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

Jahani Yekta, M. M ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.dsp.2009.03.009
  3. Publisher: 2009
  4. Abstract:
  5. 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. © 2009 Elsevier Inc. All rights reserved
  6. Keywords:
  7. Band-limited interpolation ; Binomial window ; Maximally flat FIR fractional delay filter ; Sinc function ; Uniform Lagrange interpolation ; Interpolation ; Lagrange multipliers ; Quadrature amplitude modulation ; Windows ; Frequency domain analysis
  8. Source: Digital Signal Processing: A Review Journal ; Volume 19, Issue 5 , 2009 , Pages 838-842 ; 10512004 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S1051200409000165