Abstract
In this paper, a new structure and design method are proposed for variable fractional-delay (VFD) 2-D FIR digital filters. Basing on the Taylor series expansion of the desired frequency response, a prefilter–subfilter cascaded structure can be derived. For the 1-D differentiating prefilters and the 2-D quadrantally symmetric subfilters, they can be designed simply by the least-squares method. Design examples show that the required number of independent coefficients of the proposed system is much less than that of the existing structure while the performance of the designed VFD 2-D filters is still better under the cost of larger delays.
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Deng, T.-B., & Soma, T. (1995). Design of 2-D variable digital filters with arbitrary magnitude characteristics. Signal Processing, 43(1), 17–27.
Deng, T.-B., & Soma, T. (1995). Design of zero-phase recursive 2-D variable filters with quadrantal symmetric. Multidimensional Systems and Signal Processing, 6, 137–158.
Deng, T.-B. (1998). Design of variable 2-D liner phase recursive digital filters with guaranteed stability. IEEE Transactions on Circuits and Systems: I-Fundamental Theory and Applications, 45(8), 859–863.
Deng, T.-B. (1998). Design of linear phase variable 2-D digital filters using real-complex decomposition. IEEE Transactions on Circuits and Systems: II-Analog and Digital Signal Processing, 45(3), 330–339.
Deng, T.-B., & Lu, W.-S. (2000). Weighted least-squares method for designing variable fractional delay 2-D FIR digital filters. IEEE Transactions on Circuits and Systems: II-Analog and Digital Signal Processing, 47(2), 114–124.
Deng, T.-B. (2001). Design of separable-denominator variable 2-D digital filters with guaranteed stability. Signal Processing, 81(1), 219–225.
Deng, T.-B. (2003). Design of linear-phase variable 2-D digital filters using matrix-array decomposition. IEEE Transactions on Circuits and Systems: II-Analog and Digital Signal Processing, 50(6), 267–277.
Deng, T.-B., Saito, E., & Okamoto, E. (2003). Efficient design of SVD-based 2-D digital filters using specification symmetry and order-selecting criterion. IEEE Transactions on Circuits and Systems: I-Fundamental Theory and Applications, 50(2), 217–226.
Deng, T.-B. (2005). Design of arbitrary-phase variable digital filters using SVD-based vector-array decomposition. IEEE Transactions on Circuits and Systems: I-Regular Papers, 52(1), 148–167.
Deng, T.-B., & Lian, Y. (2006). Weighted-least-squares design of variable fractional-delay FIR filters using coefficient symmetry. IEEE Transactions on Signal Processing, 54(8), 3023–3038.
Deng, T.-B. (2007). Coefficient-symmetries for implementing arbitrary-order Lagrange-type variable fractional-delay digital filters. IEEE Transactions on Signal Processing, 55(8), 4078–4090.
Deng, T.-B. (2007). Symmetric structures for odd-order maximally flat and weighted-least-squares variable fractional-delay filters. IEEE Transactions on Circuits and Systems: I-Regular Papers, 54(12), 2718–2732.
Deng, T.-B. (2010). Hybrid structures for low-complexity variable fractional-delay FIR filters. IEEE Transactions on Circuits and Systems: I-Regular Papers, 57(4), 897–910.
Farrow, C. W., (June, 1988). A continuously variable digital delay elements. In Proceedings 1988 IEEE international symposium circuits and systems, vol. 3, pp. 2641–2645.
Johansson, H., & Löwenborg, P. (2003). On the design of adjustable fractional delay FIR filters. IEEE Transactions on Circuits and Systems: II-Analog and Digital Signal Processing, 50(4), 164–169.
Kwan, H. K., & Jiang, A. (2009). FIR allpass, and IIR variable fractional-delay digital filter design. IEEE Transactions on Circuits and Systems: I-Regular Papers, 56(9), 2064–2074.
Laakso, T. I., Valimaki, V., Karjalainen, M., & Laine, U. K. (1996). Splitting the unit delay: Tools for fractional delay filter design. IEEE Signal Processing Magazine, 13(1), 30–60.
Lu, W.-S., & Deng, T.-B. (1999). An improved weighted least-squares design for variable fractional delay FIR filters. IEEE Transactions on Circuits and Systems: II-Analog and Digital Signal Processing, 46(8), 1035–1040.
Pei, S.-C., & Shyu, J.-J. (1995). Symmetric properties of two-dimensional sequences and their applications for designing linear-phase 2-D FIR digital filters. Signal Processing, 42(3), 261–271.
Pei, S.-C., & Lin, H.-S. (2009). Tunable FIR and IIR fractional-delay filter design and structure based on complex cepstrum. IEEE Transactions on Circuits and Systems: I-Regular Papers, 56(10), 2195–2206.
Shyu, J.-J., Pei, S.-C., & Huang, Y.-D. (2009). Two-dimensional Farrow structure and the design of variable fractional-delay 2-D FIR digital FIR filters. IEEE Transactions on Circuits and Systems: I-Regular Papers, 56(2), 395–404.
Shyu, J.-J., Pei, S.-C., & Huang, Y.-D. (2009). Design of variable 2-D FIR digital filters by McClellan transformations. IEEE Transactions on Circuits and Systems: I-Regular Papers, 56(3), 574–582.
Shyu, J.-J., Pei, S.-C., Chan, C.-H., Huang, Y.-D., & Lin, S.-H. (2010). A new criterion for the design of variable fractional-delay FIR digital filters. IEEE Transactions on Circuits and Systems: I-Regular Papers, 57(2), 368–377.
Tseng, C.-C. (2003). Design of 2-D variable fractional delay FIR filter using 2-D differentiators. In Proceedings 2003 IEEE international symposium circuits and systems, vol. 4, pp. 189–192.
Tseng, C.-C. (2002). Eigenfilter approach for the design of variable fractional-delay FIR and all-pass filters. IEE Proceedings—Vision and Image Signal Processing, 149(5), 297–303.
Tseng, C.-C. (2002). Design of 1-D and 2-D variable fractional delay allpass filters using weighted least-squares method. IEEE Transactions on Circuits and Systems: I-Fundamental Theory and Applications, 49(10), 1413–1422.
Tseng, C.-C., & Lee, S.-L. (2010). Design of wide band fractional-delay filters using derivative sampling method. IEEE Transactions on Circuits and Systems: I-Regular Papers, 57(8), 2087–2098.
Tsui, K. M., Chan, S. C., & Kwan, H. K. (2007). A new method for designing causal stable IIR variable fractional-delay digital filters. IEEE Transactions on Circuits and Systems: II-Express Briefs, 54(11), 999–1003.
Zarour, R., & Fahmy, M. M. (1989). A design technique for variable two-dimensional recursive digital filters. Signal Processing, 17(2), 175–182.
Zhao, R., & Lai, X. (2012). Efficient 2-D based algorithms for WLS designs of 2-D FIR filters with arbitrary weighting functions. Multidimensional Systems and Signal Processing,. doi:10.1007/s11045-011-0169-9.
Zhao, H., & Yu, J. (2006). A simple and efficient design of variable fractional delay FIR filters. IEEE Transactions on Circuits and Systems: II-Express Briefs, 53(2), 157–160.
Zhao, R., & Lai, X. (2011). A fast matrix iterative technique for the WLS design of 2-D quadrantally symmetric FIR filters. Multidimensional Systems and Signal Processing, 22, 303–317.
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Shyu, JJ., Pei, SC., Huang, YD. et al. A new structure and design method for variable fractional-delay 2-D FIR digital filters. Multidim Syst Sign Process 25, 511–529 (2014). https://doi.org/10.1007/s11045-012-0215-2
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DOI: https://doi.org/10.1007/s11045-012-0215-2