Equivalence of the Lagrange interpolator for uniformly sampled signals and the scaled binomially windowed shifted sinc function

Authors:
Mohammad Mahdi Jahani Yekta
Affiliations:
Electrical Engineering Department, Sharif University of Technology, Azadi Avenue, P.O. Box 11365-9363, Tehran, Iran
Venue:
Digital Signal Processing
Year:
2009

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Abstract

The maximally flat (MF) fractional delay (FD) filter which is in fact a Lagrange interpolator for uniformly sampled signals, has previously been shown to be equal to the scaled binomially windowed shifted version of the sinc function; the ideal interpolation kernel for band-limited signals. In this paper, another proof for this equivalence is presented. Unlike its counterparts available in the literature, the proof given here is neither strictly algebraic, nor deploys the explicit coefficient formulas of the MFFD filter. It follows a frequency domain approach based on the definition of this filter instead, and aims to provide more insight into the corresponding equivalence.