Finite Wordlength Recursive Sliding-DFT for Phase Measurement

- Journal title : Journal of Electrical Engineering and Technology
- Volume 7, Issue 6, 2012, pp.1014-1022
- Publisher : The Korean Institute of Electrical Engineers
- DOI : 10.5370/JEET.2012.7.6.1014

Title & Authors

Finite Wordlength Recursive Sliding-DFT for Phase Measurement

Kim, Byoung-Il; Cho, Min-Kyu; Chang, Tae-Gyu;

Kim, Byoung-Il; Cho, Min-Kyu; Chang, Tae-Gyu;

Abstract

This paper proposes a modified recursive sliding DFT to measure the phase of a single-tone. The modification is to provide a self error-cancelling mechanism so that it can significantly reduce the numerical error, which is generally introduced and accumulated when a recursive algorithm is implemented in finite wordlength arithmetic. The phase measurement error is analytically derived to suggest optimized distributions of quantization bits. The analytic derivation and the robustness of the algorithm are also verified by computer simulations. It shows that the maximum phase error of less than radian is obtained even when the algorithm is coarsely implemented with 4-bit wordlength twiddle factors.

Keywords

Quantization effect;Roundoff analysis;Sliding DFT;Phase measurement;

Language

English

References

1.

A. P. Liavas and P. A. Regalia, "On the numerical stability and accuracy of the conventional recursive least squares algorithm," IEEE Trans. Signal Processing, Vol. 47, pp. 88-96, Jan. 1999.

2.

J.R. Bunch and R.C. LeBorne, "Error accumulation effects for the a posteriori RLSL prediction filter," IEEE Trans. Signal Processing, Vol. 43, pp. 150-159, Jan. 1995.

3.

E. Jacobsen and R. Lyons, "The sliding DFT," IEEE Signal Processing Magazine, Vol. 20, pp. 74-80, Mar 2003.

4.

E. Jacobsen and R. Lyons, "An update to the sliding DFT," IEEE Signal Processing Magazine, Vol. 21, pp. 110-111, Jan. 2004

5.

K. P. Sozanski, "Sliding DFT control algorithm for three-phase active power filter," in Conf. 21th Annual IEEE Applied Power Electronics Conference and Exposition, pp. 1223-1229 March 2006.

6.

F. Beaufays and B. Widrow, "On the advantages of the LMS spectrum analyzer over nonadaptive implementations of the sliding-DFT," IEEE Trans. Circuits and Systems I: Fundamental Theory and Applications, Vol. 42, pp. 218-220, April 1995.

7.

J. H. Kim and T. G. Chang, "Analytic derivation of finite wordlength effect of the twiddle factors in recursive implementation of the sliding-DFT," IEEE Trans. Signal Processing, Vol. 48, pp. 1485-1488, May 2000.

8.

J. Z. Yang and C. W. Liu, "A precise calculation of power system frequency and phasor," IEEE Trans. Power Delivery, Vol. 15, pp. 494-499, April 2000.

9.

B.S. Ahn, B.I. Kim and T.G. Chang, "A sliding-DFT based power-line phase measurement algorithm and its FPGA implementation," in Conf. 8th IEE Int. Conf. Developments in Power System Protection, Vol. 1, pp 44-47, April 2004.