Skip to content


  • Research Article
  • Open Access

Generalized Sampling Theorem for Bandpass Signals

EURASIP Journal on Advances in Signal Processing20062006:059587

  • Received: 29 September 2005
  • Accepted: 26 February 2006
  • Published:


The reconstruction of an unknown continuously defined function from the samples of the responses of linear time-invariant (LTI) systems sampled by the th Nyquist rate is the aim of the generalized sampling. Papoulis (1977) provided an elegant solution for the case where is a band-limited function with finite energy and the sampling rate is equal to 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

Authors’ Affiliations

Department of Radio Electronics, Brno University of Technology, Purkynova 118, Brno, 612 00, Czech Republic


  1. Kohlenberg A: Exact interpolation of band-limited functions. Journal of Applied Physics 1953, 24(12):1432–1436. 10.1063/1.1721195MathSciNetView ArticleGoogle Scholar
  2. Linden DA: A discussion of sampling theorems. Proceedings of the IRE 1959, 47: 1219–1226.View ArticleGoogle Scholar
  3. Coulson AJ: A generalization of nonuniform bandpass sampling. IEEE Transactions on Signal Processing 1995, 43(3):694–704. 10.1109/78.370623View ArticleGoogle Scholar
  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. 10.1109/82.664240View ArticleGoogle Scholar
  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. 10.1109/78.869037MathSciNetView ArticleGoogle Scholar
  6. Linden DA, Abramson NM: A generalization of the sampling theorem. Information and Control 1960, 3(1):26–31. 10.1016/S0019-9958(60)90242-4MathSciNetView ArticleGoogle Scholar
  7. Papoulis A: Generalized sampling expansion. IEEE Transactions on Circuits and Systems 1977, 24(11):652–654. 10.1109/TCS.1977.1084284MathSciNetView ArticleGoogle Scholar
  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.1981.1084954MathSciNetView ArticleGoogle Scholar
  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. Meyer CD: Matrix Analysis and Applied Linear Algebra. SIAM, Philadelphia, Pa, USA; 2000.View ArticleGoogle Scholar


© Prokes 2006