Minimum Roundoff Noise Realization for Variable IIR Digital Filters Based on M-D Polynomial Approximation

In design of Variable Digital Filters (VDFs), Multi-Dimensional (M-D) polynomial approximation is well known as one of the powerful techniques. Although a number of methods for such VDF design can be seen in the literature, nothing has been proposed in this field with emphasis on high-accuracy filter structures with respect to the finite wordlength effects such as coefficient quantization error and roundoff noise. This paper presents M-D polynomial approximation-based VDFs with such a high-accuracy structure. To this end, we first decompose the pre-designed set of constant filters into second-order sections. Then, using the theory proposed in the literature, all of the second-order sections are described in terms of state-space representation of second-order Minimum Roundoff Noise (MRN) structure. Finally the resultant state-space coefficients are approximated by M-D polynomials based on spectral parameters. A numerical example demonstrates that the proposed method simultaneously attains the desired variable characteristics and approximately optimal performances with respect to the finite wordlength effects.

[1]  S. Hwang.  Minimum uncorrelated unit noise in state-space digital filtering , 1977 .

[2]  Victor E. DeBrunner,et al.  Multiple fully adaptive notch filter design based on allpass sections , 2000, IEEE Trans. Signal Process..

[3]  Anthony G. Constantinides,et al.  Frequency tracking using constrained adaptive notch filters synthesised from allpass sections , 1990 .

[4]  M. Kawamata,et al.  Statistical sensitivity and minimum sensitivity structures with fewer coefficients in discrete time linear systems , 1990 .

[5]  Ya Jun Yu,et al.  Mixed-Radix Fast Filter Bank Approach for the Design of Variable Digital Filters With Simultaneously Tunable Bandedge and Fractional Delay , 2012, IEEE Transactions on Signal Processing.

[6]  Masayuki Kawamata,et al.  Closed Form Solutions to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters with Real Poles , 2010, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[7]  Masayuki Kawamata,et al.  Design of Variable Digital Filters Based on State-Space Realizations , 2001 .

[8]  Honggang Zhang,et al.  Linear-Phase VDF Design With Unabridged Bandwidth Control Over the Nyquist Band , 2014, IEEE Transactions on Circuits and Systems II: Express Briefs.

[9]  Naoya Onizawa,et al.  High-Accuracy and Area-Efficient Stochastic FIR Digital Filters Based on Hybrid Computation , 2017, IEICE Trans. Inf. Syst..

[10]  Masayuki Kawamata,et al.  Closed Form Solutions to L2-Sensitivity Minimization Subject to L2-Scaling Constraints for Second-Order State-Space Digital Filters with Real Poles , 2010, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[11]  Masayuki Kawamata,et al.  A closed form solution to L/sub 2/-sensitivity minimization of second-order state-space digital filters , 2008, 2006 IEEE International Symposium on Circuits and Systems.

[12]  Kok Lay Teo,et al.  Variable Digital Filter With Group Delay Flatness Specification or Phase Constraints , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[13]  L. Jackson.  Digital filters and signal processing , 1985 .

[14]  Ya Jun Yu.  Low-Complexity Design of Variable Bandedge Linear Phase FIR Filters With Sharp Transition Band , 2019 .

[15]  Naoyuki Aikawa,et al.  A design of fir filters with variable notches considering reduction method of polynomial coefficients for real-time signal processing , 2013 .

[16]  S. C. Chan,et al.  On the design and implementation of FIR and IIR digital filters with variable frequency characteristics , 2002 .

[17]  Sanjit K. Mitra,et al.  Design of recursive digital filters with variable characteristics , 1990, Int. J. Circuit Theory Appl..

[18]  Takao Hinamoto,et al.  L 2-Sensitivity Minimization of One-and Two-Dimensional State – Space Digital Filters Subject to L 2-Scaling Constraints , 2006 .

[19]  Honggang Zhang,et al.  Low complexity and efficient dynamic spectrum learning and tunable bandwidth access for heterogeneous decentralized cognitive radio networks , 2015, Digit. Signal Process..

[20]  Someshwar C. Gupta,et al.  Wave digital filter structures with variable frequency characteristics , 1976 .

[21]  M. M. Fahmy,et al.  A design technique for variable digital filters , 1989 .

[22]  Masayuki Kawamata,et al.  Realization of high accuracy 2-D variable IIR digital filters based on the reduced-dimensional decomposition form , 2003, Proceedings of the 2003 International Symposium on Circuits and Systems, 2003. ISCAS '03..

[23]  Håkan Johansson,et al.  On linear-phase FIR filters with variable bandwidth , 2004, IEEE Transactions on Circuits and Systems II: Express Briefs.

[24]  Wei-Yong Yan,et al.  On L2-Sensitivity Minimization of Linear , 1992 .

[25]  C. Barnes.  On the design of optimal state-space realizations of second-order digital filters , 1984 .

[26]  Masayuki Kawamata,et al.  A Closed Form Solution to L2-Sensitivity Minimization of Second-Order State-Space Digital Filters Subject to L2-Scaling Constraints , 2008, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[27]  Naoyuki Aikawa,et al.  A Design Method for Variable Linear-Phase FIR Filters with Changing Multifactors for Checkweighers , 2010, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[28]  Takao Hinamoto,et al.  L/sub 2/-sensitivity minimization of one- and two-dimensional state-space digital filters subject to L/sub 2/-scaling constraints , 2006, IEEE Transactions on Signal Processing.

[29]  Kok Lay Teo,et al.  Variable Digital Filter With Least-Square Criterion and Peak Gain Constraints , 2007, IEEE Transactions on Circuits and Systems II: Express Briefs.

[30]  R. Rohini.  Low Complexity Reconfigurable Fast Filter Bank for Multi-Standard Wireless Receivers , 2015 .

[31]  Thibault Hilaire.  On the Transfer Function Error of State-Space Filters in Fixed-Point Context , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[32]  Masato Ito,et al.  A synthesis of variable wave digital filters , 1994 .

[33]  Takao Hinamoto,et al.  Minimization of L/sub 2/-sensitivity for state-space digital filters subject to L/sub 2/-dynamic-range scaling constraints , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[34]  Tian-Bo Deng.  Design of recursive 1-D variable filters with guaranteed stability , 1997 .

[35]  Masayuki Kawamata,et al.  Design and Realization of Variable IIR Digital Filters as a Cascade of Identical Subfilters , 2001 .

[36]  A. Prasad Vinod,et al.  Efficient Implementation of Reconfigurable Warped Digital Filters With Variable Low-Pass, High-Pass, Bandpass, and Bandstop Responses , 2013, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[37]  Masayuki Kawamata,et al.  On the Absence of Limit Cycles in State-Space Digital Filters With Minimum $L_{2}$-Sensitivity , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[38]  Anthony G. Constantinides,et al.  Spectral Transformations for Digital Filters , 1970 .

[39]  Tian-Bo Deng.  Closed-form design and efficient implementation of variable digital filters with simultaneously tunable magnitude and fractional delay , 2004, IEEE Trans. Signal Process..

[40]  阿部 正英,et al.  On the Absence of Limit Cycles in State-Space Digital Filters With Minimum L2-Sensitivity , 2008 .

[41]  Shing-Chow Chan,et al.  Design of complex-valued variable FIR digital filters and its application to the realization of arbitrary sampling rate conversion for complex signals , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

[42]  Masayuki Kawamata,et al.  A unified approach to the optimal synthesis of fixed-point state-space digital filters , 1985, IEEE Trans. Acoust. Speech Signal Process..

[43]  Honggang Zhang,et al.  Reconfigurable Filter Bank With Complete Control Over Subband Bandwidths for Multistandard Wireless Communication Receivers , 2015, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[44]  Shunsuke Koshita,et al.  Adaptive IIR Band-Pass/Band-Stop Filtering Using High-Order Transfer Function and Frequency Transformation , 2013 .

[45]  Shing-Chow Chan,et al.  A new method for designing FIR filters with variable characteristics , 2004, IEEE Signal Processing Letters.

[46]  Shunsuke Koshita,et al.  High-performance variable band-pass/band-stop state-space digital filters using Gramian-preserving frequency transformation , 2014, Digit. Signal Process..

[47]  Masayuki Kawamata,et al.  Variable Digital Filters , 1997 .

[48]  Tian-Bo Deng.  New method for designing stable recursive variable digital filters , 1998, Signal Process..

[49]  M.N.S. Swamy,et al.  Digital bandpass and bandstop filters with variable center frequency and bandwidth , 1976, Proceedings of the IEEE.

[50]  Wei-Yong Yan,et al.  On L/sup 2/-sensitivity minimization of linear state-space systems , 1992 .

[51]  Lothar Thiele,et al.  On the sensitivity of linear state-space systems , 1986 .

[52]  V. Tavsanoglu,et al.  Optimal design of state - space digital filters by simultaneous minimization of sensitivity and roundoff noise , 1984 .

[53]  Masayuki Kawamata,et al.  A closed form solution to L2-sensitivity minimization of second-order state-space digital filters , 2006, ISCAS.

[54]  Takao Hinamoto,et al.  Analysis and minimization of L/sub 2/-sensitivity for linear systems and two-dimensional state-space filters using general controllability and observability Gramians , 2002 .

[55]  Håkan Johansson,et al.  Improved Filter Bank Approach for the Design of Variable Bandedge and Fractional Delay Filters , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[56]  Masayuki Kawamata,et al.  Derivation of the Class of Digital Filters With All Second-Order Modes Equal , 2011, IEEE Transactions on Signal Processing.