A versatile iterative framework for the reconstruction of bandlimited signals from their nonuniform samples

In this paper, we study a versatile iterative framework for the reconstruction of uniform samples from nonuniform samples of bandlimited signals. Assuming the input signal is slightly oversampled, we first show that its uniform and nonuniform samples in the frequency band of interest can be expressed as a system of linear equations using fractional delay digital filters. Then we develop an iterative framework, which enables the development and convergence analysis of efficient iterative reconstruction algorithms. In particular, we study the Richardson iteration in detail to illustrate how the reconstruction problem can be solved iteratively, and show that the iterative method can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. Under the proposed framework, we also present a completed and systematic convergence analysis to determine the convergence conditions. Simulation results show that the iterative method converges more rapidly and closer to the true solution (i.e. the uniform samples) than conventional iterative methods using truncation of sinc series. © 2010 The Author(s).published_or_final_versionSpringer Open Choice, 21 Feb 201

Динамічне перетворення частоти дискретизації на основі поліфазного фільтра

Розглянуто можливість використання поліфазного фільтра на основі структури Ферроу для динамічного перетворення частоти дискретизації і застосування його в цифровій обробці звукових сигналів.Рассмотрена возможность использования полифазного фильтра на основе структуры Ферроу для динамического преобразования частоты дискретизации и применение его в цифровой обработке звуковых сигналов.The possibility of using polyphase filter on the basis of the Farrow structure for dynamic sample rate conversion and its application in digital signal processing are considered

A Novel Iterative Structure for Online Calibration of M-Channel Time-Interleaved ADCs

published_or_final_versio

Iterative correction of frequency response mismatches in time-interleaved ADCs: A novel framework and case study in OFDM systems

In this paper, we study a versatile iterative framework for the correction of frequency response mismatch in time-interleaved ADCs. Based on a general time varying linear system model, we establish a flexible iterative framework, which enables the development of various efficient iterative correction algorithms. In particular, we study the Gauss-Seidel iteration in detail to illustrate how the correction problem can be solved iteratively, and show that the iterative structure can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. Simulation results show that the proposed iterative structure performs better than conventional compensation structures. Moreover, a preliminary study on the BER performance of OFDM systems due to TI ADC mismatch is conducted. © 2010 IEEE.published_or_final_versionThe 1st International Conference on Green Circuits and Systems (ICGCS 2010), Shanghai, China, 21-23 June 2010. In Proceedings of the 1st ICGCS, 2010, p. 253-25

New iterative framework for frequency response mismatch correction in time-interleaved ADCs: Design and performance analysis

This paper proposes a new iterative framework for the correction of frequency response mismatch in time-interleaved analog-to-digital converters. Based on a general time-varying linear system model for the mismatch, we treat the reconstruction problem as a linear inverse problem and establish a flexible iterative framework for practical implementation. It encumbrances a number of efficient iterative correction algorithms and simplifies their design, implementation, and performance analysis. In particular, an efficient Gauss-Seidel iteration is studied in detail to illustrate how the correction problem can be solved iteratively and how the proposed structure can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. We also study important issues, such as the sufficient convergence condition and reconstructed signal spectrum, derive new lower bound of signal-to-distortion-and-noise ratio in order to ensure stable operation, and predict the performance of the proposed structure. Furthermore, we propose an extended iterative structure, which is able to cope with systems involving more than one type of mismatches. Finally, the theoretical results and the effectiveness of the proposed approach are validated by means of computer simulations. © 2011 IEEE.published_or_final_versio

Signal Processing using Chromatic Derivatives and Chromatic Approximation

Modern Digital Signal Processing (DSP) is based upon the fundamental Whittaker–Kotel’nikov–Nyquist–Shannon Sampling Theorem, which, as we will argue, is complementary to the Taylor Theorem. Whilst the sampling theorem provides global signal representation, its truncations fail to provide an accurate, localised view of the original signal. The Taylor series, on the other hand, provides satisfactory local representation of the signal, but is deficient in providing a global signal representation because its truncations rapidly diverge for values of the input that are far away from the point of expansion. Taylor series is also very sensitive to noise when high order derivatives are numerically evaluated from samples of the input signal. Chromatic derivatives operators were developed to overcome the inaccuracy and instability issues in numerically evaluating higher order derivatives. The corresponding chromatic expansions combine the benefits of both the sampling theorem and Taylor expansion; its truncations, named chromatic approximations, are globally uniformly converging approximations based on a numerically robust set of differential operators. Chromatic Approximations are capable of not only recovering signals in the global sense, but also provide excellent accurate local approximations. Experimental results, detailed in this body of work, involving the use of chromatic derivatives and chromatic approximations to recover band limited signals under various unfavourable conditions, provide an insight into the potential use of these operators as an alternative or enhancement to the current, state-of-the-art digital signal processing methods. Specifically, we explore and present successful experimentation results for the following: • Two point chromatic approximation and signal reconstruction from an analog filterbank (Chapter 2) • Signal resampling algorithm using a chromatic approximation that can operate with rational and non rational resampling rates (Chapter 2) • Signal recovery from non uniform samples and recovery of distorted signals (missing samples) from partial content using a novel, iterative algorithm (Chapter 3) • A novel, adaptive denoising algorithm that significantly enhances the performance of common frequency estimation methods such as ESPRIT and MUSIC (Chapter 4

Reconstruction from non-uniform samples

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 79-81).Exact reconstruction of a band-limited signal from its non-uniform samples involves the use of Lagrange interpolation, which is impractical to implement as it is computationally difficult. This thesis develops approximate reconstruction methods based on time-warping to obtain reconstruction of band-limited signals from non-uniform samples. A review of non-uniform sampling theorems is presented followed by an alternative interpretation of the Lagrange interpolation kernel by decomposing the kernel into its constituent components. A discussion of time-warping and its use in the context of non-uniform sampling is made. This includes an alternative interpretation known as the delay-modulation, which we show to be a simpler representation for a specific case of non-uniform sampling where the sample instants are deviations from a uniform grid. Based on some essential characteristics of the Lagrange kernel, a framework using a modulated time-warped sine function is formed to obtain various approximations to the Lagrange kernel. The thesis also formulates a vector space representation of non-uniform sampling and interpolation and incorporates warped sinc functions to obtain faster convergence in iterative algorithms for reconstruction of band-limited signals from non-uniform samples.by Kwang Siong Jeremy Leow.S.M

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide