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Sampling Rate Converters

  • Lars WanhammarEmail author
  • Tapio Saramäki
Chapter
  • 152 Downloads

Abstract

In this chapter, we discuss several efficient algorithms to change the sampling frequency, i.e., decimate or interpolate the sampling frequency, without significantly modifying the signal information. Such algorithms are used in multirate systems, where the sampling rate is changed during the signal processing. In many cases, multiple sampling frequencies are used to simplify and reduce the computational complexity and to achieve performances that are difficult by traditional approaches. This chapter contains 28 solved examples.

References

  1. 1.
    Bellanger, M.: Digital Processing of Signals, 3rd edn. Wiley, Chichester, England (2000)zbMATHGoogle Scholar
  2. 2.
    Crochiere, R.E., Rabiner, L.R.: Multirate Digital Signal Processing. Prentice-Hall, Englewood Cliffs, N.J. (1983)CrossRefGoogle Scholar
  3. 3.
    Fliege, N.J.: Multirate Digital Signal Processing. Wiley (1994)Google Scholar
  4. 4.
    Johansson, H., Wanhammar, L.: Design and implementation of multirate digital filters, Chapter 9. In: Jovanovic-Dolecek, G. (ed.) Multirate Systems: design and Applications. Idea Group Publ. Hersey, USA (2001)Google Scholar
  5. 5.
    Lim, J.E., Oppenheim, A.V. (eds.): Advanced Topics in Signal Processing. Prentice-Hall, Englewood Cliffs, N.J. (1988)zbMATHGoogle Scholar
  6. 6.
    Mitra, S.K., Kaiser, J.F. (eds.): Handbook for Digital Signal Processing. Wiley (1993)Google Scholar
  7. 7.
    Ramstad, A.T.: Digital two-rate IIR and hybrid IIR/FIR filters for sampling rate conversion. IEEE Trans. Commun. 30(7), 1466–1476 (1982)CrossRefGoogle Scholar
  8. 8.
    Ramstad, A.T.: Digital methods for conversion between arbitrary sampling frequencies. IEEE Trans. Acoust. Speech Signal Process. 32(3), 577–591 (1984)CrossRefGoogle Scholar
  9. 9.
    Candy, J.C., Temes, G.C.: Oversampling Delta-Sigma Data Converters: Theory, Design, and Simulation. IEEE Press (1992)Google Scholar
  10. 10.
    MATLAB: Signal Processing Toolbox. http://se.mathworks.com/help/signal/
  11. 11.
    Milić, L.: Multirate Filtering for Digital Signal Processing: MATLAB Applications. Information Science Reference (2009)Google Scholar
  12. 12.
    Mitra, S.K.: Digital Signal Processing, A Computer Based Approach. McGraw-Hill (2006)Google Scholar
  13. 13.
    Vaidyanathan, P.P.: Multirate Systems and Filter Banks. Prentice-Hall, Englewood Cliffs, N.J. (1993)zbMATHGoogle Scholar
  14. 14.
    Blad, A., Gustafsson, O.: Integer linear programming-based bit-level optimization for high-speed FIR decimation filter architectures. In: Circuits, Systems and Signal Processing—Special Issue, Low Power Digital Filters, p. 21 (2009)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Renfors, M., Saramäki, T.: Recursive Nth-band digital filters—part I: design and properties. IEEE Trans. Circ. Syst. 34(1), 24–39 (1987)CrossRefGoogle Scholar
  16. 16.
    Renfors, M., Saramäki, T.: Recursive Nth-band digital filters—Part II: design of multistage decimators and interpolators. IEEE Trans. Circ. Syst. 34(1), 40–51 (1987)CrossRefGoogle Scholar
  17. 17.
    Johansson, H., Wanhammar, L.: Filter structures composed of all pass and FIR filters for interpolation and decimation with factors of two. In: IEEE International Symposium on Circuits and Systems, ISCAS-98, vol. 5, pp. 45–48, Monterey, California, May 31–June 3 (1998)Google Scholar
  18. 18.
    Johansson, H., Wanhammar, L.: Filter structures composed of allpass and FIR filters for interpolation and decimation by a factor of two. IEEE Trans. Circ. Syst. Part II 6(7), 896–905 (1999)CrossRefGoogle Scholar
  19. 19.
    Lim, Y.C., Yang, R.: On the synthesis of very sharp decimators and interpolators using the frequency-response masking technique. IEEE Trans. Signal Process. 53(4), 1387–1397 (2005)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Saramäki, T.: Multirate signal processing. Lecture notes for a graduate course, the Institute of Signal Processing. Tampere University of Technology, Finland (2001). http://www.cs.tut.fi/~ts/
  21. 21.
    Johansson H.: A class of Mth-band linear-phase FIR filters using the frequency-response masking approach. In: IEEE Nordic Signal Processing Symposium on NORSIG-02, On board Hurtigruten from Tromsö to Trondheim, Norway, 4–7 Oct 2002Google Scholar
  22. 22.
    Johansson, H., Gustafsson O.: Mth-band linear-phase FIR filter interpolators and decimators utilizing the Farrow structure. In: IEEE International Symposium on Circuits Systems, pp. 129–132, Vancouver, Canada, 23–26 May 2004Google Scholar
  23. 23.
    Johansson, H., Gustafsson, O.: Linear-phase FIR interpolation, decimation, and Mth-band filters utilizing the Farrow structure. IEEE Trans. Circuits Syst. Part I 52(10), 2197–2207 (2005)CrossRefGoogle Scholar
  24. 24.
    Gustafsson, O., Johansson, H.: Complexity comparison of linear-phase Mth-band and general FIR filters. In: IEEE International Symposium on Circuits and Systems, pp. 2335–2338, New Orleans, LA, 27–30 May 2007Google Scholar
  25. 25.
    Saramäki, T., Neuvo, Y.: A class of FIR Nyquist (Mth-band) filters with zero intersymbol interference. IEEE Trans. Circuits Syst. 34(10), 1182–1190 (1987)CrossRefGoogle Scholar
  26. 26.
    Mintzer, F.: On halfband, third-band, and Nth-band FIR filters and their design. IEEE Trans. Acoust. Speech Signal Process. 30(5), 734–738 (1982)CrossRefGoogle Scholar
  27. 27.
    Gustafsson, O., Johansson, K., Johansson, H., Wanhammar, L.: Implementation of polyphase decomposed FIR filters for interpolation and decimation using multiple constant multiplication techniques. In: Asia-Pacific Conference on Circuits and Systems, pp. 924–927, Singapore, 4–7 Dec 2006Google Scholar
  28. 28.
    Maeng, S.J., Lee, B.G.: A design of linear-phased IIR Nyquist filters. IEEE Trans. Sel. Areas Commun. 13(1), 167–175 (1995)CrossRefGoogle Scholar
  29. 29.
    Yli-Kaakinen, J., Saramäki, T.: A systematic algorithm for designing multiplierless computationally efficient recursive decimators and interpolators. In: Proceedings of the International Symposium on Image and Signal Processing and Analysis, pp. 167–172 (2005)Google Scholar
  30. 30.
    Renfors, M., Saramäki, T.: A class of approximately linear phase digital filters composed of allpass subfilters. In: IEEE International Symposium on Circuits and Systems, ISCAS-86, pp. 678–681, San Jose, CA (1986)Google Scholar
  31. 31.
    Saramäki, T., Renfors, M.: A novel approach for the design of IIR filters as a tapped cascaded interconnection of identical allpass subfilters. In: IEEE International Symposium on Circuits and Systems, ISCAS-87, vol. 2, pp. 629–632, Philadelphia, 4–7 May 1987Google Scholar
  32. 32.
    Johansson, H., Palmkvist, K., Vesterbacka, M., Wanhammar, L.: High-speed lattice wave digital filters for interpolation and decimation. In: National Conference on Radio Science and Communication, RVK-96, pp. 543–547, Luleå, Sweden, 3–6 June 1996Google Scholar
  33. 33.
    Ohlsson, H., Johansson, H., Wanhammar, L.: Implementation of a combined interpolator and decimator for an OFDM system demonstrator. IEEE NorChip Conference, Turku, Finland, pp. 47–52, 6–7 Nov 2000Google Scholar
  34. 34.
    Johansson, H., Wanhammar, L.: Digital Hilbert transformers composed of identical allpass subfilters. In: IEEE International Symposium on Circuits and Systems, vol. 5, pp. 437–440, ISCAS-98, Monterey, California, May 31–June 3 1998Google Scholar
  35. 35.
    Elliott, D.F. (ed.): Handbook of Digital Signal Processing, Engineering Applications. Academic Press (1988)Google Scholar
  36. 36.
    Johansson, H., Wanhammar, L.: High-speed recursive filter structures composed of identical allpass subfilters for interpolation, decimation, and QMF banks with perfect magnitude reconstruction. IEEE Trans. Circuits Syst. Part II 6(1), 16–28 (1999)CrossRefGoogle Scholar
  37. 37.
    Saramäki, T., Neuvo, Y.: An implicit solution for IIR filters with equiripple group delay. IEEE Trans. Circuits Syst. 32(5), 476–478 (1985)CrossRefGoogle Scholar
  38. 38.
    Jovanović-Dolećek, G., Mitra, S.K.: CIC filter for rational sample rate conversion. In: Proceedings of the 2006 IEEE Asia Pacific Conference on Circuits and Systems—APCCAS, pp. 918–921 (2006)Google Scholar
  39. 39.
    Saramäki, T., Mitra, S.K.: Multiple branch FIR filters for sample rate conversions. In: IEEE International Symposium on Circuits and Systems, ISCAS-92, pp. 1007–1010, San Diego, California (1992)Google Scholar
  40. 40.
    Johansson, H., Wanhammar, L.: Two-stage polyphase interpolators and decimators for sample rate conversions with prime numbers. In: VIII European Signal Processing Conference on EUSIPCO-96, vol. II, pp. 1207–1210, Trieste, Italy, 10–13 Sept 1996Google Scholar
  41. 41.
    Johansson, H.: High-Speed Recursive Digital Filters, Linköping Studies in Science and Technology, Thesis No. 620. Linköping University, Sweden (1997)Google Scholar
  42. 42.
    Johansson, H., Göckler, H.: Two-stage-based polyphase structures for arbitrary-integer sample rate conversion. IEEE Trans. Circuits Syst. Part II 62(5), 486–492 (2015)CrossRefGoogle Scholar
  43. 43.
    Saramäki, T.: A class of linear-phase FIR filters for decimation, interpolation, and narrow-band filtering. IEEE Trans. Acoust. Speech Signal Process. 32(5), 1023–1036 (1984)CrossRefGoogle Scholar
  44. 44.
    Hogenauer, E.B.: An economical class of digital filters for decimation and interpolation. IEEE Trans. Acoust. Speech Signal Process. 29, 155–162 (1981)CrossRefGoogle Scholar
  45. 45.
    Abbas, M., Gustafsson, O., Wanhammar, L.: Power estimation of recursive and non-recursive CIC filters implemented in deep-submicron technology, pp. 21–23. IEEE International Conference on Green Circuits Systems, Shanghai, China (2010)Google Scholar
  46. 46.
    Meher, P.K., Stouraitis, T., Chang, C.-H., Gustafsson, O., Vinod, A.-P., Faust, M. (eds.): Shift-Add Circuits for Multiplications, Chapter 2 in Arithmetic Circuits for DSP Applications. Wiley-IEEE Press (2017)Google Scholar
  47. 47.
    Jovanović-Dolećek, G., Mitra, S.K.: A new two-stage sharpened comb decimator. IEEE Trans. Circuits Syst. Part I 52(7), 1414–1420 (2005)MathSciNetCrossRefGoogle Scholar
  48. 48.
    Martin, U., Schüssler, W.: On digital systems with negative group delay. Frequenz 47, 106–113 (1993)CrossRefGoogle Scholar
  49. 49.
    Johansson, H., Wanhammar, L.: High-speed recursive digital filters based on the frequency-response masking approach. IEEE Trans. Circuits Syst. Part II 47(1), 48–61 (2000)CrossRefGoogle Scholar
  50. 50.
    Lim, Y.C.: Frequency-response masking approach for the synthesis of sharp linear phase digital filters. IEEE Trans. Circuits Syst. 33(4), 357–364 (1986)CrossRefGoogle Scholar
  51. 51.
    Aboushady, H., Dumonteix, Y., Louerat, M.M., Mehrez, H.: Efficient polyphase decomposition of comb decimator filters in ΣΔ analog-to-digital converters. IEEE Trans. Circuits Syst-II 48(10), 898–903 (2001)CrossRefGoogle Scholar
  52. 52.
    Jovanović-Dolećek, G.: Low power sharpened comb decimation filter, (Invited paper). IEEE Conference on ICGCS 2010, pp. AM2-R6-1-4, Shangai, China (2010)Google Scholar
  53. 53.
    Mondal, K., Mitra, S.: Non-recursive decimation filters with arbitrary integer decimation factors. IET Circuits Devices Syst. 1–11 (2012)Google Scholar
  54. 54.
    Candan, C.: An efficient filtering structure for Lagrange interpolation. IEEE Signal Process. Lett. 14(1), 17–19 (2007)MathSciNetCrossRefGoogle Scholar
  55. 55.
    Schüssler, H.W., Dehner, G., Rabenstein, R., Steffen, P.: Digitale Signalverarbeitung, vol. 2. Springer (2009) (In German)Google Scholar
  56. 56.
    Oetken, G., Parks, T.W., Schüβler, H.W.: New results in the design of digital interpolators. IEEE Trans. Acoust. Speech Signal Process. 27(6), 637–643 (1979)CrossRefGoogle Scholar
  57. 57.
    Vesma, J., Saramäki, T.: Optimization and efficient implementation of FIR filters with adjustable fractional delay. In: IEEE International Symposium on Circuits Systems, vol. IV, pp. 2256–2259, Hong Kong, 9–12 June 1997Google Scholar
  58. 58.
    Farrow, C.W.: A continuously variable delay element. In: IEEE International Symposium on Circuits, Systems, vol. 3, pp. 2641–2645, Espoo, Finland, 7–9 June 1988Google Scholar
  59. 59.
    Deng, T.-B.: Symmetric structures for odd-order maximally flat and weighted-least-squares variable fractional-delay filters. IEEE Trans. Circuits Syst. Part I 54(12), 2718–2732 (2007)CrossRefGoogle Scholar
  60. 60.
    Deng, T.-B.: Hybrid structures for low-complexity variable fractional delay filters. IEEE Trans. Circuits Syst. Part I 57(4), 897–910 (2010)MathSciNetCrossRefGoogle Scholar
  61. 61.
    Diaz-Carmona, J., Jovanovic-Dolecek, J.: Frequency-based optimization design for fractional delay FIR filters with software-defined radio applications. Int. J. Digit. Multimed. Broadcast. 53(6), 1–6 (2010)Google Scholar
  62. 62.
    Hermanowicz, E.: On designing a wideband fractional delay filter using the Farrow approach. In: Proceedings of XII European Signal Processing Conference, pp. 961–964. Vienna, Austria, 6–10 Sept 2004Google Scholar
  63. 63.
    Hermanowicz, E., Johansson, H.: On designing minimax adjustable wide band fractional delay FIR filters using two-rate approach. In: Proceedings of European Conference Circuit Theory Design, vol. 3, pp. 437–440, Cork, Ireland, Aug 29–Sept 1 2005Google Scholar
  64. 64.
    Johansson, H., Gustafsson, O., Johansson, K., Wanhammar, L.: Adjustable fractional-delay FIR filters using the Farrow structure and multirate techniques. In: Proceedings of IEEE Asia Pacific Conference Circuits Systems, pp. 1055–1058, Singapore, 4–7 Dec 2006Google Scholar
  65. 65.
    Johansson, H., Löwenborg, P.: On the design of adjustable fractional delay FIR filters. IEEE Trans. Circuits Syst. Part II 50(4), 164–169 (2003)CrossRefGoogle Scholar
  66. 66.
    Jovanović-Dolećek, G., Diaz-Carmona, J.: One structure for wide-bandwidth and high-resolution fractional delay filter. Proceedings of the IEEE International Conference on Electronics Circuits Systems 3, 485–486 (2002)Google Scholar
  67. 67.
    Yli-Kaakinen, J., Saramäki, T.: Multiplication-free polynomial-based FIR filters with an adjustable fractional delay. Circuits, Syst. Signal Process. 25(2), 265–294 (2006)CrossRefGoogle Scholar
  68. 68.
    Yli-Kaakinen, J., Saramäki, T.: A simplified structure for FIR filters with an adjustable fractional delay. In: Proceedings of IEEE International Symposium Circuits System, pp. 3439–3442, New Orleans, USA, 27–30 May 2007Google Scholar
  69. 69.
    Laakso, T.I., Välimäki, V., Karjalainen, M., Laine, U.K.: Splitting the unit delay. IEEE Signal Process Mag. 30–60 (1996). http://legacy.spa.aalto.fi/software/fdtools/
  70. 70.
    Thiran, J.-P.: Recursive digital filters with maximally flat group delay. IEEE Trans. Circuit Theory 18(6), 659–664 (1971)MathSciNetCrossRefGoogle Scholar
  71. 71.
    Johansson, H., Löwenborg, P.: Linear programming design of linear-phase FIR filters with variable bandwidth. In: Proceedings of IEEE Symposium Circuits and Systems, vol. 3, pp. 554–557, Bangkok, Thailand (2003)Google Scholar
  72. 72.
    Löwenborg, P., Johansson, H.: Minimax design of linear-phase FIR filters with adjustable bandwidths. In: IEEE International Symposium Circuits and Systems, vol. 3, pp. 657–660, Vancouver, Canada (2004)Google Scholar
  73. 73.
    Löwenborg, P., Johansson, H.: Minimax design of adjustable-bandwidth linear-phase FIR filters. IEEE Trans. Circuits Syst. Part I 53(2), 431–439 (2006)CrossRefGoogle Scholar
  74. 74.
    Abbas, M., Gustafsson, O., Johansson, H.: On the fixed-point implementation of fractional-delay filters based on the farrow structure. IEEE Trans. Circuits Syst. 60(4), 926–937 (2013)MathSciNetCrossRefGoogle Scholar
  75. 75.
    Olsson, M., Löwenborg, P., Johansson, H.: Scaling and round-off noise in multistage interpolators and decimators. In: Proceedings Fourth International Workshop Spectral Methods Multirate Signal Processing. Vienna, Austria (2004)Google Scholar
  76. 76.
    Olsson, M., Löwenborg, P., Johansson, H.: Scaling of multistage interpolators. In: Proceedings XIV European Signal Processing Conference. EUSIPCO’04Google Scholar

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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Linköping UniversityLinköpingSweden
  2. 2.Tampere University of TechnologyTampereFinland

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