Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

This paper introduces a filterbank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods. An identity, which is referred to as the interpolation identity, is developed and is used to obtain particularly efficient discrete-time systems for interpolation of generalized samples as well as a class of nonuniform samples, to uniform Nyquist samples, either for further processing in that form or for conversion to continuous time. The interpolation identity also leads to new sampling strategies including an extension of Papoulis' (1977) generalized sampling expansion.

• Publication year

  2000

• Venue

  IEEE Transactions on Signal Processing

• Publication date

  2000-10-01

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  DOI 10.1109/78.869037
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Multirate Systems and Filter Banks

  2002cited by this paper
• A level-crossing sampling scheme for A/D conversion

  1996cited by this paper
• Reconstruction of sequences from nonuniform samples

  1995cited by this paper
• New sampling theorems for MRA subspaces

  1995cited by this paper
• A novel iterative method for the reconstruction of signal from nonuniformly spaced samples

  1994cited by this paper
• Iterative algorithms in irregular sampling: a first comparison of methods

  1991cited by this paper
• Discrete-Time Signal Pro-cessing

  1989cited by this paper
• Recovery of signals from nonuniform samples using iterative methods

  1989cited by this paper
• Correction to "The Shannon sampling theorem—Its various extensions and applications: A tutorial review"

  1979cited by this paper
• Recovery of Bandlimited Signals from Unequally Spaced Samples

  1978cited by this paper
• Generalized sampling expansion

  1977influential reference
• The Shannon sampling theorem—Its various extensions and applications: A tutorial review

  1977cited by this paper
• On Some Stability and Interpolatory Properties of Nonuniform Sampling Expansions

  1967cited by this paper
• Error-Free Recovery of Signals from Irregularly Spaced Samples

  1966cited by this paper
• On Nonuniform Sampling of Bandwidth-Limited Signals

  1956cited by this paper
• Some general aspects of the sampling theorem

  1956cited by this paper
• Theory of Functions

  1899cited by this paper

• Real-Time Recovery of Missing Data in Wireless Sensor Networks using Chromatic Derivatives

  2026cites this paper
• DySpect-Net: Neural Network Predicting Spectrum From Non-Uniformly Sampled Data

  2025cites this paper
• Invisible Ears at Your Fingertips: Acoustic Eavesdropping via Mouse Sensors

  2025cites this paper
• Accelerating the convergence of a two-dimensional periodic nonuniform sampling series through the incorporation of a bivariate Gaussian multiplier

  2024cites this paper
• Real-Time Synthetic Aperture Radar Imaging with Random Sampling Employing Scattered Power Mapping

  2024cites this paper
• Continuous time systems disruptive signal processing and accurate real time signal reconstruction

  2024cites this paper
• Generalized Sampling-Based Multi-Channel Sampling of Signals Realized With Pure Delay Analog Filters and Digital FIR Reconstruction Filters

  2023cites this paper
• Iterative reconstruction of bandlimited signals from nonuniform samples by sliding periodization of nonuniformity

  2023cites this paper
• Periodic nonuniform sinc-Gauss sampling

  2023cites this paper
• A Novel Method for Staggered SAR Imaging in an Elevation Multichannel System

  2023cites this paper
• Multi-Channel Sampling on Graphs and Its Relationship to Graph Filter Banks

  2022cites this paper
• Parameter Tuning-Free Missing-Feature Reconstruction for Robust Sound Recognition

  2021cites this paper
• A Review of Streamline Calibration Approaches for Digital Storage Oscilloscopes with Time-Interleaved Channels

  2021cites this paper
• Lattice-based multi-channel sampling theorem for linear canonical transform

  2021cites this paper
• Fractional Spectrum Analysis for Nonuniform Sampling in the Presence of Clock Jitter and Timing Offset

  2020cites this paper
• An Efficient Coherent Integration Method for Maneuvering Target Detection With Nonuniform Pulse Sampling Based on Filterbank Framework

  2020cites this paper
• Convolution and Multichannel Sampling for the Offset Linear Canonical Transform and Their Applications

  2019cites this paper
• A Fast Recursive Algorithm for Spectrum Tracking in Power Grid Systems

  2019cites this paper
• Representation and Reconstruction of Finite-Energy Band-Limited Signals via Pulse-Width Modulation

  2019cites this paper
• A Novel Baseline Estimation Method for Multichannel HRSW SAR System

  2019cites this paper
• Gaussian Regularized Periodic Nonuniform Sampling Series

  2019cites this paper
• A Novel Multi-channel High-Resolution Imaging Method for MIMO-SAR System Based on Filterbank Framework Reconstruction Theory

  2019influential citation
• Adaptive reconstruction for azimuth signal of multichannel HRWS SAR imaging system

  2018cites this paper
• Nonuniform sampling theorems for random signals in the linear canonical transform domain

  2018influential citation
• Nonuniform Sampling Theorems for Bandlimited Signals in the Offset Linear Canonical Transform

  2018cites this paper
• Higher-Order Derivative Sampling Associated with Fractional Fourier Transform

  2018cites this paper
• Chromatic Derivatives and Approximations in Practice—Part II: Nonuniform Sampling, Zero-Crossings Reconstruction, and Denoising

  2018cites this paper
• Ground clutter filtering for Weather radar using staggered pulse repetition time

  2018cites this paper
• Nonuniform Sampling Theorems for Bandlimited Signals in the Offset Linear Canonical Transform

  2018cites this paper
• Signal processing with Fourier analysis, novel algorithms and applications

  2017cites this paper
• Signal reconstruction from recurrent samples in fractional Fourier domain and its application in multichannel SAR

  2017cites this paper
• Nonuniform sampling theorems for random signals in the offset linear canonical transform domain

  2017cites this paper
• Fractional Hilbert Transform Sampling Method and Its Filter Bank Reconstruction

  2017cites this paper
• Doppler laser radar for measuring range and speed simultaneously

  2016cites this paper
• Frequency estimation of sinusoids from nonuniform samples

  2016cites this paper
• Density Theorems for Nonuniform Sampling of Bandlimited Functions Using Derivatives or Bunched Measurements

  2016cites this paper
• Optimum short-time polynomial regression for signal analysis

  2016cites this paper
• Azimuth signal reconstruction for HRWS SAR from recurrent nonuniform samples

  2016influential citation
• Geosynchronous spaceborne-airborne bistatic SAR for earth observation: Advantages and main aspects

  2016cites this paper
• Asymmetric Multi-channel Sampling in a Series of Shift Invariant Spaces

  2016cites this paper
• System design of optronic processing for azimuth signal reconstruction in HRWS SAR based on filterbank framework

  2016cites this paper
• Reconstruction of azimuth signal for multichannel HRWS SAR imaging based on periodic extension

  2016cites this paper
• Bounds for truncation and perturbation errors of nonuniform sampling series

  2016cites this paper
• Multi-channel sampling expansion for band-pass signals without channels constraints

  2016cites this paper
• On the reconstruction of derivative sampling method of band-limited signal

  2016cites this paper
• Generalized Sampling Expansions with Multiple Sampling Rates for Lowpass and Bandpass Signals in the Fractional Fourier Transform Domain

  2016influential citation
• Bounds for truncation and perturbation errors of nonuniform sampling series

  2015cites this paper
• Calibration of the sampling jitter effect on wind direction measurement from platform-based HF radar

  2015cites this paper
• Compensation numérique pour convertisseur large bande hautement parallélisé.

  2015cites this paper
• Signal Reconstruction Algorithms for Time-Interleaved ADCs

  2015cites this paper
• Low Cost Sparse Multiband Signal Characterization Using Asynchronous Multi-Rate Sampling: Algorithms and Hardware

  2015cites this paper
• Consensus on State and Time: Decentralized Regression With Asynchronous Sampling

  2015influential citation
• Aliasing in Recurrently Sampled Signals With an Application to Synthetic Aperture Imaging

  2015cites this paper
• Universal lower bounds on sampling rates for covariance estimation

  2015cites this paper
• Spectral Analysis of Sampled Band-Limited Signals in the Offset Linear Canonical Transform Domain

  2015cites this paper
• Sampling Theory: Beyond Bandlimited Systems

  2015cites this paper
• Event-driven sampling of signal with quadratic prediction

  2015cites this paper
• MIMO radar: signal processing, waveform design, and applications to synthetic aperture imaging

  2015cites this paper
• Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain

  2014cites this paper
• Density Theorems for Nonuniform Sampling of Bandlimited Functions Using Derivatives or Bunched Measurements

  2014cites this paper
• Time-Reversal Wireless Paradigm for Green Internet of Things: An Overview

  2014cites this paper
• Sampling and distortion tradeoffs for bandlimited periodic signals

  2014cites this paper
• Low-cost sub-Nyquist sampling hardware and algorithm co-design for wideband and high-speed signal characterization and measurement

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

  2014cites this paper
• Event-triggered sampling and reconstruction of sparse real-valued trigonometric polynomials

  2014cites this paper
• Gyrophone: Recognizing Speech from Gyroscope Signals

  2014influential citation
• Sampling and Quantization

  2014cites this paper
• FFT Interpolation From Nonuniform Samples Lying in a Regular Grid

  2014cites this paper
• Multichannel sampling theorem for bandpass signals in the linear canonical transform domain

  2014cites this paper
• Relationship between sampling and multirate filterbanks in the linear canonical transform domain

  2013cites this paper
• A study on digital filter banks for reconstruction of uniformly sampled signals from nonuniform samples

  2013influential citation
• Reconstruction of N-th order nonuniformly sampled bandlimited signals using digital filter banks

  2013influential citation
• Adaptive signal conditioning algorithms to enable wideband signal digitization

  2013cites this paper
• Signal to symbol converters: Overview, opportunities and challenges

  2013cites this paper
• Calibration of mismatch effects in time-interleaved analog-to-digital converters

  2013influential citation
• A comprehensive review of past and present vision-based techniques for gait recognition

  2013cites this paper
• Enabling high-speed, high-resolution ADCs using signal conditioning algorithms

  2013cites this paper
• Reconstruction of periodic nonuniform samples using Lagrange interpolation in time-interleaved ADCs

  2013influential citation
• 8-channel 20 kHz to 200 MHz Nyquist and compressive sampler in 0.5 μm CMOS

  2013cites this paper
• Sampling reconstruction of N-dimensional bandlimited images after multilinear filtering in fractional Fourier domain

  2013cites this paper
• Design of a Parallel Sampling Encoder for Analog to Information (A2I) Converters: Theory, Architecture and

  2013cites this paper
• Sampled-data Networked Control Systems: A Lyapunov-Krasovskii Approach

  2013cites this paper
• Multidimensional Filter Banks and Multiscale Geometric Representations

  2012cites this paper
• Recovering Periodically Spaced Missing Samples

  2012cites this paper
• An analytical approach for wideband speech coding with the help of filter bank

  2012cites this paper
• Non-uniform sampling: algorithms and architectures

  2012cites this paper
• A Fast Image Reconstruction Algorithm Using Adaptive R-Tree Segmentation and B-Splines

  2012cites this paper
• Spectral Analysis of Sampled Signals in the Linear Canonical Transform Domain

  2012cites this paper
• Channel Capacity Under Sub-Nyquist Nonuniform Sampling

  2012cites this paper
• Multi-channel sampling expansion in fractional Fourier domain and its application to superresolution

  2011cites this paper
• Multi-Gigabit Reception with Time-interleaved Analog-to-Digital Converters

  2011cites this paper
• A Versatile Iterative Framework for the Reconstruction of Bandlimited Signals from Their Nonuniform Samples

  2011cites this paper
• Sampling random signals in a fractional Fourier domain

  2011cites this paper
• Sinc Interpolation of Nonuniform Samples

  2011cites this paper
• New Iterative Framework for Frequency Response Mismatch Correction in Time-Interleaved ADCs: Design and Performance Analysis

  2011cites this paper
• A Novel SAR Signal Reconstruction Method from Non-uniform Sampling Associated with Fractional Fourier Transform

  2011cites this paper
• Finite representation of finite energy signals

  2011cites this paper
• Sampling and quantization for optimal reconstruction

  2011influential citation
• Signal Recovery in Power-Line Communications Systems Based on the Fractals

  2011cites this paper
• On the correction of linear time-varying systems by means of time-varying FIR filters

  2011cites this paper