Circuits, Systems, and Signal Processing

, Volume 31, Issue 3, pp 961–985 | Cite as

A Class of Multimode Transmultiplexers Based on the Farrow Structure



This paper introduces multimode transmultiplexers (TMUXs) in which the Farrow structure realizes the polyphase components of general lowpass interpolation/decimation filters. As various lowpass filters are obtained by one set of common Farrow subfilters, only one offline filter design enables us to cover different integer sampling rate conversion (SRC) ratios. A model of general rational SRC is also constructed where the same fixed subfilters perform rational SRC. These two SRC schemes are then used to construct multimode TMUXs. Efficient implementation structures are introduced and different filter design techniques such as minimax and least-squares (LS) are discussed. By means of simulation results, it is shown that the performance of the transmultiplexer (TMUX) depends on the ripples of the filters. With the error vector magnitude (EVM) as the performance metric, the LS method has a superiority over the minimax approach.


Multistandard communications Transmultiplexers Sampling rate conversion Farrow structure 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    B. Arbesser-Rastburg et al., R&D directions for next generation broadband multimedia systems: an ESA perspective, in AIAA Int. Commun. Satellite Syst. Conf. Exhibit (2002) Google Scholar
  2. 2.
    D. Babic et al., Implementation of the transposed Farrow structure, in IEEE Int. Symp. Circuits Syst. (2002), pp. 5–8 Google Scholar
  3. 3.
    F.D. Beaulieu et al., Design of prototype filters for perfect reconstruction DFT filter bank transceivers. Signal Process. 89(1), 87–98 (2009) MATHCrossRefGoogle Scholar
  4. 4.
    M. Bellanger, On computational complexity in digital filters, in Eur. Conf. Circuit Theory Design (1981), pp. 58–63 Google Scholar
  5. 5.
    S.C. Chan et al., Design and complexity optimization of a new digital IF for software radio receivers with prescribed output accuracy. IEEE Trans. Circuits Syst. II 54(2), 351–366 (2007) CrossRefGoogle Scholar
  6. 6.
    A. Eghbali et al., An arbitrary bandwidth transmultiplexer and its application to flexible frequency-band reallocation networks, in Eur. Conf. Circuit Theory Design (2007), pp. 248–251 CrossRefGoogle Scholar
  7. 7.
    A. Eghbali et al., Reconfigurable nonuniform transmultiplexers using uniform modulated filter banks. IEEE Trans. Circuits Syst. I 58(3), 539–547 (2011) MathSciNetCrossRefGoogle Scholar
  8. 8.
    A. Eghbali et al., A multimode transmultiplexer structure. IEEE Trans. Circuits Syst. II 55(3), 279–283 (2008) CrossRefGoogle Scholar
  9. 9.
    A. Eghbali, Contributions to flexible multirate digital signal processing structures. Licentiate Thesis, Linköping University, Sweden (2009). ISBN:978-91-7393-678-1 Google Scholar
  10. 10.
    A. Eghbali et al., On the filter design for a class of multimode transmultiplexers, in IEEE Int. Symp. Circuits Syst. (2009), pp. 89–92 CrossRefGoogle Scholar
  11. 11.
    A. Eghbali et al., A Farrow-structure-based multi-mode transmultiplexer, in IEEE Int. Symp. Circuits Syst. (2008), pp. 3114–3117 Google Scholar
  12. 12.
    H. Elwan et al., A new generation of global wireless compatibility. IEEE Circuits Devices Mag. 17(1), 7–19 (2001) CrossRefGoogle Scholar
  13. 13.
    B. Evans et al., Integration of satellite and terrestrial systems in future multimedia communications. IEEE Wirel. Commun. Mag. 12(5), 72–80 (2005) CrossRefGoogle Scholar
  14. 14.
    C.W. Farrow, A continuously variable digital delay element, in IEEE Int. Symp. Circuits Syst. (1988), pp. 2641–2645 Google Scholar
  15. 15.
    H.G. Göckler et al., Tree-structured MIMO FIR filter banks for flexible frequency reallocation, in Int. Symp. Image Signal Processing Anal. (2007) Google Scholar
  16. 16.
    C.Y.-F. Ho et al., Optimal design of nonuniform FIR transmultiplexer using semi-infinite programming. IEEE Trans. Signal Process. 53(7), 2598–2603 (2005) MathSciNetCrossRefGoogle Scholar
  17. 17.
    T. Hentschel et al., Sample rate conversion for software radio. IEEE Commun. Mag. 38(8), 142–150 (2000) CrossRefGoogle Scholar
  18. 18.
    T. Ihalainen et al., Generation of filter bank-based multicarrier waveform using partial synthesis and time domain interpolation. IEEE Trans. Circuits Syst. I 57(7), 1767–1778 (2010) MathSciNetCrossRefGoogle Scholar
  19. 19.
    H. Johansson et al., Linear-phase FIR interpolation, decimation, and M-th band filters utilizing the Farrow structure. IEEE Trans. Circuits Syst. I 52(10), 2197–2207 (2005) CrossRefGoogle Scholar
  20. 20.
    H. Johansson et al., On the design of adjustable fractional delay FIR filters. IEEE Trans. Circuits Syst. II 50(4), 164–169 (2003) MathSciNetCrossRefGoogle Scholar
  21. 21.
    H. Johansson, Farrow-structure-based reconfigurable bandpass linear-phase FIR filters for integer sampling rate conversion. IEEE Trans. Circuits Syst. II 58(1), 46–50 (2011) CrossRefGoogle Scholar
  22. 22.
    J.F. Kaiser, Nonrecursive digital filter design using I 0-sinh window function, in IEEE Int. Symp. Circuits Syst. (1974), pp. 20–23 Google Scholar
  23. 23.
    J. Kovac̆ević et al., Perfect reconstruction filter banks with rational sampling factors. IEEE Trans. Signal Process. 41(6), 2047–2066 (1993) CrossRefGoogle Scholar
  24. 24.
    J. Li et al., A simple design method for near-perfect-reconstruction nonuniform filter banks. IEEE Trans. Signal Process. 45(8), 2105–2109 (1997) CrossRefGoogle Scholar
  25. 25.
    T.I. Laakso et al., Splitting the unit delay–tools for fractional delay filter design. IEEE Signal Process. Mag. 13(1), 30–36 (1996) CrossRefGoogle Scholar
  26. 26.
    T. Liu et al., Design of multichannel nonuniform transmultiplexers using general building blocks. IEEE Trans. Signal Process. 49(1), 91–99 (2001) CrossRefGoogle Scholar
  27. 27.
    R. Mahesh et al., Filter bank channelizers for multi-standard software defined radio receivers. J. Signal Process. Syst. (2008). doi: 10.1007/s11265-008-0327-y Google Scholar
  28. 28.
    S.K. Mitra, Digital Signal Processing: A Computer Based Approach (McGraw-Hill, New York, 2006) Google Scholar
  29. 29.
    J. Princen, The design of nonuniform modulated filter banks, in IEEE Int. Symp. Time-Frequency Time-Scale Anal. (1994), pp. 112–115 CrossRefGoogle Scholar
  30. 30.
    C.K.S. Pun et al., On the design and efficient implementation of the Farrow structure. IEEE Signal Process. Lett. 10(7), 189–192 (2003) CrossRefGoogle Scholar
  31. 31.
    Y. Shi et al., 2-norm based recursive design of transmultiplexers with designable filter length. Circuits Syst. Signal Process. 25(4), 447–462 (2006) MATHCrossRefGoogle Scholar
  32. 32.
    W.H.W. Tuttlebee, Software-defined radio: facets of a developing technology. IEEE Pers. Commun. Mag. 6(2), 38–44 (1999) CrossRefGoogle Scholar
  33. 33.
    J. Vesma et al., Interpolation filters with arbitrary frequency response for all-digital receivers, in IEEE Int. Symp. Circuits Syst. (1996) Google Scholar
  34. 34.
    P.P. Vaidyanathan et al., Transmultiplexers as precoders in modern digital communications: a tutorial review, in IEEE Int. Symp. Circuits Syst. (2004), pp. 405–412 Google Scholar
  35. 35.
    P.P. Vaidyanathan, Multirate Systems and Filter Banks (Prentice-Hall, Englewood Cliffs, 1993) MATHGoogle Scholar
  36. 36.
    A.K. Wang et al., EVM simulation and analysis techniques, in IEEE Military Commun. Conf. (2006), pp. 1–7 Google Scholar
  37. 37.
    X.M. Xie et al., Design of linear-phase recombination nonuniform filter banks. IEEE Trans. Signal Process. 54(7), 2809–2814 (2006) CrossRefGoogle Scholar
  38. 38.
    X.M. Xie et al., A simple design method of linear-phase nonuniform filter banks with integer decimation factors, in IEEE Int. Midwest Symp. Circuits Syst. (2005), pp. 7–10 Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Amir Eghbali
    • 1
  • Håkan Johansson
    • 1
  • Per Löwenborg
    • 2
  1. 1.Division of Electronics Systems, Department of Electrical EngineeringLinköping UniversityLinköpingSweden
  2. 2.Signal Processing Devices ABLinköpingSweden

Personalised recommendations