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access icon free Synthesis of recursive linear-phase filters for fixed-point hardware platforms

© The Institution of Engineering and Technology
Received 30/03/2016, Accepted 20/01/2017, Revised 14/12/2016, Published 26/01/2017

This study presents a methodology for recursive implementation of linear-phase finite impulse response (FIR) filters in fixed-point hardware platforms. The work uses a modified version of the switching and reset method to efficiently implement recursive linear-phase exponential filters. An error analysis is presented that defines the upper error bounds resulting from the switching and reset implementation of the exponential filters in fixed-point hardware. The exponential filters are then used as basis functions to synthesise other filters of interest. Gaussian filters are used as an example. The suggested recursive implementation delivers an accurate approximation of the Gaussian function. Unlike traditional techniques for implementing FIR filters, the hardware size of this recursive technique is O(1). In other words, increasing the order of a filter does not proportionally increase its hardware size. The results show that when implementing Gaussian filters on FPGAs, doubling the size of the filter, only increased the hardware size by an average of 6.12%.

Inspec keywords: recursive filters; FIR filters; field programmable gate arrays; Gaussian processes; linear phase filters

Other keywords: Gaussian filters; fixed-point hardware platforms; reset method; exponential filters; recursive linear-phase FIR filters; FPGA; switching method; Gaussian function; linear-phase finite impulse response filters

Subjects: Digital filters; Logic circuits; Digital filters; Logic and switching circuits

References

    1. 1)
      • 8. Charalambous, C., Antoniou, A.: ‘Equalization of recursive digital filters’, Proc. IEEE, 1980, 127, pp. 219–225.
    2. 2)
      • 22. Hassan, F., Khorbotly, S.: ‘An improved switching and reset architecture for linear phase recursive filters’. IEEE Int. Conf. on Electronics, Circuits, and Systems, Abu Dhabi, UAE, December 2013.
    3. 3)
      • 4. Tran, T., deQueiroz, R., Nguyen, T.: ‘Linear-phase perfect reconstruction filter bank: lattice structure, design, and application in image coding’, IEEE Trans. Signal Process., 2000, 48, pp. 133–147.
    4. 4)
      • 27. Gilat, A., Subramaniam, V.: ‘Numerical methods for engineers and scientists, an introduction with applications using MATLAB’ (John Wiley and Sons, Inc., 2nd edn. 2011).
    5. 5)
      • 13. Lehto, R., Saramaki, T., Vainio, O.: ‘Synthesis of narrowband linear-phase FIR filters with a piecewise-polynomial impulse response’, IEEE Trans. Circuits Syst. I Reg. Pap., 2007, 54, (10), pp. 2262–2276.
    6. 6)
      • 24. Arian, P., Saramaki, T., Fam, A.: ‘Unstable IIR-like filter blocks for generating linear-phase FIR filters: a noise analysis’. IEEE TENCON, 2005.
    7. 7)
      • 23. Fang, Z., Carletta, J.E., Veillette, R.J.: ‘A methodology for FPGA-based control implementation’, IEEE Trans. Control Syst. Technol., 2005, 13, (6), pp. 977–987.
    8. 8)
      • 18. Taurén, T., Vainio, O., Lehto, R.: ‘Recursive FIR filter structures on FPGA’. IEEE NORCHIP, Trondheim, Norway, 2009.
    9. 9)
      • 21. Saramaki, T., Mitra, S.K.: ‘Design and implementation of narrow-band linear-phase FIR filters with piecewise polynomial impulse response’. IEEE Int. Symp. on Circuits and Systems, 1999, vol. 3.
    10. 10)
      • 5. Proakis, J., Manolakis, D.: ‘Digital signal processing: principles, algorithms, and applications’ (Prentice Hall, 2006, 4th edn.).
    11. 11)
      • 20. Saramaki, T., Fam, A.T.: ‘Properties and structures of linear-phase FIR filters based on switching and resetting of IIR filters’. IEEE Int. Symp. on Circuits and Systems, Piscataway, NJ, 1990.
    12. 12)
      • 6. Inukai, T.: ‘A unified approach to optimal recursive digital filter design’, IEEE Trans. Circuits Syst., 1980, 27, pp. 646–649.
    13. 13)
      • 16. Khorbotly, S., Hassan, F.: ‘Recursive implementation of gaussian filters with switching and reset hardware’. IEEE Midwestern Symp. on Circuits and Systems, Columbus, OH, August 2013.
    14. 14)
      • 19. Lehto, R., Taurén, T., Vainio, O.: ‘Recursive FIR filter structures on FPGA’, J. Microprocess. Microsyst., 2011, 35, (7), pp. 595–602.
    15. 15)
      • 15. Lathi, B.: ‘Linear systems and signals’ (Oxford University Press, 2005, 2nd edn.).
    16. 16)
      • 14. Hassan, F., Khorbotly, S.: ‘Recursive Implementation of Exponential Linear-Phase FIR Filters’. IEEE Int. Conf. on Electronics, Circuits, and Systems, Beirut, Lebanon, December 2011.
    17. 17)
      • 1. Antoniou, A.: ‘Digital filters: analysis, design, and applications’ (McGraw-Hill, New York, 1993, 2nd edn.).
    18. 18)
      • 7. Cortelazzo, G., Lightner, M.R.: ‘Simultaneous design in both magnitude and group delay of IIR filters based on multiple criterion optimization’, IEEE Trans. Signal Process., 1993, 41, pp. 949–967.
    19. 19)
      • 11. Arian, P., Saramaki, T., Fam, A.: ‘A decomposition technique for cascaded IIR-like filter blocks generating linear-phase FIR filters’. Proc. of IEEE Int. Symp. on Circuits and Systems, 2005.
    20. 20)
      • 17. Powell, S., Chau, P.: ‘A technique for realizing linear phase IIR filters’, IEEE Trans. Signal Process., 1991, 3, pp. 2425–2435.
    21. 21)
      • 25. Khorbotly, S., Hassan, F.: ‘A modified approximation of 2D Gaussian smoothing filters for fixed-point platforms’. IEEE Southeast Symp. on System Theory, Auburn, AL, March 2011.
    22. 22)
      • 12. Wang, A., Smith, J.: ‘On fast FIR filters implemented as tail-canceling IIR filters’, IEEE Trans. Signal Process., 1997, 45, pp. 1415–1427.
    23. 23)
      • 26. Basu, M.: ‘Gaussian based edge detection methods—a survey’, IEEE Trans. Syst. Man Cybern. C Appl. Rev., 2002, 32, (3), pp. 252–260.
    24. 24)
      • 2. Sunwoo, J., Un, C.: ‘Fast sequential least squares design of FIR filters with linear phase’, Proc. IEEE, 1988, 76, pp. 1247–1248.
    25. 25)
      • 3. Chen, T., Vaidyanathan, P.: ‘Phase linearization of filters in analysis/synthesis filter banks’. IEEE Int. Conf. on Acoustics, Speech, and Signal Processing, 1994.
    26. 26)
      • 9. Sreeram, V., Agathoklis, P.: ‘Design of linear-phase IIR filters via impulse-response gramians’, IEEE Trans. Signal Process., 1992, 40, pp. 389–394.
    27. 27)
      • 10. Fam, A.: ‘FIR filters that approach IIR filters in their computational efficiency’. Asilomar Conf. on Signals, Systems, and Computers, Pacific Grove, CA, 1987.
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