Two Classes of Cosine-Modulated IIR/IIR and IIR/FIR NPR Filter Banks

This paper introduces two classes of cosine-modulated causal and stable filter banks (FBs) with near perfect reconstruction (NPR) and low implementation complexity. Both classes have the same infinite-length impulse response (IIR) analysis FB but different synthesis FBs utilizing IIR and finite-length impulse response (FIR) filters, respectively. The two classes are preferable for different types of specifications. The IIR/FIR FBs are preferred if small phase errors relative to the magnitude error are desired, and vice versa. The paper provides systematic design procedures so that PR can be approximated as closely as desired. It is demonstrated through several examples that the proposed FB classes, depending on the specification, can have a lower implementation complexity compared to existing FIR and IIR cosine-modulated FBs (CMFBs). The price to pay for the reduced complexity is generally an increased delay. Furthermore, two additional attractive features of the proposed FBs are that they are asymmetric in the sense that one of the analysis and synthesis banks has a lower computational complexity compared to the other, which can be beneficial in some applications, and that the number of distinct coefficients is small, which facilitates the design of FBs with large numbers of channels.

[1]  Per Löwenborg,et al.  A class of cosine-modulated causal IIR filter banks , 2002, 9th International Conference on Electronics, Circuits and Systems.

[2]  Tapio Saramäki,et al.  An efficient approach for designing nearly perfect-reconstruction low-delay cosine-modulated filter banks , 2002, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353).

[3]  Lars Wanhammar,et al.  Tree-structured IIR/FIR uniform-band and octave-band filter banks with very low-complexity analysis or synthesis filters , 2003, Signal Process..

[4]  Yong Ching Lim,et al.  Frequency-response masking approach for the synthesis of sharp linear phase digital filters , 1986 .

[5]  Håkan Johansson,et al.  On high-speed recursive digital filters , 2000, 2000 10th European Signal Processing Conference.

[6]  Tapio Saramäki,et al.  A systematic technique for designing prototype filters for perfect reconstruction cosine modulated and modified DFT filter banks , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).

[7]  Behrouz Farhang-Boroujeny,et al.  Multicarrier modulation with blind detection capability using cosine modulated filter banks , 2003, IEEE Trans. Commun..

[8]  Chang D. Yoo,et al.  Highly selective M-channel IIR cosine-modulated filter banks , 2003 .

[9]  Lars Wanhammar,et al.  High-speed recursive digital filters based on the frequency-response masking approach , 2000 .

[10]  S.C. Chan,et al.  Theory and design of a class of M-channel IIR cosine-modulated filter banks , 2000, IEEE Signal Processing Letters.

[11]  Jrg Kaiser,et al.  Nonrecursive digital filter design using the I-sinh window function , 1977 .

[12]  Simon Haykin,et al.  Digital Communications , 2017 .

[13]  L. Rabiner,et al.  A computer program for designing optimum FIR linear phase digital filters , 1973 .

[14]  Håkan Johansson,et al.  An Approach for Synthesis of Modulated-Channel FIR Filter Banks Utilizing the Frequency-Response Masking Technique , 2006, EURASIP J. Adv. Signal Process..

[15]  Tapio Saramäki,et al.  On the design of high-complexity cosine-modulated transmultiplexers based on the frequency-response masking approach , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[16]  Håkan Johansson,et al.  Flexible Frequency-Band Reallocation Networks Using Variable Oversampled Complex-Modulated Filter Banks , 2007, EURASIP J. Adv. Signal Process..

[17]  Lajos Gazsi,et al.  Explicit formulas for lattice wave digital filters , 1985 .

[18]  Truong Q. Nguyen,et al.  On perfect-reconstruction allpass-based cosine-modulated IIR filter banks , 1994, Proceedings of IEEE International Symposium on Circuits and Systems - ISCAS '94.

[19]  Robert Bregovic,et al.  Multirate Systems and Filter Banks , 2002 .

[20]  B. Arbesser-Rastburg,et al.  R&D DIRECTIONS FOR NEXT GENERATION BROADBAND MULTIMEDIA SYSTEMS: AN ESA PERSPECTIVE , 2002 .

[21]  P. Noll,et al.  MPEG digital audio coding , 1997, IEEE Signal Process. Mag..

[22]  Sergio L. Netto,et al.  Design of cosine-modulated filter bank prototype filters using the frequency-response masking approach , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[23]  K.M.M. Prabhu,et al.  A class of M-channel reduced complexity IIR cosine modulated filter banks , 2003, TENCON 2003. Conference on Convergent Technologies for Asia-Pacific Region.

[24]  Pierre Siohan,et al.  A fast design method for biorthogonal modulated filter banks , 2002, EUSIPCO.

[25]  P. Vaidyanathan.  Multirate Systems And Filter Banks , 1992 .

[26]  Tapio Saramäki,et al.  Design of practically perfect-reconstruction cosine-modulated filter banks: a second-order cone programming approach , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[27]  Tapio Saramäki,et al.  An efficient approach for designing nearly perfect-reconstruction cosine-modulated and modified DFT filter banks , 2001, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221).

[28]  P. P. Vaidyanathan,et al.  Filter banks in digital communications , 2001 .

[29]  Lars Wanhammar,et al.  Wave digital filter structures for high-speed narrow-band and wide-band filtering , 1999 .

[30]  Patrick A. Naylor,et al.  Subband adaptive filtering for acoustic echo control using allpass polyphase IIR filterbanks , 1998, IEEE Trans. Speech Audio Process..

[31]  Pierre Siohan,et al.  A fast design method for biorthogonal modulated filter banks , 2002, 2002 11th European Signal Processing Conference.

[32]  Terri S. Fiez,et al.  A comparative analysis of parallel delta-sigma ADC architectures , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.

[33]  S. Znidar.  Cosine-modulated perfect reconstruction IIR filter bank with good time-frequency resolution , 1997, Proceedings of 13th International Conference on Digital Signal Processing.

[34]  M. Lang,et al.  Optimal weighted phase equalization according to the L∞-norm , 1992, Signal Process..

[35]  Truong Q. Nguyen.  Near-perfect-reconstruction pseudo-QMF banks , 1994, IEEE Trans. Signal Process..

[36]  A. Fettweis.  Wave digital filters: Theory and practice , 1986, Proceedings of the IEEE.

[37]  Truong Q. Nguyen,et al.  A general formulation of modulated filter banks , 1999, IEEE Trans. Signal Process..

[38]  Håkan Johansson,et al.  Asymmetric cosine modulated causal IIR/FIR NPR filter banks , 2002 .

[39]  Lars Wanhammar,et al.  Two-channel digital and hybrid analog/digital multirate filter banks with very low-complexity analysis or synthesis filters , 2003, IEEE Trans. Circuits Syst. II Express Briefs.

[40]  Håkan Johansson,et al.  Flexible frequency-band reallocation network based on variable oversampled complex-modulated filter banks [satellite communication applications] , 2005, Proceedings. (ICASSP '05). IEEE International Conference on Acoustics, Speech, and Signal Processing, 2005..

[41]  E. D. Re,et al.  Design of biorthogonal M-channel cosine-modulated FIR/IIR filter banks , 2000, IEEE Trans. Signal Process..