2006)
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
Brookner, E.: Practical Phased-array Antenna Systems. Artech House (1991)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2021 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
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
Download citation
DOI: https://doi.org/10.1007/978-981-15-2584-1_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-2583-4
Online ISBN: 978-981-15-2584-1
eBook Packages: EngineeringEngineering (R0)