Multidimensional IIR filters and robust rational interpolation
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
It is well-known that IIR filters can have a much lower order than FIR filters with the same performance. On the downside is that the implementation of an IIR filter is an iterative procedure while that of an FIR filter is a one-shot computation. But in higher dimensions IIR filters are definitely more attractive. We offer a technique where the filter’s performance specifications, stability constraints, its convergence speed and a protection against possible adverse effects of perturbations are all included in the design from the start. The technique only needs an off-the-shelf LP solver because the filter is obtained as a Chebyshev center of a convex polytope. The method deals with general non-causal non-separable filters.
- Cuyt, A. & Salazar Celis, O. (2012). Multivariate data fitting with error control. TR Universiteit Antwerpen (in preparation).
- Dumitrescu, B. (2005) Optimization of two-dimensional IIR filters with nonseparable and separable denominator. IEEE Transactions on Signal Processing 53: pp. 1768-1777 CrossRef
- Gorinevsky, D., Boyd, S. (2006) Optimization-based design and implementation of multi-dimensional zero-phase IIR filters. IEEE Transactions on Circuits and Systems 53: pp. 372-383 CrossRef
- Harris, D. (1981) Design of 2-D rational digital filters. Acoustics, Speech, and Signal Processing 6: pp. 696-699
- Jiang, A., Kwan, H. K. (2010) Minimax design of IIR digital filters using SDP relaxation technique. IEEE Transactions on Circuits and Systems I 57: pp. 378-390 CrossRef
- Li, Z., Marks, R. (1989) Accelerated convergence of an iterative implementation of a two-dimensional IIR filter. IEEE International Symposium on Circuits and Systems 2: pp. 1483-1486 CrossRef
- Lu, W. S., & Hinamoto, T. (2011). Minimax design of stable IIR filters with sparse coefficients. In: International Symposium on Circuits and Systems (ISCAS 2011), May 15–19 2011. Brazil: Rio de Janeiro, pp. 398–401. IEEE. http://dx.doi.org/10.1109/ISCAS.2011.5937586 .
- Piyachaiyakul, N., & Charoenlarpnopparut, C. (2011). Design of three-dimensional adaptive IIR notch filters. Multidimensional Systems and Signal Processing, 1–12. doi:10.1007/s11045-011-0170-3 .
- Pomentale, T. (1968) On discrete rational least squares approximation. Numerische Mathematik 12: pp. 40-46 CrossRef
- Reddy, H., Khoo, I., Rajan, P. (2003) 2-D symmetry: Theory and filter design applications. IEEE Circuits and Systems Magazine 3: pp. 4-33 CrossRef
- Salazar Celis, O., Cuyt, A., Verdonk, B. (2007) Rational approximation of vertical segments. Numerical Algorithms 45: pp. 375-388 CrossRef
- Wu-Sheng, L., Soo-Chang, P., Chien-Cheng, T. (1998) Design of 2-D recursive digital filters using nonsymmetric half-plane allpass filters. IEEE Transactions on Signal Processing 46: pp. 1-10 CrossRef
- Multidimensional IIR filters and robust rational interpolation
Multidimensional Systems and Signal Processing
Volume 25, Issue 3 , pp 447-471
- Cover Date
- Print ISSN
- Online ISSN
- Springer US
- Additional Links
- Multidimensional digital filters
- Linear programming
- Quadratic programming
- Rational approximation
- Industry Sectors