Abstract
A review is presented first of the evolution of transmultiplexers since about 1966, in the context of a long progression of theoretical advances and developments leading to recent proposals to fundamentally improve OFDM type systems using principles of perfect reconstruction filter (PRF) banks. The equivalence of transmultiplexers to OFDM type multi-user systems is discussed. The desirable goals for performance and implementation of transmultiplexers or multiband, multiuser communication systems that are addressed and met in this paper using filter bank trees are set down. Then modifications and extensions are presented of the designs and architectures of wavelet packet based synthesis and analysis pairs of filter bank trees (Sablatash and Lodge in Digital Signal Process 13: 58–92, 2003) that can be used as transmultiplexers. These exhibit a number of advantages over the previous designs and address three shortcomings of the designs used to illustrate basic principles in Sablatash and Lodge (Digital Signal Process 13:58–92, 2003). The first of these is the asymmetry of the magnitude frequency responses of the multiplexer channels, which is addressed using a symmetric design for a lowpass and highpass quadrature mirror filter (QMF) pair described herein. The second is the problem of minimizing the total delay of the signal in passing through the analysis and synthesis filter banks. This is addressed using an architecture involving DFT polyphase synthesis filter banks to replace the wideband VSB filters at the roots of the two identical synthesis filter bank trees, but results in the multiplexer having fewer levels. In this way a tradeoff is effected of lower delay and complexity with fewer levels of bandwidth on demand. At the receiver matching DFT polyphase analysis filters and the other matching analysis filters are implemented. The third shortcoming is the difficulty in designing a synchronization scheme if the filters in the synthesis and analysis filter banks have non-linear phase. This is addressed by designing linear phase filters that do not affect the ISI to any significant degree for communication purposes, although exact perfect reconstruction is lost, but greatly ease and improve the design of the synchronization scheme. Relationships of this paper and its advantages over recent research studies and IEEE 802.22 standards proposals using PR filter banks for multi-user systems to greatly improve on OFDM systems are discussed.
Similar content being viewed by others
References
Sablatash M. and Lodge J. (2003). Spectrally efficient multiplexing of O-QPSK or VSB signals using wavelet packet-based filter banks. Digital Signal Process. 13(1): 58–92
Chang R.W. (1966). High-speed multichannel data transmission with bandlimited orthogonal signals. Bell Sys. Tech. J. XLV(10): 1775–1796
Saltzberg B.R. (1967). Performance of an efficient parallel data transmission system. IEEE Trans. Commun. Technol. COM-15(6): 805–811
Weaver D.K. Jr. (1956). A third method of generation and detection of single-sideband signals. Proc. IRE 44(12): 1703–1705
Darlington, S.: Some circuits for single-sideband modulation, Proceedings of the 3rd annual princeton conference on information sciences and systems, Princeton University, Princeton, (1969)
Darlington S. (1970). On digital single-sideband modulators. IEEE Trans. Circuit Theory CT-17(3): 409–414
Kurth C.F. (1971). SSB /FDM utilizing TDM digital filters. IEEE Trans. Commun. Technol. COM-19(1): 63–71
Freeny S.L., Kieburtz R.B., Mina K.V. and Tewksbury S.K. (1971). Design of digital filters for an all digital frequency division multiplex-time division multiplex translator. IEEE Trans. Circuit Theory CT-18(6): 702–711
Freeny S.L., Kieburtz R.B., Mina K.V. and Tewksbury S.K. (1971). Systems analysis of a TDM-FDM translator/digital A-type channel bank. IEEE Trans. Commun. Technol. COM-19(6 Pt. 1): 1050–1059
Singh S., Renner K. and Gupta S.C. (1973). Digital single-sideband modulation. IEEE Trans. Commun. COM-21(3): 255–262
Bellanger M.G. and Daguet J.L. (1974). TDM-FDM transmultiplexer: digital polyphase and FFT. IEEE Trans. Commun. COM-22(9): 1199–1205
Terrell P.M. and Rayner P.J.W. (1975). A digital block processor for SSB-FDM modulation and demodulation. IEEE Trans. Commun. COM-23(2): 282–286
Kieburtz R.B. (1978). Introduction to papers on TDM/FDM transmultiplexers. IEEE Trans. Commun. COM-26(5): 697–698
Takahata F., Hirata Y., Ogawa A. and Inagaki K. (1978). Development of a TDM/FDM transmultiplexer. IEEE Trans. Commun. COM-26(5): 726–733
Maruta R. and Tomozawa A. (1978). An improved method for digital SSB-FDM modulation and demodulation. IEEE Trans. Commun. COM-26(5): 720–725
Bonnerot G., Coudreuse M. and Bellanger M. (1978). Digital processing techniques in the 60 channel transmultiplexer. IEEE Trans. Commun. COM-26(5): 698–706
Tsuda T., Morita S. and Fujii Y. (1978). Digital TDM-FDM translator with multistage structure. IEEE Trans. Commun. COM-26(5): 734–741
Peled A. and Winograd S. (1978). TDM-FDM conversion requiring reduced computation complexity. IEEE Trans. Commun. COM-26(5): 707–719
Scheuermann H. and Göckler H. (1981). A comprehensive survey of digital transmultiplexing methods. Proc. IEEE 69(11): 1419–1450
Takahata, F., Inagaki, K., Ogawa, A.: Design of digital signal processor in a TDM/FDM transmultiplexer. Proceedings of the IEEE International Conference on Communication (ICC ’80), vol. 1, Seattle, June 8–12, 1980, pp. 47.2.1–47.2.6
Aoyama T., Mano F., Wakabayashi K., Maruta R. and Tomozawa A. (1980). 120-channel transmultiplexer design and performance. IEEE Trans. Commun. COM-28(9): 1709–1717
Aoyama T., Mano F. and Wakabayashi K. (1980). An experimental TDM-FDM transmultiplexer using CMOS LSI circuits. Rev. Elec. Commun. Lab. (Tokyo) 28(1–2): 1–27
Classen T.A.C.M. and Mecklenbräuker W.F.G. (1978). A generalized scheme for an all-digital time-division multiplex to frequency-division multiplex translator. IEEE Trans. Circuits Systems CAS-25(5): 252–259
Kurth, C.F., Bures, K.J., Gagnon, P.R. (1981) Per-channel, memory-oriented transmultiplexer with logarithmic processing—architecture and simulation. Proceedings of the IEEE International Conference on Communication (ICC ’81), vol. 1, Denver, CO, June 14–18,, pp. 7.3.1–7.3.5
Kurth, C.F., Gagnon, P.R., Bures, K.J.: Per-channel, memory-oriented transmultiplexer with logarithmic processing—lab model implementation and testing. Proceedings of the IEEE International Conference on Communication (ICC ’81), Vol. 1, Denver, CO, June 14–15, 1981, pp. 7.4.1–7.4.4
Del Re, E.: A new approach to transmultiplexer implementation. Proceedings of the IEEE International Conferences on Communication, (ICC ‘81), vol. 1, Denver, CO, June 14–15, 1981, pp. 18.4.1–18.4.4
Daguet J.L., Bellanger M. and Bonnerot G. (1975). Méthode Simplifiée de Multiplexage en Fréquence de Signaux Numériques Réels. Câbles et Transmission 29(3): 259–265
Roche B., LeCorre Y.-L., Bonnerot G., Coudreuse M. and Sourgens J. (1977). Transmultiplexeur numériques à 60 Voies. Câbles et Transmission 31(4): 444–463
Drageset, O., Foss, O.: The transmultiplexer—a new type of equipment for conversion between PCM and FDM systems. Part IV—Implementation, Telektronikk, (1), 19–24 (1978)
Røste T., Hasberg O. and Ramstad T.A. (1979). A radix-4 FFT processor for application in a 60-channel transmultiplexer using TTL technology. IEEE Trans. Acoust., Speech, Signal Process. ASSP-27(6): 746–751
Polloni, D.P.C.: Dimensionierung von Digitalen TDM-FDM—Transmultiplexern nach der Polyphasenmethode, Ph.D. Dissertation, ETH Zürich, Switzerland, No. 6283, (1979)
Tomlinson M. and Wong K.M. (1976). Techniques for the digital interfacing of T.D.M.-F.D.M. systems. Proc Inst. Elec. Eng. 123(6): 1285–1292
Narasimha, M.J., Peterson, A.M.: Design of a 24-channel transmultiplexer. IEEE Trans. Acoust. Speech Signal Process. Vol. ASSP-27, Part II, No. 6, 1979, pp. 752–762
Marshall, T.G.: A multiple VLSI signal processor realization of a transmultiplexer. Proceedings of the IEEE International Conference on Communication (ICC’81), vol. 1, Denver, CO, June 14–18, 1981, pp. 7.7.1–7.7.5
Kao, C.Y.: An exploratory TDM-FDM SSB generator. Proceedings National Electronics Conference vol. 27, Chicago, IL, October 1972, pp. 47–51
Lagadec, R.: Digital channel translation based on quadrature processing, Ph.D. dissertation, ETH Zürich, Switzerland, No. 5470, (1975)
Tsuda T., Morita S. and Fujii Y. (1979). Realization of a TDM-FDM transmultiplexer with multistage structure using ROM multipliers. Fujitsu Sci. Tech. J. 15(1): 17–37
Bellanger M.G., Daguet J.L. and Lepagnol G.P. (1974). Interpolation, extrapolation and reduction of computation speed in digital filters. IEEE Trans. Acoust. Speech Signal Process. ASSP-22(4): 231–235
Constantinides, A.G., Valenzuela, R.A.: A new modular low complexity transmultiplexer design. Proceedings of the IEEE International Conference on Communicaton (ICC ‘81), vol. 1, Denver, CO, June 14–18, 1981, pp. 18.8.1–18.8.5
Fettweis A. (1978). Principles for multiplier-free single-way PCM/FDM and audio/FDM conversion. Archiv. Elektr. Übertragungstechnik AEÜ-32(11): 441–446
Fettweis A. (1978). Multiplier-free modulation schemes for PCM/FDM and audio/FDM conversion. Archiv. Elektr. Übertragungstechnik AEÜ-32(12): 447–485
Fettweis A. (1971). Digital filter structures related to classical filter networks. Archiv. Elektr. Übertragungstechnik AEÜ-25(2): 79–89
Gazai, L.: Simulation and testing of transmultiplexers using wave digital filters. Proceedings of the IEEE International Conference on Communication (ICC’81), vol. 1, Denver, CO, pp. 18.6.1–18.6.5 (1981)
Fettweis, A.: Concepts for efficient design of transmultiplexers with robust performance. Proceedings of the IEEE International Conference On Communication (ICC’81), vol. 1, Denver, CO, pp.18.5.1–18.5.5 (1981)
Molo, F.: Transmultiplexer realization with multistage filtering. Proceedings of the IEEE International Conference on Communication (ICC’81), vol.1, Denver, CO, pp. 18.7.1–18.7.5 (1981)
IEEE Trans. Commun. Special Issue on Transmultiplexers, Vol. COM-30, No. 7, pp. 1457–1655 (1982)
Bellanger M.G. (1982). On computational complexity in digital transmultiplexer filters. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1461–1465
Røste T. (1982). The impact of some CCITT recommendations on transmultiplexer design. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1483–1492
Narasimha M.J. (1982). Design of FIR filter banks for a 24-channel transmultiplexer. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1506–1510
Takahata F., Inagaki K., Hirata Y. and Ogawa A. (1982). A digital 60-channel transmultiplexer: algorithm minimizing multiplications rate and hardware implementation. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1511–1519
Kurth C.F., Bures K.J., Gagnon P.R. and Etzel M.H. (1982). A per-channel memory-oriented transmultiplexer with logarithmic processing. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1520–1527
Maruta R., Kanemasa A., Sakaguchi H., Hibino M. and Nakayama K. (1982). 24- and 120-channel transmultiplexers built with new digital signal processing LSI’s. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1528–1539
Rossiter T.J.M., Chitsaz S., Gingell M.J. and Humphrey L.D. (1982). A modular transmultiplexer system using custom LSI devices. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1540–1551
Maruta, R., Kanemasa, A., Sakaguchji, H., Hibino, M., Kawayachi, N.: A 24-channel transmultiplexer. Proceedings of the IEEE International Conference on Communication (ICC’81), vol. 1, Denver, CO, June 14–18 pp. 7.5.1–7.5.5 (1981)
Wakabayashi K., Aoyama T., Murano K. and Amano F. (1982). TDM-FDM transmultiplexer using a digital signal processor. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1552–1559
Marshall T.G. (1982). A multiple VLSI signal processor realization of a transmultiplexer. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1560–1568
Bellanger M.G., Bonnerot G. and Coudreuse M. (1976). Digital filtering by polyphase network: application to sample-rate alteration and filter banks. IEEE Trans. Acoust. Speech Signal Process. ASSP-24(2): 109–114
Freeny, S.L.: An introduction to the use of digital signal processing for TDM/FDM conversion. Proceedings of the IEEE International Conference on Communication (ICC’78), vol III, Toronto, ON, Canada, pp. 39.1.1–39.1.7 (1978)
Freeny S.L. (1980). TDM/FDM translation as an application of digital signal processing. IEEE Commun. Mag. 18(1): 5–15
Narasimha, M.J., Peterson, M.J.: Design and applications of uniform digital bandpass filter banks. Proceedings of the IEEE International Conference Acoustie Speech Signal Processing (ICASSP ’78), Tulsa, OK, 10–12, 1978, pp. 499–503
Ansari R. and Liu B. (1982). Transmultiplexer design using all-pass filters. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1569–1574
Fettweis A. (1982). Transmultiplexers with either analog conversion circuits, wave digital filters, or SC filters—a Review. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1575–1586
Gazsi L. (1982). DSP-based implementation of a transmultiplexer using wave digital filters. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1587–1597
Göckler H. and Scheuermann H. (1982). A modular approach to a digital 60-channel transmultiplexer using directional filters. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1598–1613
Molo F. (1982). Transmultiplexer realization with multistage filtering. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1614–1622
Del Re E. and Emiliani P.L. (1982). An analytic signal approach for transmultiplexers: theory and design. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1623–1628
Constantinides A.G. and Valenzuela R.A. (1982). An efficient and modular transmultiplexer design. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1629–1641
Cariolaro G.L., Cucchi S. and Molo F. (1982). Transmultiplexer via spread-spectrum modulation. IEEE Trans. Commun. (Special Issue on Transmultiplexers) COM-30(7): 1642–1655
Hirosaki B. (1980). An analysis of automatic equalizers for orthogonally multiplexed QAM systems. IEEE Trans Commun. COM-28(1): 73–83
Hirosaki B. (1981). An orthogonally multiplexed QAM system using the discrete fourier transform. IEEE Trans Commun. COM-29(7): 982–989
Hirosaki B., Hasegawa S. and Sabato A. (1986). Advanced groupband data modem using orthogonally multiplexed QAM technique. IEEE Trans. Commun. COM-34(6): 587–592
Sablatash, M., Lodge, J.H., McGee, W.F.: Equivalence between vestigial sideband (VSB) and offset quadrature phase shift (OQPSK) modulations and relationships to wavelet packet-based multiplexing. Proceedings of the 18th Biennial Symposium on Communication, Queen’s University, Kingston, June 2–5, 1996, pp. 339–342
Vetterli, M.: Analysis, synthesis and computational complexity of digital filter banks. Ph.D. Dissertation, Ecole Polytechnique Fédérale de Lausanne, Switzerland, No. 617, (1986)
Vetterli, M.: Perfect transmultiplexers. Proceedings of the IEEE International Conference Acoustics, Speech Signal Processing (ICASSP’86), vol. 4, Tokyo, Japan, April 7–11, 1986, pp. 48.9.1–48.9.4
Vetterli M. (1986). Filter banks allowing perfect reconstruction. Signal Process. 10(3): 219–244
Vetterli M. (1987). A theory of multirate filter banks. IEEE Trans. Acoust. Speech Signal Process. ASSP-35(3): 356–372
Koilpillai R.D., Nguyen T.Q. and Vaidyanathan P.P. (1991). Some results in the theory of cross-talk free transmultiplexers. IEEE Trans. Signal Process. 39(1): 2174–2183
Ramachandran R.P. and Kabal P. (1992). Bandwidth efficient transmultiplexers, Part 1: synthesis. IEEE Trans. Signal Process. 40(1): 70–84
Ramachandran R.P. and Kabal P. (1992). Bandwidth efficient transmultiplexers, Part 2: subband complements and performance aspects. IEEE Trans. Signal Process. 40(5): 1108–1121
Nussbaumer, H.J., Vetterli, M.: Computationally efficient QMF filter banks. Proceedings of the IEEE International Conference Acoustics, Speech, Signal Process. (ICASSP’84), Vol. I, San Diego, CA, March 19–21, pp. 11.3.1–11.3.4, (1984)
Akansu A.N., Duhamel P., Lin X. and Courville M. (1998). Orthogonal transmultiplexers in communication: a review. IEEE Trans. Signal Process. 46(4): 979–995
Sandberg S.D. and Tzannes M.A. (1995). Overlapped discrete multitone modulation for high speed copper wire communications. IEEE J. Selected Areas Commun. 13(9): 1571–1585
Sablatash, M., Lodge, J.H., McGee, W.F.: The design of filter banks with specified minimum stopband attenuation for wavelet packet-based multiple access communications. Proceedings of the 18th Biennial Symposium on Communication, Queen’s University, Kingston, pp. 53–56, (1996)
Mathieu, S., Fortier, P., Roy, S., Huynh, H.T.: Discrete wavelet modulation for wireless channels. Proceedings of the 21st Biennial Symposium on Communication, Queen’s University, Kingston, pp. 120–123, (2002)
Wu, J.: The wavelet packet division multiplexing system– theory, design and performance analyses, Ph.D. thesis, McMaster University, Hamilton, (1998)
Wickerhauser, M.V.: Adapted wavelet analysis from theory to software, A.K. Peters, Wellesley, Ch. 7, pp.237–271, (1994)
Fliege, N.J.: Multirate digital signal processing: multirate systems, filter banks, wavelets, wiley, Toronto, (1994)
Sablatash, M., McGee, W.F., Lodge, J.H.: Bandwidth-on-demand multiple access communications system design combining wavelet packet trees and DFT polyphase filter banks. Proceedings of the NJIT’97, A One-Day Symposium on Wavelet, Subband and Block Transforms in Communications, New Jersey Institute of Technology, Department of Electrical and Computer Engineering, Center for Communication and Signal Processing Research & New Jersey Center for Multimedia Research, Newark, 21 March, 13 pp, (1997)
Sablatash, M., Lodge, J.: Bandwidth-on-demand multiple access communications using wavelet packet-based and DFT polyphase filter banks. In: Kschischang, F.R., Khandani, A.K. (eds.) Proceedings of the 1997 Workshop on Inform. Theory, The Fields Institute for Research in the Mathematical Sciences, University of Toronto, Toronto, pp. 65–68, (1997)
Sablatash, M., McGee, W.F., Lodge, J.: Designs of prototype filters for calculation of polyphase components of DFT filter banks and simulation studies to evaluate the bit error rate performance of a multiplexer-demultiplexer filter bankTransmitter-receiver for downstream transmission with phase and timing errors at the receiver. In: Proceedings of the Wireless ’97, The 9th International Conference on Wireless Communication, vol. 1, Calgary, Alberta, pp. 222–241, (1997)
Sablatash, M., Lodge, J.: Theory and design of spectrum-efficient bandwidth-on-demand multiplexer demultiplexer pairs based on wavelet packet tree and polyphase filter banks. Proceedings of the 1998 International Conference on Acoustics, Speech Signal Processing (ICASSP’98), vol. 3, Seattle, pp. 1797–1800, (1998)
Sablatash, M., McGee, W.F., Lodge, J.: Spectrum-efficient bandwidth-on-demand multi-user transmission based on concatenation of filter bank trees and polyphase filters. Proceedings of the of the 19th Biennial Symposium on Communication, Queen’s University, Kingston, pp. 382–385, (1998)
Sablatash, M., Lodge, J.: Theory and design of an advanced multi-user bandwidth-on-demand mobile communication system using tree-structured and polyphase filter banks. Proceedings of the IMSC’99, The 6th International Mobile Satellite Conference, Ottawa, pp. 120–127, (1999)
Vetterli, M., Kovacevic, J.: Wavelets and subband coding, Prentice Hall, Englewood Cliffs, Ch. 3, pp. 133–135, (1995)
Sablatash, M., Lodge, J.: Advantages of using linear phase filters in a multi-user communication system based on filter bank trees. Proceedings of the 20th Biennial Symposium on Communication, Queen’s University, Kingston, May 28–31, pp. 47–51, (2000)
Sablatash, M., Lodge, J.: Design of a synchronization scheme for a bandwidth-on-demand multiplexer-demultiplexer pair based on wavelet packet tree filter banks. Proceedings of the 1999 International Conference on Acoustics, Speech, Signal Processing, (ICASSP’99), vol.4, Phoenix, pp. 2211–2214, (1999)
Sablatash, M., Lodge, J.: Wavelet packet based bandwidth-on-demand multi-user communication system: receiver simplification and synchronization scheme. Proceedings of the Wireless’99, The 11th International Conference on Wireless Communication, vol. 2, Calgary, July 12–14, pp. 366–383, (1999)
McGee, W.F., Sablatash, M., Lodge, J.: Pilot symbol synchronization for bandwidth-on-demand filter-tree communication systems. Proceedings of the 4th European Workshop on Mobile/ Personal Satellite Communication (EMPS 2000), London, September 18–21 pp. 44–52, (2000)
Zarowski, C.J.: Notes on orthogonal wavelets and wavelet packets. Report 1–95, Department of Electrical and Computer Engineering, Queen’s University, Kingston, (1995)
Learned, R.E., Krim, H., Claus, B., Willsky, A.S., Karl, W.C.: Wavelet-packet-based multiple access communication. Proceedings of the SPIE International Symposium on Optics, imaging and instrumentation-mathematical imaging wavelet applications in signal and image Processing, vol. 2303, San Diego, July 27–29 pp. 246–259, (1994)
Lindsey, A.R.: Generalized orthogonally multiplexed communication via wavelet packet basis, Ph.D. dissertation, Faculty of the Russ College of Engineering and Technology, Ohio University, Ohio (1995)
Lindsey A.R. (1997). Wavelet packet modulation for orthogonally multiplexed communications. IEEE Trans. Signal Process. 45(5): 1336–1339
Wu, J., Wong, K.M., Jin, Q.: Multiplexing based on wavelet packets. Proceedings of the SPIE International Symposium on AEROSENSE, Vol. 2491, Part I, Orlando, pp. 315–326, (1995)
Wong K.M., Wu J., Davidson T.N. and Jin Q. (1997). Wavelet packet division multiplexing and wavelet packet design under timing error effects. IEEE Transaction Signal Processing 45(12): 2877–2890
Sablatash, M., Lodge, J.H., Zarowski, C.J.: Theory and design of communication systems based on scaling functions, wavelets, wavelet packets and filter banks. Proceedings of the Wireless’96, The 8th International Conference on Wireless Communication, vol. 2, Calgary, pp. 640–659, (1996)
Lawton W. (1993). Applications of complex-valued wavelet transforms to subband decomposition. IEEE Trans. Signal Process. 41(12): 3566–3569
Sablatash, M., McGee, W.F., Lodge, J.: The performance of a spectrum-efficient multicarrier transmission system with phase and timing offsets. Proceedings of the Wireless’98, The 10th International Conference on Wireless Communication, vol. 1, Calgary, pp. 418–434, (1998)
Zarowski, C.J.: Notes on orthogonal wavelets and wavelet packets, Report (2nd edition), Department of Electrical and Computer Engineering, Queen’s University, Kingston, (1996)
Sablatash, M., Cooklev, T., Lodge, J.: Design and implementation of wavelet packet-based filter bank trees for multiple access communications. Proceedings of the IEEE International Conference on Communication (ICC’97), vol. 1, Montreal, pp. 176–180, (1997)
Sablatash, M., Lodge, J.: Turbo-coded and synchronized spectrum-efficient bandwidth-on-demand multi-user transmission system based on filter trees. Proceedings of the of the 20th Biennial Symposium on Communication, Queen’s University, Kingston, pp. 18–22, (2000)
Sablatash, M., Lodge, J.: Performance of turbo-coded and synchronized spectrum-efficient bandwidth-on demand multi-user out-bound transmission system based on trees of linear phase filters with almost perfect reconstruction. Proceedings of the Wireless 2000, The 12th International Conference on Wireless Communication, vol 1, Calgary, pp. 351–369, (2000)
LaSalle, R., Alard, M.: Principles of modulation and channel coding for digital broadcasting for mobile receivers. EBU Review-Tech. No. 224, pp. 168–190, (1987)
Daubechies, I.: Ten lectures on wavelets, CBMS-NSF regional conference series in applied mathematics No. 61, Society for Industrial and Applied Mathematics, Philadelphia, (1992)
Coifman, R.R., Wickerhauser, M.V.: Entropy-based algorithms for best basis selection. IEEE Trans. Inform Theory, Vol. IT-38, No. 2, Part II, pp. 713–718, (1992)
Siclet, C., Siohan, P.: Design of BFDM/OQAM systems based on biorthogonal modulated filter banks. Proceedings of the IEEE Globecom 2000, vol. 2, San Francisco, CA, November 27-December 1, pp. 701–705, (2000)
Siohan P., Siclet C. and Lacaille N. (2002). Analysis and design of OFDM/OQAM systems based on filter bank theory. IEEE Trans. Signal Process. 50(5): 1170–1183
Viholainen, A., Ihalainen, T., Renfors, M.: Performance of time-frequency localized and frequency selective filter banks in multicarrier systems. Proceedings of the 2006 IEEE International Symposium on Circuits and Systems (ISCAS 2006), Island of Kos, Greece, May 21–24, on CD-ROM, (2006)
Bölcskei H., Duhamel P. and Hleiss R. (2003). Orthogonalization of OFDM/OQAM pulse shaping filters using the zak transform. Signal Process. 83(7): 1379–1391
A cognitive PHY/MAC proposal for IEEE 802.22 WRAN systems, Nov. 7, 2005
A cognitive PHY/MAC proposal for IEEE 802.22 WRAN systems, Part 1: The cognitive PHY, Nov. 7, 2005
Author information
Authors and Affiliations
Corresponding author
Additional information
Financial support under Industry Canada’s Spectrum Research Funding is gratefully acknowledged.
Rights and permissions
About this article
Cite this article
Sablatash, M. Designs and architectures of filter bank trees for spectrally efficient multi-user communications: review, modifications and extensions of wavelet packet filter bank trees. SIViP 2, 9–37 (2008). https://doi.org/10.1007/s11760-007-0033-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-007-0033-4