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**Design of IIR linear-phase nonuniform-division filter banks with signed powers-of-two coefficients.**
*(English)*
Zbl 1190.93059

Summary: This paper deals with the minimax design of two-channel Linear-Phase (LP) Nonuniform-Division Filter (NDF) banks using Infinite Impulse Response (IIR) Digital All-Pass Filters (DAFs) with Signed Powers-of-Two (SPT) coefficients. Based on the theory of two-channel NDF banks using two IIR DAFs, the design problem is appropriately formulated to result in an appropriate Chebyshev approximation for the desired phase responses of the IIR DAFs. Through a frequency sampling and iterative approximation method, the optimization problem for finding the SPT coefficients for the IIR DAFs can be solved by utilizing a weighted least-squares approach in conjunction with a coordinate rotational digital computer (CORDIC) algorithm. The resulting two-channel SPT coefficient NDF banks can possess approximately LP response without magnitude distortion. Several simulation examples are presented for illustration and comparison.

### MSC:

93C80 | Frequency-response methods in control theory |

93C95 | Application models in control theory |

90C47 | Minimax problems in mathematical programming |

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\textit{J.-H. Lee} et al., Int. J. Circuit Theory Appl. 37, No. 7, 811--834 (2009; Zbl 1190.93059)

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### References:

[1] | Veldhuis, Subband coding of digital audio signals, Philips Journal of Research 44 (2-3) pp 329– (1989) |

[2] | Saleh, On the design of two channel perfect construction QMF filters, International Journal of Circuit Theory and Applications 28 pp 209– (2000) · Zbl 1039.93042 |

[3] | Gülzow, Spectral-subtraction speech enhancement in multirate systems with and without non-uniform and adaptive bandwidths, Signal Processing 83 (8) pp 1613– (2003) · Zbl 1144.94337 |

[4] | Cvetkovic, Nonuniform oversampled filler banks for audio signal processing, IEEE Transactions on Speech and Audio Processing 11 (5) pp 393– (2003) |

[5] | Cassidy RJ, Smith JO. A tunable, nonsubsampled, nonuniform filter bank for multiband audition and level modification of audio signals. Proceedings of the Thirty-eighth Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, U.S.A., vol. 2, November 2004; 2228-2232. |

[6] | Nguyen TT, Oraintara S. A multiresolution directional filter bank for image applications. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Montreal, Que., Canada, vol. 3, May 2004; 37-40. |

[7] | Deng, Low-delay nonuniform pseudo-QMF banks with application to speech enhancement, IEEE Transactions on Signal Processing 55 (5) pp 2110– (2007) · Zbl 1391.94192 |

[8] | Nayebi, Nonuniform filter banks: a reconstruction and design theory, IEEE Transactions on Signal Processing 41 (3) pp 1114– (1993) · Zbl 0775.93272 |

[9] | Wada, Design of nonuniform division multirate FIR filter banks, IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing 42 (2) pp 115– (1995) |

[10] | Lee, Design of two-channel nonuniform-division maximally decimated filter banks using L1 criteria, IEE Proceedings-Vision, Image and Signal Processing 143 (2) pp 79– (1996) |

[11] | Lee, Design of two-channel low-delay IIR nonuniform-division filter banks using L1 error criteria, IEE Proceedings-Vision, Image and Signal Processing 149 (5) pp 304– (2002) |

[12] | Lee, Optimal design of two-channel nonuniform-division FIR filter banks with -1, 0, and +1 coefficients, IEEE Transactions on Signal Processing 47 (2) pp 422– (1999) |

[13] | Lee, Design of two-channel IIR nonuniform-division filter banks with arbitrary group delay, IEE Proceedings-Vision, Image and Signal Processing 147 (6) pp 534– (2000) |

[14] | Lee, Minimax design of two-channel nonuniform-division FIR filter banks, IEE Proceedings-Vision, Image and Signal Processing 145 (2) pp 88– (1998) |

[15] | Lee, Minimax design of two-channel nonuniform-division FIR filter banks with -1, 0, and +1 coefficients, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 46 (10) pp 1184– (1999) |

[16] | Lee, Minimax design of two-channel nonuniform-division filter banks using IIR allpass filters, IEEE Transactions on Signal Processing 52 (11) pp 3227– (2004) |

[17] | Lim, A width-recursive depth-first tree search approach for the design of discrete coefficient perfect reconstruction lattice filter bank, IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing 50 (6) pp 257– (2003) |

[18] | Yu YJ, Lim YC. Signed power-of-two allocation scheme for the design of lattice orthogonal filter banks. Proceedings of the IEEE International Symposium on Circuits and Systems, Kobe, Japan, vol. 2, May 2005; 1819-1822. |

[19] | Chan, Multiplierless perfect reconstruction modulated filter banks with sum-of-power-of-two coefficients, IEEE Signal Processing Letters 8 (6) pp 163– (2001) |

[20] | Wu, A unified view for vector rotational CORDIC algorithms and architectures based on angle quantization approach, IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 49 (10) pp 1442– (2002) |

[21] | Wu AY, Lee IH, Wu CS. Angle quantization approach for lattice IIR filter implementation and its Trellis-allocation algorithm. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Hong Kong, vol. 2, April 2003; 673-676. |

[22] | Park SY, Cho NI. Design of perfect reconstruction QMF lattice with signed power-of-two coefficients using CORDIC algorithm. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Philadelphia, PA, U.S.A., vol. 4, March 2005; 565-568. |

[23] | Vaidyanathan, A new approach to the realization of low sensitivity IIR digital filters, IEEE Transactions on Acoustics, Speech, and Signal Processing ASSP-34 pp 350– (1986) |

[24] | Lim, A weighted least squares algorithm for quasi-equiripple FIR and IIR digital filter design, IEEE Transactions on Signal Processing 40 (3) pp 551– (1992) |

[25] | Ikehara, Design of complex all-pass networks using Remez algorithm, IEEE Transactions on Circuits and Systems-II: Analog and Digital Signal Processing 39 (8) pp 549– (1992) · Zbl 0775.93257 |

[26] | Vaidyanathan, Multirate Systems and Filter Banks (1992) · Zbl 0784.93096 |

[27] | Cheney, Introduction to Approximation Theory (1966) · Zbl 0161.25202 |

[28] | Wu CS, Wu AY. A novel Trellis-based searching scheme for EEAS-based CORDIC algorithm. Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Salt Lake City, UT, U.S.A., vol. 2, April 2001; 1229-1232. |

[29] | Nelder, A simplex method for function minimization, The Computer Journal 7 pp 308– (1965) · Zbl 0229.65053 |

[30] | Sandberg, Recent representation results for linear system maps: a short survey, International Journal of Circuit Theory and Applications 35 pp 497– (2007) · Zbl 1128.93027 |

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