Time-frequency localization with the Hartley S-transform

  • Authors:

  • C. Robert Pinnegar;Lalu Mansinha

  • Affiliations:

  • Department of Earth Sciences, BGS Building, University of Western Ontario, London, Ontario, Canada N6A 5B7 and Seaman Family MR Research Centre, Foothills Medical Centre, 1403-29th St. NW, Calgary ...;Department of Earth Sciences, BGS Building, University of Western Ontario, London, Ontario, Canada N6A 5B7

  • Venue:
  • Signal Processing
  • Year:
  • 2004

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Abstract

The Hartley transform, like the Fourier transform, is used for determining the spectrum of a complete time series. However, problems arise if the time series has time-dependent spectral content, since the Hartley kernel has no time localization. To this end, a short-time Hartley transform has been proposed and defined in analogy with the short-time Fourier transform. The frequency invariance of the window used in the short-time Hartley transform, though, leads to problems similar to those encountered in the short-time Fourier transform; namely, poor time resolution at high frequencies, and artifacts at low frequencies. In the Fourier case, these problems can be addressed through use of the S-transform, whose window scales with frequency to accommodate the scaling of the Fourier sinusoid. We apply the same principles to define the Hartley S-transform, using a scalable window.