Generalized Sampling Theorem for Bandpass Signals

  • Ales ProkesEmail author
Open Access
Research Article


The reconstruction of an unknown continuously defined function Open image in new window from the samples of the responses of Open image in new window linear time-invariant (LTI) systems sampled by the Open image in new window th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where Open image in new window is a band-limited function with finite energy and the sampling rate is equal to Open image in new window times cutoff frequency. In this paper, the scope of the Papoulis theory is extended to the case of bandpass signals. In the first part, a generalized sampling theorem (GST) for bandpass signals is presented. The second part deals with utilizing this theorem for signal recovery from nonuniform samples, and an efficient way of computing images of reconstructing functions for signal recovery is discussed.


Information Technology Sampling Rate Quantum Information Generalize Sampling Signal Recovery 


  1. 1.
    Kohlenberg A: Exact interpolation of band-limited functions. Journal of Applied Physics 1953, 24(12):1432–1436. 10.1063/1.1721195MathSciNetCrossRefGoogle Scholar
  2. 2.
    Linden DA: A discussion of sampling theorems. Proceedings of the IRE 1959, 47: 1219–1226.CrossRefGoogle Scholar
  3. 3.
    Coulson AJ: A generalization of nonuniform bandpass sampling. IEEE Transactions on Signal Processing 1995, 43(3):694–704. 10.1109/78.370623CrossRefGoogle Scholar
  4. 4.
    Lin Y-P, Vaidyanathan PP: Periodically nonuniform sampling of bandpass signals. IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing 1998, 45(3):340–351. 10.1109/82.664240CrossRefGoogle Scholar
  5. 5.
    Eldar YC, Oppenheim AV: Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples. IEEE Transactions on Signal Processing 2000, 48(10):2864–2875. 10.1109/78.869037MathSciNetCrossRefGoogle Scholar
  6. 6.
    Linden DA, Abramson NM: A generalization of the sampling theorem. Information and Control 1960, 3(1):26–31. 10.1016/S0019-9958(60)90242-4MathSciNetCrossRefGoogle Scholar
  7. 7.
    Papoulis A: Generalized sampling expansion. IEEE Transactions on Circuits and Systems 1977, 24(11):652–654. 10.1109/TCS.1977.1084284MathSciNetCrossRefGoogle Scholar
  8. 8.
    Brown J Jr.: Multi-channel sampling of low-pass signals. IEEE Transactions on Circuits and Systems 1981, 28(2):101–106. 10.1109/TCS.1981.1084954MathSciNetCrossRefGoogle Scholar
  9. 9.
    Prokeš A: Parameters determining character of signal spectrum by higher order sampling. Proceedings of the 8th International Czech-Slovak Scientific Conference (Radioelektronika '98), June 1998, Brno, Czech Republic 2: 376–379.Google Scholar
  10. 10.
    Meyer CD: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia, Pa, USA; 2000.CrossRefGoogle Scholar

Copyright information

© Prokes 2006

Authors and Affiliations

  1. 1.Department of Radio ElectronicsBrno University of TechnologyBrnoCzech Republic

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