Skip to main content
SpringerLink
Log in

Spectra of data sampled at frequency-modulated rates in application to cardiovascular signals: Part 2 evaluation of Fourier transform algorithms

  • Signal Processing
  • Published:
Medical & Biological Engineering & Computing Aims and scope Submit manuscript

Abstract

For three direct Fourier transform algorithms we quantified the influence of pulse frequency modulation (PFM) on the spectral estimation of pulse amplitude modulation (PAM). The simulation study is based on sinusoid functions sampled according to a pulse sequence which is the output of an integral pulse frequency modulator (IPFM). One algorithm exactly reproduces the theoretical spectrum derived in Part 1. The other two, including the classical FFT, scale all PFM-induced components in a different way, and in addition, generate higher modulating frequency harmonics. For a PFM depth below 30%, the sum of spurious PFM components is almost linearly dependent on this modulation depth, for all three algorithms. Dividing the effect of PFM in a ‘harmonic’ and ‘aliasing’ distortion, we found that the FFT has a relatively high harmonic distortion, compared to an algorithm that takes into account the non-uniform character of the data. In the cardiovascular (worst) case of 30% modulation in heart rate (PFM) at a frequency of 0.1 Hz, the FFT spectrum of beat-to-beat systolic blood pressure variations contains approximately 20% of spurious components caused solely by the modulation in time occurrences of the blood pressure samples. The ‘non-uniform’ algorithm performs twice as well in this case.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Bayly, E. J. (1968): ‘Spectral analysis of pulse frequency modulation in the nervous systems,’IEEE Trans.,BME-15, pp. 257–265

    Google Scholar 

  • Berger, R. D., Akselrod, S., Gordon, D., andCohen, R. J. (1986): ‘An efficient algorithm for spectral analysis of heart rate variability,’IEEE Trans.,BME-33, pp. 900–904

    Google Scholar 

  • Brigham, E. O. (1988): ‘The fast Fourier transform and its applications’ (Prentice-Hall International)

  • DeBoer, R. W., Karemaker, J. M., andStrackee, J. (1984): ‘Comparing spectra of a series of point events particularly for heart rate variability data,’IEEE Trans.,BME-31, pp. 384–387

    Google Scholar 

  • DeBoer, R. W., andKaremaker, J. M. (1985): ‘Relationships between short-term blood-pressure fluctuations and heart-rate variability in resting subjects I: a spectral analysis approach,’Med. Biol. Eng. Comput.,23, pp. 352–358

    Article  Google Scholar 

  • Gaster, M., andRoberts, J. B. (1977): ‘The spectral analysis of randomly sampled records by a direct transform,’Proc. R. Soc. Lond.,354, pp. 27–58

    Article  MathSciNet  Google Scholar 

  • Kay, S. M., andMarple, S. L. (1981): ‘Spectrum analysis—a modern perspective,’Proc. IEEE,5, pp. 289–310

    Google Scholar 

  • Lanting, P., Faes, Th. J. C., Heimans, J. J., TenVoorde, B. J., Nauta, J., andRompelman, O. (1990): ‘Spectral analysis of spontaneous heart rate variation in diabetic and control subjects,’Diabetic Med.,7, pp. 705–710

    Article  Google Scholar 

  • Pagani, M., Lombardi, F., Guzetti, S., Rimoldi, O., Furlan, R., Pizzinelli, P., Sandrone, G., Malfatto, G., Dell’Orto, S., Picculagu, E., Turiel, M., Baselli, G., Cerutti, S., andMalliani, A. (1986): ‘Power spectral analysis of heart rate and arterial pressure variabilities as a marker of sympatho-vagal interaction in man and conscious dogs,’Circ. Res.,59, pp. 178–193

    Google Scholar 

  • Pomeranz, B., Macaulay, R. J. B., Caudill, M. A., Kutz, I., Adam, D., Gordon, D., Kilborn, K. M., Barger, A. C., Shannon, D. C., Cohen, R. J., andBenson, H. (1985): ‘Assessment of autonomic function humans,’Am. J. Physiol. (Heart Circ. Physiol. 17),248, pp. H151-H153

    Google Scholar 

  • Rompelman, O., Snijders, J. B. I. M., andVan Spronsen, C. J. (1982): ‘The measurement of heart rate variability spectra with the help of a personal computer,’IEEE Trans.,BME-29, pp. 503–510

    Google Scholar 

  • Rompelman, O. (1986): ‘Tutorial review on processing the cardiac event series: a signal analysis approach,’Automedica,7, pp. 191–212

    Google Scholar 

  • TenVoorde, B. J., Faes, Th. J. C., andRompelman, O. (1994): ‘Spectra of data sampled at pulse modulated rates in application to cardiovascular signals: Part I analytical derivation of the spectra,’Med. Biol. Eng. Comput.,32, 63–70

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Medical Physics & Informatics, Vrije Universiteit, AZVU-Poli, De Boelelaan 1118, 1081 HV, Amsterdam, The Netherlands

    B. J. TenVoorde & Th. J. C. Faes

  2. Information Theory Group, Delft University of Technology, Delft, The Netherlands

    O. Rompelman

Authors
  1. B. J. TenVoorde
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Th. J. C. Faes
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. O. Rompelman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

TenVoorde, B.J., Faes, T.J.C. & Rompelman, O. Spectra of data sampled at frequency-modulated rates in application to cardiovascular signals: Part 2 evaluation of Fourier transform algorithms. Med. Biol. Eng. Comput. 32, 71–76 (1994). https://doi.org/10.1007/BF02512481

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02512481

Keywords

Search

Navigation