Continuous time domain properties of causal cubic splines

  • Authors:

  • D. Petrinovic

  • Affiliations:

  • Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia, Unska 3, 10000 Zagreb, Croatia

  • Venue:
  • Signal Processing
  • Year:
  • 2009

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Abstract

The paper studies the continuous time domain properties of causal cubic splines with equidistant knots. Causality is achieved by truncating the impulse response of the ideal interpolator to a chosen length. The introduced error affects the final interpolation differently depending on the considered output filter formulation. For the first formulation it is the regularity that is sacrificed while for the second it is the interpolation and splitting of unit delay properties. The analysis of the casual cardinal splines' spectra also demonstrates different manifestation of the causality induced error that affects either the pass-band region only or both the pass-band and the stop-band region. The frequency kernel is used for objective comparison of the causal and the non-causal interpolators including the causal piecewise cubic MOMS interpolator. Their relative interpolation performance was determined both for wide-band as well as for oversampled narrow-band input signals. The transparent delay is identified for which the causal and the non-causal interpolators achieve identical band-limited reconstruction accuracy.