Abstract
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.
Similar content being viewed by others
References
B. Arbesser-Rastburg, R. Bellini, F. Coromina, R. De Gaudenzi, O. del Rio, M. Hollreiser, R. Rinaldo, P. Rinous, A. Roederer, R&D directions for next generation broadband multimedia systems: An ESA perspective, in Proc. Int. Comm. Satellite Syst. Conf., Montreal, May 2002
F. Argenti, E.D. Re, Design of biorthogonal M-channel cosine-modulated FIR/IIR filter banks. IEEE Trans. Signal Process. 48(3), 876–881 (2000)
R. Bregovic, T. Saramäki, An efficient approach for designing nearly perfect-reconstruction low-delay cosine-modulated filter banks, in Proc. IEEE Int. Symp. Circuits Syst., vol. 1, May 2002, pp. 825–828
R. Bregovic, T. Saramäki, A systematic technique for designing linear-phase FIR prototype filters for perfect-reconstruction cosine-modulated and modified DFT filter banks. IEEE Trans. Signal Process. 53, 3193–3201 (2005)
R.E. Crochiere, L.R. Rabiner, Multirate Digital Signal Processing (Prentice-Hall, Englewood Cliffs, 1983)
P.S.R. Diniz, L.C.R. de Barcellos, S.L. Netto, Design of cosine-modulated filter bank prototype filters using the frequency-response masking approach, in Proc. IEEE Int. Conf. Acoust. Speech, Signal Processing, vol. 6, Salt Lake City, USA, 2001, pp. 3621–3624
E. Elias, P. Löwenborg, H. Johansson, L. Wanhammar, Tree-structured IIR/FIR uniform-band and octave-band filter banks with very low-complexity analysis or synthesis filters. Signal Process. (EURASIP) 83(9), 1997–2009 (2003)
A. Eshraghi, T.S. Fiez, A comparative analysis of parallel delta-sigma ADC architectures. IEEE Trans. Signal Process. 51(3), 450–458 (2004)
B. Farhang-Boroujeny, Multicarrier modulation with blind detection capability using cosine modulated filter banks. IEEE Trans. Commun. 51(12), 2057–2070 (2003)
A. Fettweis, Wave digital filters: Theory and practice. Proc. IEEE 74(2), 270–327 (1986)
N.J. Fliege, Multirate Digital Signal Processing (Wiley, New York, 1994)
M.B. Furtado Jr., P.S.R. Diniz, S.L. Netto, T. Saramäki, On the design of high-complexity cosine-modulated transmultiplexers based on the frequency-response masking approach. IEEE Trans. Circuits Syst. I, Regul. Pap. 52(11), 2413–2426 (2005)
L. Gazsi, Explicit formulas for lattice wave digital filters. IEEE Trans. Circuits Syst. CAS-32(1) (1985)
S. Haykin, Digital Communications (Wiley, New York, 1988)
P.N. Heller, T. Karp, T.Q. Nguyen, A general formulation of modulated filter banks. IEEE Trans. Signal Process. 47(4), 986–1002 (1999)
H. Johansson, On high-speed recursive digital filters, in Proc. X European Signal Processing Conf., vol. 2. Tampere, Finland, Sept. 2000.
H. Johansson, P. Löwenborg, Flexible frequency-band reallocation network based on variable oversampled complex-modulated filter banks, in Proc. IEEE Int. Conf. Acoust. Speech, Signal Processing, Philadelphia, USA, Mar. 2005
H. Johansson, P. Löwenborg, Flexible frequency-band reallocation networks using variable oversampled complex-modulated filter banks. EURASIP J. Adv. Signal Process. 2007, Article ID 63714, 15 pp. (2007), doi:10.1155/2007/63714
H. Johansson, L. Wanhammar, Wave digital filter structures for high-speed narrow-band and wide-band filtering. IEEE Trans. Circuits Syst. II CAS-46(6) (1999)
H. Johansson, L. Wanhammar, High-speed recursive digital filters based on the frequency-response masking approach. IEEE Trans. Circuits Syst. II 47(1), 48–61 (2000)
J.F. Kaiser, Nonrecursive digital filter design using I 0-sinh window function, in Proc. IEEE Int. Symp. Circuits Syst., vol. 3, 1974, pp. 20–23
S.G. Kim, C.D. Yoo, Highly selective M-channel IIR cosine-modulated filter banks. Electron. Lett. 39(20), 1478–1479 (2003)
M. Lang, Optimal weighted phase equalization according to the L ∞-norm. Signal Process. 27(1), 87–98 (1992)
Y.C. Lim, Frequency-response masking approach for the synthesis of sharp linear phase digital filters. IEEE Trans. Circuits Syst. CAS-33(4), 357–364 (1986)
W.S. Lu, T. Saramäki, R. Bregovic, Design of practically perfect-reconstruction cosine-modulated filter banks: A second-order cone programming approach. IEEE Trans. Circuits Syst. 51, 552–563 (2004)
P. Löwenborg, H. Johansson, L. Wanhammar, Two-channel digital and hybrid analog/digital multirate filter banks with very low complexity analysis or synthesis filters. IEEE Trans. Circuits Syst. II 50(7) (2003)
J.S. Mao, S.C. Chan, K.L. Ho, Theory and design of a class of M-channel IIR cosine-modulated filter banks. IEEE Signal Process. Lett. 7(2), 38–40 (2000)
J.H. McClellan, T.W. Parks, L.R. Rabiner, A computer program for designing optimum FIR linear phase digital filters. IEEE Trans. Audio Electroacoust. AU-21, 506–526 (1973)
P.A. Naylor, O. Tarikulu, A.G. Constantinides, Subband adaptive filtering for acoustic echo control using allpass polyphase IIR filterbanks. IEEE Trans. Signal Process. 6(2), 143–155 (1998)
T.Q. Nguyen, Near-perfect-reconstruction pseudo-QMF banks. IEEE Trans. Signal Process. 42(1), 65–76 (1994)
T.Q. Nguyen, T.I. Laakso, T.E. Tuncer, On perfect-reconstruction allpass-based cosine-modulated IIR filter banks, in Proc. IEEE Int. Symp. Circuits Syst., vol. 2, London, England, 1994, pp. 33–36
P. Noll, MPEG digital audio coding. IEEE Signal Process. Mag. 14(5), 59–81 (1997)
D. Pinchon, R. Siohan, C. Sidet, A fast design method for orthogonal modulated filter banks, in Proc. IEEE Int. Acoustics, Speech, and Signal Processing, vol. 2, 2002, pp. 1177–1180
M. Renfors, T. Saramäki, A class of approximately linear phase digital filters composed of allpass subfilters, in Proc. IEEE Int. Symp. Circuits Syst., vol. 1, San José, CA, May 1986, pp. 678–681
L. Rosenbaum, P. Löwenborg, H. Johansson, An approach for synthesis of modulated M-channel FIR filter banks utilizing the frequency-response masking technique. EURASIP J. Adv. Signal Process. 2007, Article ID 68285, 13 p. (2007). doi:10.1155/2007/68285
T. Saramäki, A generalized class of cosine modulated filter banks, in Proc. First Int. Workshop Transforms Filter Banks, Feb. 1998, pp. 336–365
T. Saramäki, R. Bregovic, An efficient approach for designing nearly perfect-reconstruction cosine-modulated and modified DFT filter banks, in Proc. IEEE Int. Conf. Acoust. Speech, Signal Processing, vol. 6, May 2001, pp. 3617–3620
T. Saramäki, R. Bregovic, Multirate systems and filter banks, in Multirate Systems: Design & Applications, ed. by G. Jovanovic-Dolecek, Chap. 2 (Idea Group Publ., 2002), pp. 27–85
L. Svensson, P. Löwenborg, H. Johansson, Asymmetric cosine modulated causal IIR/FIR NPR filter banks, in Proc. Second Int. Workshop Spectral Methods Multirate Signal Processing, Toulouse, France, Sept. 2002
L. Svensson, P. Löwenborg, H. Johansson, A class of cosine modulated causal IIR filter banks, in Proc. IEEE Int. Conf. Electronics Circuits Syst., Dubrovnik, Croatia, vol. 3, Sept. 2002, pp. 915–918
P.P. Vaidyanathan, Multirate Systems and Filter Banks (Prentice-Hall, Englewood Cliffs, 1993)
P.P. Vaidyanathan, Filter banks in digital communications. IEEE Circuits Syst. Mag. 1(2), 4–25 (2001)
S. Vanka, M.J. Dehghani, R. Aravind, K.M.M. Prabhu, A class of M-channel reduced complexity IIR cosine modulated filter banks, in Proc. Conf. on Convergent Technologies for Asia-Pacific Region, TENCON 03, vol. 3, Oct. 2003, pp. 1040–1043
S. Znidar, Cosine-modulated perfect reconstruction IIR filter bank with good time-frequency resolution, in Proc. 13th Int. Conf. Digital Signal Processing, vol. 2, 1997, pp. 1067–1070
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rosenbaum, L., Löwenborg, P. & Johansson, H. Two Classes of Cosine-Modulated IIR/IIR and IIR/FIR NPR Filter Banks. Circuits Syst Signal Process 29, 103–133 (2010). https://doi.org/10.1007/s00034-009-9115-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00034-009-9115-6