Abstract

In this paper, a simple approach is proposed to design recursive digital differentiators and integrators by applying the concept of time-constant analysis. The time-constant combined with the magnitude response describes the system behavior of a digital differentiator and an integrator. Further, new recursive digital differentiator and integrator designs of first-order systems are also obtained for more accurate or comparable magnitude responses as compared to the existing designs of higher-order systems over wideband. These designs are more suitable for control systems and signal processing applications.

References

• Al-Alaoui, M. A. 1988. A stable differentiator with a controllable signal to Noise ratio. IEEE Trans. IM-37, pp. 383-388.
• Al-Alaoui, M. A. 1992. Novel approach to designing digital differentiators. Electron. Lett., vol. 28(15), pp. 1376–1378.
• Al-Alaoui, M. A. 1993. Novel digital integrator and differentiator. Electron. Lett., vol. 29(4), pp. 376–378.
• Bihan, J. L. 1993. Novel class of digital integrators and differentiators. Electron. Lett., vol. 29(11), pp. 971–973.
• Al-Alaoui, M. A. 1994. Novel IIR differentiator from the Simpson integration rule. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 41(2), pp. 186–187.
• Al-Alaoui, M. A. 1995. A class of second-order integrators and low-pass differentiators. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 42(4), pp. 220–223.
• Al-Alaoui, M. A. 1997. Filling the gap between the bilinear and the backward difference transforms: an interactive design approach. International Journal of Electrical Engineering, vol. 34(4), pp. 331-337.
• Al-Alaoui, M. A. 2001. Novel stable higher order s to z transforms,” IEEE Trans. Circuits Syst. I, Fundam. Theory and Appl., vol. 48(11), pp. 1326-1329.
• Al-Alaoui, M. A. 2007. Linear phase low pass IIR digital differentiators. IEEE Trans. Signal Processing, vol. 55(2), pp. 697-706, February.
• Al-Alaoui, M. A. 2008. Al-Aloui operator and the new transformation polynomials for discretization of analogue systems. Electrical Engineering, vol. 90(4), pp. 455-567.
• Papamarkos N. and Chamzas, C. 1996. A new approach for the design of digital integrators. IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., vol. 43(9), pp. 785–791.
• Ngo, N. Q. 2006. A New Approach for the Design of Wideband Digital Integrator and Differentiator. IEEE Transactions on circuits and systems—II, vol. 53(9), pp. 936-940.
• Pei, S.C. and Hsu, H.J. 2008. Fractional bilinear transform for analog to digital conversion. IEEE Trans. Signal Processing, vol. 56(5), pp. 2122-2127.
• Gupta, M., Varshney, P., Viswewaran G.S. and Kumar, B. 2008. Novel digital differentiator and corresponding fractional order differentiator models. Sigmap, pp. 47-54.
• Gupta, M., Jain M. and Kumar, B. 2009. “Wideband digital integrator,” Proceedings of IEEE, IMPACT. pp. 106-108.
• Al-Alaoui, M. A. 2009. Novel class of digital integrators and differentiators. IEEE Trans. Signal Processing, DOI: 10.1109/TSP.2008.929668.
• Gupta, M., Jain, M. and Kumar, B. 2010. Recursive wideband digital integrator and differentiator. Wiley Int. J. Circ. Theor.Appl., DOI:10.1002/cta.658.
• Upadhyay, D. 2010. Recursive wideband digital differentiators. Electron. Lett., 46(25), pp. 1661-1662.
• Oppenheim, A. V., Schaffer, R. W. and Buck, J. R. 1999. Discrete time signal processing, PHI.
• Kumar, B. and Dutta Roy, S.C. 1988. Design of digital differentiators. Proceedings of IEEE, vol. 76(3), pp. 287-289.
• Kumar, B. and Dutta Roy, S.C. 1989. Maximally linear FIR digital differentiators for high frequencies. IEEE Trans. Circuits and Systems, vol. 36(4), pp. 890-893.
• Sunder, S. and Ramachandran, V.1994. Design of equripple non recursive digital differentiators and Hilbert transformers using a weighted least square technique. IEEE Trans. Signal Processing, vol. 42(9), pp. 2504-2509.
• Mollova, G. 1999. Compact formulas for least-squares design of digital differentiators. Electron. Lett., 35(20), pp. 1695-1697.
• Tsai, L.-C. and Wu, Y.-T. 2009. Time-Constant Control analysis of microwave differentiators. IET Microw. Antennas Propag., vol.3, pp.1044-1050.