FFT Interpolation From Nonuniform Samples Lying in a Regular Grid

This paper presents a method to interpolate a periodic band-limited signal from its samples lying at nonuniform positions in a regular grid, which is based on the FFT and has the same complexity order as this last algorithm. This kind of interpolation is usually termed “the missing samples problem” in the literature, and there exists a wide variety of iterative and direct methods for its solution. The one presented in this paper is a direct method that exploits the properties of the so-called erasure polynomial and provides a significant improvement on the most efficient method in the literature, which seems to be the burst error recovery (BER) technique of Marvasti's The paper includes numerical assessments of the method's stability and complexity.

• Publication year

  2014

• Venue

  IEEE Transactions on Signal Processing

• Publication date

  2014-08-16

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  DOI 10.1109/TSP.2015.2419178arXiv 1408.3717
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Distributed Source-Channel Coding Based on Real-Field BCH Codes

  2014cited by this paper
• A sub-band based reconstructor for M-channel time-interleaved ADCS with missing samples

  2014cited by this paper
• A Novel Iterative Structure for Online Calibration of $M$-channel Time-Interleaved ADCs

  2014cited by this paper
• Spectral compressive sensing

  2013cited by this paper
• Compressed Sensing Off the Grid

  2012cited by this paper
• Compressed Sensing

  2012cited by this paper
• Matrix Computations

  2011cited by this paper
• Channel Estimation in Wireless OFDM Systems With Irregular Pilot Distribution

  2010cited by this paper
• Design of Barycentric Interpolators for Uniform and Nonuniform Sampling Grids

  2010cited by this paper
• Functionally Weighted Lagrange Interpolation of Band-Limited Signals From Nonuniform Samples

  2009cited by this paper
• Some nonlinear/adaptive methods for fast recovery of the missing samples of signals

  2008cited by this paper
• Block-Based Methods for the Reconstruction of Finite-Length Signals From Nonuniform Samples

  2007cited by this paper
• Random Sampling for Analog-to-Information Conversion of Wideband Signals

  2006cited by this paper
• The Design and Implementation of FFTW3

  2005cited by this paper
• Subspace-based error and erasure correction with DFT codes for wireless channels

  2004cited by this paper
• Discrete Time Signal Processing

  2004cited by this paper
• Stable DFT codes and frames

  2003cited by this paper
• Nonuniform sampling : theory and practice

  2001cited by this paper
• Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

  2000cited by this paper
• Efficient algorithms for burst error recovery using FFT and other transform kernels

  1999cited by this paper
• Channel estimation for wireless OFDM systems

  1998cited by this paper
• Understanding Digital Signal Processing

  1996cited by this paper
• Interpolation and the discrete Papoulis-Gerchberg algorithm

  1994cited by this paper
• Incomplete sampling series and the recovery of missing samples from oversampled band-limited signals

  1992cited by this paper
• A new algorithm in spectral analysis and band-limited extrapolation.

  1975cited by this paper

• Spectrum analysis of non-uniformly sampled signals*

  2025cites this paper
• Recovery of missing samples in Orthogonal Frequency Division Multiplexing signals with optimisation using data carriers

  2024cites this paper
• Enhancing Weather Target Detection with Non-Uniform Pulse Repetition Time (NPRT) Waveforms

  2024cites this paper
• FFT reconstruction of signals from MIMO sampled data

  2024cites this paper
• FFT-Based Approximations for Black-Box Optimization

  2023cites this paper
• Eigenvalue Decomposition of a Parahermitian Matrix: Extraction of Analytic Eigenvalues

  2021cites this paper
• Research and implementation on high-precision power quality monitoring system of EAST power supply

  2021cites this paper
• Fast and L2-optimal recovery for periodic nonuniformly sampled bandlimited signal

  2021cites this paper
• Measuring Smoothness of Trigonometric Interpolation Through Incomplete Sample Points

  2020cites this paper
• Application of VMD and Hilbert Transform Algorithms on Detection of the Ripple Components of the DC Signal

  2020cites this paper
• Optimized Composite Convolution Window for Power-Harmonic Analysis by Dual-Spectrum Interpolation FFT Algorithms

  2019cites this paper
• Maximally Smooth Dirichlet Interpolation from Complete and Incomplete Sample Points on the Unit Circle

  2019cites this paper
• Measuring Smoothness of Real-Valued Functions Defined by Sample Points on the Unit Circle

  2019cites this paper
• Spatial domain morphological filtering for interpolation of the Fourier domain

  2018cites this paper
• Multichannel reconstruction from nonuniform samples with application to image recovery.

  2018influential citation
• Multichannel Interpolation for Periodic Signals via FFT, Error Analysis and Image Scaling

  2018cites this paper
• Multichannel interpolation of nonuniform samples with application to image recovery

  2018cites this paper
• New Smoothed Time-Frequency Rate Representations for Suppressing Cross Terms

  2017cites this paper
• European Option Pricing With a Fast Fourier Transform Algorithm for Big Data Analysis

  2016cites this paper
• Doppler laser radar for measuring range and speed simultaneously

  2016cites this paper
• Non-iterative Type 4 and 5 Nonuniform FFT Methods in the One-Dimensional Case

  2016cites this paper