Abstract
In the analysis of time-varying signals various functions of time and frequency are used in order to describe the signal as a composition of several frequency bands with varying contributions to the intensity of the signal. For some of them, e.g. the spectrogram, a trade-off has to be made between spectral and temporal resolution. For others, e.g. the complex energy-density function, the interpretation is complicated and confusing. Another function of time and frequency, the Wigner distribution of the analytic signal, lacks both these undesirable properties. The lucid and transparent way in which this real function displays the temporal as well as the spectral characteristics of a real signal, make it a powerful tool in the analysis of time-varying physiological signals.
Similar content being viewed by others
References
Ackroyd, M.H.: Short-time spectra and time-frequency energy distributions. J. Acoust. Soc. Am. 50, 1229–1231 (1971)
Allen, J.B.: Short-term spectral analysis and synthesis and modification by discrete Fourier transform. IEEE Trans. ASSP 25, 235–238 (1977)
Allen, J.B., Rabiner, L.R.: A unified approach to short-time Fourier analysis and synthesis. Proc. IEEE 65, 1558–1564 (1977)
Bracewell, R.N.: The fast Hartley transform. Proc. IEEE 72, 1010–1018 (1984)
Claasen, T.A.C.M., Mecklenbräuker, W.F.G.: The aliasing problem in discrete-time Wigner distributions. IEEE Trans. ASSP-31, 1067–1072 (1983)
Gabor, D.: Theory of communication. J. Inst. Electr. Eng. (London), Part III 93, 429–457 (1946)
Johannesma, P., Aertsen, A., Cranen, B., Van Erning, L.: The phonochrome: a coherent spectro-temporal representation of sound. Hearing Res. 5, 123–145 (1981)
Levin, M.J.: Instantaneous spectra and ambiguity functions. IEEE Trans. IF-10, 95–97 (1964)
Papoulis, A.: Signal analysis. New York: McGraw-Hill 1977
Portnoff, M.R.: Time-frequency representation of digital signals and systems based on short-time Fourier analysis. IEEE Trans. ASSP-28, 55–69 (1980)
Potter, R.K., Kopp, G.A., Green, H.C.: Visible speech. New York: Van Nostrand 1947
Rihaczek, A.W.: Signal energy distribution in time and frequency. IEEE Trans. IT-14, 369–374 (1968)
Shannon, C.E.: Communication in the presence of noise. Proc. IRE 37, 10–21 (1949); reprinted Proc. IEEE 72, 1192–1202 (1984)
Stutt, C.A.: Some results on real part/imaginary part and magnitude/phase-relations in ambiguity functions. IEEE Trans. IT-10, 321–327 (1964)
Sussman, S.M.: Least square synthesis of radar ambiguity functions. IRE Trans. IT-8, 246–254 (1962)
Ville, J.: Theorie et application de la notion de signal analytique. Cables Transm. 2, 61–74 (1948)
Wigner, E.: On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hermes, D.J. Separation of time and frequency. Biol. Cybern. 52, 109–115 (1985). https://doi.org/10.1007/BF00364001
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00364001