Email this article 
Open Access
Subscription or Fee Access
FIR Digital Differentiator as an Efficient Versatile Multifunction Configuration
Abstract
In this paper, a method is described for designing Digital Differentiator (DD) whose impulse response weights are related with weights of other FIR filters like Digital Hilbert Transformer, Half-band Low-pass/High-pass filter, Band-pass/Band-stop filter, All pass filter and Digital Frequency discriminator. This relationship among the impulse responses of different filters can be used to calculate the weighting coefficients of different filters in terms of weights of differentiator. In this paper, various filters have been derived from the Differentiator and their responses observed and compared by varying the order of the filter. It is observed that maximal linearity of frequency response of Differentiator also yields maximally flat/linear frequency response for other filters.
Keywords
References
P. Ramesh Babu, Digital Signal Processing, Scitech, 4th Edition, 2008
L.R. Rabiner and R.W.Schafer, “On the behaviour of minimax relative error FIR digital differentiators”, Bell Syst. Tech. J., Vol. 53, No. 2, February 1974, p.p. 331–361.
J.H. McClellan, T.W. Parks and L.R. Rabiner, “A computer program for designing optimum FIR linear phase digital filters”, IEEE Trans. Audio Electroacount., Vol. AU-21, No. 6, December 1973, p.p. 506–526.
Soo-Chang Pie and Jong-Jy Shyu, “Relationships among digital one/half band filters, low/high order differentiators, & discrete/differentiating Hilbert transformers”, IEEE Trans., Signal processing, Vol. 40, No. 3, March 1992, p.p. NJ, 1975.
Balbir Kumar, S.C Dutta Roy and Sangeeta Sabharwal – Interrelations between the coefficients of FIR digital differentiators and other FIR filters and a versatile multifunction configuration, Signal Processing 39(1994) page 247 – 262.
L.R. Rabiner and R.W.Schafer, “On the behaviour of minimax FIR digital Hilbert transformers”, Bell Syst. Tech. J., Vol. 53, No. 2, February 1974, p.p. 363–390.
S.C Dutta Roy and B.Kumar, “On digital differentiators, Hilbert transformers and half band low pass filters”, IEEE Trans. Education, Vol. 32, No. 3, August 1989, p. 314–318 (Special issue).
L.B.Jackson, “On the relationship between digital Hilbert transformers and certain low pass filters”, IEEE Trans. Acoust, Speech signal process., Vol. ASSP-23,August 1975, pp. 381–383.
Balbir Kumar, S.C Dutta Roy, “Design of efficient digital differentiators and Hilbert transformers for mid-band frequency ranges”, Internat J. Circuit Theory Applications, Vol. 17, No. 4, October 1989, p.p. 483–488.
B. Kumar and S.C. Dutta Roy, “Maximally linear FIR digital differentiators for mid-band frequencies,” Int. J. Circuit Theory Applications, Vol. 17, pp. 21-27, 1989.
Ishtiaq Rasool Khan, “Design of FIR digital differentiators using maximal linearity constraints,” IEICE Trans. Fundamentals, Vol. E87-A, no.8, pp. 2010-2017, August 2004.
Ivan W. Selesnick, “Maximally Flat Low pass Digital Differentiators”, IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, Vol. 8, Feb 2001.
J. Le Bihan, “Maximally linear FIR digital differentiators,” J. Circuits, Systems, Signal Processing, Vol. 14, no.5, pp. 633-637, 1995.
J. Le Bihan, “Coefficients of FIR digital differentiators and Hilbert transformers for mid-band frequencies,” IEEE trans. On Circuit and System-II: Analog and Digital Signal Processing, Vol. 43, no. 3, pp. 272-274, March 1996.
S.C. Pei and J.J. Shyu, “Design of FIR Hilbert transformers and differentiators by eigenfilter”, IEEE Trans. Circuits Syst., vol. CAS-35, pp. 1457-1461, Nov. 1988.
Refbacks
- There are currently no refbacks.
This work is licensed under a Creative Commons Attribution 3.0 License.