Skip to main content
Log in

New method and circuit for processing of band-limited periodic signals

  • Original Paper
  • Published:
Signal, Image and Video Processing Aims and scope Submit manuscript

Abstract

The paper presents a reconstruction of analogue multi-harmonic signals, from a number of integrated values of input signals. Based on the value of the integral of the original input signal, with a known frequency spectrum but unknown amplitudes and phases, a reconstruction of its basic parameters is done by the means of derived analytical and summarized expressions. It is applied to signal reconstruction, spectral estimation, system identification, as well as in other important signal processing problems. The proposed method of processing can be used for precise RMS measurements (or power and energy) of periodic signal based on the presented signal reconstruction. Subsequent calculation of all relevant indicators related to the monitoring and processing of ac voltage and current signals is provided in this manner. The paper investigates the errors related to the signal parameter estimation, and there is a computer simulation that demonstrates the accuracy of these algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Proakis J.G., Manolakis D.G.: Digital Signal Processing: Principles, Algorithms, Applications. 3rd edn. Prentice-Hall, Englewood Cliffs, NJ (1996)

    Google Scholar 

  2. Prendergast R.S., Levy B.C., Hurst P.J.: Reconstruction of band-limited periodic nonuniformly sampled signals through multirate filter banks. IEEE Trans. Circ. Syst.-I 51(8), 1612–1622 (2004)

    Article  MathSciNet  Google Scholar 

  3. Marziliano P., Vetterli M., Blu T.: Sampling and exact reconstruction of bandlimited signals with additive shot noise. IEEE Trans. Inform. Theory 52(5), 2230–2233 (2006)

    Article  MathSciNet  Google Scholar 

  4. Margolis, E., Eldar, Y. C.: Reconstruction of nonuniformly sampled periodic signals: algorithms and stability analysis. Electronics, Circuits and Systems, 2004. ICECS 2004. Proceedings of the 2004 11th IEEE International Conference, 13–15 Dec 2004, pp. 555-558

  5. Sun W., Zhou X.: Reconstruction of band-limited signals from local averages. IEEE Trans. Inf. Theory 48(11), 2955–2963 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  6. Petrovic P., Marjanovic S., Stevanovic M.: Measuring of slowly changing AC signals without sample and hold circuit. IEEE Trans. Instrum. Meas. 49(6), 1245–1248 (2000)

    Article  Google Scholar 

  7. Petrovic P.: New digital multimeter for accurate measurement of synchronously sampled AC signals. IEEE Trans. Instrum. Meas. 53(3), 716–725 (2004)

    Article  MathSciNet  Google Scholar 

  8. Pejovic P., Saranovac L., Popovic M.: Comments on “new algorithm for measuring 50/60 Hz AC values based on the usage of slow A/D Converters” and “measuring of slowly changing AC signals without sample-and-hold circuit. IEEE Trans. Instrum. Meas. 52(5), 1688–1692 (2003)

    Article  Google Scholar 

  9. Muciek A.K.: A method for precise RMS measurements of periodic signals by reconstruction technique with correction. IEEE Trans. Instrum. Meas. 56(2), 513–516 (2007)

    Article  Google Scholar 

  10. Petrovic P., Stevanovic M.: A reply to comments on “new algorithm for measuring 50/60 Hz AC values based on the usage of slow A/D converters” and “measuring of slowly changing AC signals without sample-and-hold circuit. IEEE Trans. Instrum. Meas. 55(5), 1859–1862 (2006)

    Article  Google Scholar 

  11. Bos A.V.D.: Estimation of fourier coefficients. IEEE Trans. Instrum. Meas. 38(5), 1005–1007 (1989)

    Article  Google Scholar 

  12. Bos A.V.D.: Estimation of complex fourier coefficients. IEE Proc.-Control Theory Appl. 142(3), 253–256 (1995)

    Article  MATH  Google Scholar 

  13. Pintelon R., Schoukens J.: An improved sine-wave fitting procedure for characterizing data acquisition channels. IEEE Trans. Instrum. Meas. 45(2), 588–593 (1996)

    Article  MathSciNet  Google Scholar 

  14. Xiao Y., Tadokaro Y., Shida K.: Adaptive algorithm based on least mean p-power error criteterion for fourier analysis in additive noise. IEEE Trans. Signal Proc. 47(4), 1172–1181 (1999)

    Article  Google Scholar 

  15. Agrawal M, Prasad S, Roy S.C.D.: A simple solution for the analytic inversion of van der monde and confluent van der monde matrices. IETE J. Res. 47(5), 217–219 (2001)

    Google Scholar 

  16. Gohberg I., Olshevsky V.: The fast generalized parker-traub algorithm for inversion of van der monde and related matrices. J. Complexity 13(2), 208–234 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  17. Jog C.S.: On the explicit determination of the polar decomposition in n-dimensional vector spaces. J. Elast. 66(2), 159–169 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  18. Neagoe V.E.: Inversion of the van der monde matrix. IEEE Signal Processing Lett. 3(4), 119–120 (1996)

    Article  Google Scholar 

  19. Petrovic, P.: New approach to reconstruction of nonuniformly sampled AC signals. Proceedings of 2007 IEEE International Symposium on Industrial Electronics (ISIE 2007), Vigo, Spain, pp. 1693–1698 (2007)

  20. Seber G.: Linear Regression Analysis. Wiley, New York (1977)

    MATH  Google Scholar 

  21. Reeves S.J., Heck L.P.: Selection of observations in signal reconstruction. IEEE Trans. Signal Proc. 43(3), 788–791 (1995)

    Article  Google Scholar 

  22. So H.C., Chan K.W., Chan Y.T., Ho K.C.: Linear prediction approach for efficient frequency estimation of multiple real sinusoids: algorithms and analyses. IEEE Trans. Signal Proc. 53(7), 2290–2305 (2005)

    Article  MathSciNet  Google Scholar 

  23. Wu, B., Bodson, M.: Frequency estimation using multiple source and multiple harmonic components. American Control Conference, 2002. Proceedings of the 2002 1, pp. 21–22 (2002)

  24. Nigham N.J.: Accuracy and Stability of Numerical Algorithms. 2nd edn. SIAM, Philadelphia, PA (2002)

    Google Scholar 

  25. Feichtinger, H.G.: Reconstruction of band-limited signals from irregular samples, a short summary. 2nd International Workshop on Digital Image Processing and Computer Graphics with Applications, pp. 52–60 (1991)

  26. Cooklev T.: An efficient architecture for orthogonal wavlet transforms. IEEE Signal Proc. Lett. 13(2), 77–79 (2006)

    Article  Google Scholar 

  27. Schoukens J., Rolain Y., Simon G., Pintelon R.: Fully automated spectral analysis of periodic signals. IEEE Trans. Instrum. Meas. 52(4), 1021–1024 (2003)

    Article  Google Scholar 

  28. Reeves S.J.: An efficient implementation of the backward greedy algorithm for sparse signal reconstruction. IEEE Signal Proc. Lett. 6(10), 266–268 (1999)

    Article  Google Scholar 

  29. Daboczi T.: Uncertainty of signal reconstruction in the case of jitter and noisy measurements. IEEE Trans. Instrum. Meas. 47(5), 1062–1066 (1998)

    Article  Google Scholar 

  30. Wang G., Han W.: Minimum error bound of signal reconstruction. IEEE Signal Proc. Lett. 6(12), 309–311 (1999)

    Article  Google Scholar 

  31. Poberezhskiy Y.S., Poberezhskiy G.Y.: Sampling and signal reconstruction circuits performing internal antialiasing filtering and their influence on the design of digital receivers and transmitters. IEEE Trans. Circ. Sys.-I 51(1), 118–129 (2004)

    Article  Google Scholar 

  32. Hoseini H.Z., Kale I., Shoaei O.: Modeling of switched- capacitor delta-sigma modulators in SIMULINK. IEEE Trans. Instrum. Meas. 54(4), 1646–1654 (2005)

    Article  Google Scholar 

  33. Vendersteen G., Pintelon R.: Maximum likelihood estimator for jitter noise models. IEEE Trans. Instrum. Meas. 49(6), 1282–1284 (2000)

    Article  Google Scholar 

  34. Coakley K.J., Wang C.M., Hale P.D., Clement T.S.: Adaptive characterization of jitter noise in sampled high-speed signals. IEEE Trans. Instrum. Meas. 52(5), 1537–1547 (2003)

    Article  Google Scholar 

  35. Stenbakken, G.N., Deyst, J.P.: Timebase Distortion Measurements Using Multiphase Sinewaves. IEEE Instrum. Meas. Techn. Conf., Ottawa, Canada, May 1997, pp. 1003–1008 (1997)

  36. Hidalgo R.M., Fernandez J.G., Rivera R.R., Larrondo H.A.: A simple adjustable window algorithm to improve FFT measurements. IEEE Trans. Instrum. Meas. 51(1), 31–36 (2002)

    Article  Google Scholar 

  37. Tse, N.C.F., Lai, L.L.: Wavelet-based algorithm for signal analysis. EURASIP J. Adv. Signal Process., 2007, Article ID 38916, p. 10 (2007)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Predrag B. Petrović.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Petrović, P.B. New method and circuit for processing of band-limited periodic signals. SIViP 6, 109–123 (2012). https://doi.org/10.1007/s11760-010-0173-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11760-010-0173-9

Keywords

Navigation