Review of Unbiased FIR Filters, Smoothers, and Predictors for Polynomial Signals

Extracting an estimate of a slowly varying signal corrupted by noise is a common task. Examples can be found in industrial, scientific and biomedical instrumentation. Depending on the nature of the application the signal estimate is allowed to be a delayed estimate of the original signal or, in the other extreme, no delay is tolerated. These cases are commonly referred to as filtering, prediction, and smoothing depending on the amount of advance or lag between the input data set and the output data set. In this review paper we provide a comprehensive set of design and analysis tools for designing unbiased FIR filters, predictors, and smoothers for slowly varying signals, i.e. signals that can be modeled by low order polynomials. Explicit expressions of parameters needed in practical implementations are given. Real life examples are provided including cases where the method is extended to signals that are piecewise slowly varying. A critical view on recursive implementations of the algorithms is provided

Design of sparse FIR filters with low group delay

The aim of the work is to present the method for designing sparse FIR filters with very low group delay and approximately linear-phase in the passband. Significant reduction of the group delay, e.g. several times in relation to the linear phase filter, may cause the occurrence of undesirable overshoot in the magnitude frequency response. The method proposed in this work consists of two stages. In the first stage, FIR filter with low group delay is designed using minimax constrained optimization that provides overshoot elimination. In the second stage, the same process is applied iteratively to reach sparse solution. Design examples demonstrate the effectiveness of the proposed method

A Design of a low-pass FIR filter using Hamming Window Functions in Matlab

The reduction and filtering of the input components of an original signal in one or more frequency bands using a finite impulse response, better known as FIR, is designed using a function of the Hamming window. Although there are various window functions such as the Blackman window function, the Hanning window function and the rectangular window functions that can be used as digital filters, the Hamming window function was used in this study for the reason of its minimum damping/decibel of the stopband with a reduced transition bandwidth. Among the other three widow functions that can be used, the Blackman window function is closest to the Hamming window function in terms of minimum bandstop attenuation/decibel, since both have a dB value greater than -50. However, in terms of transition bandwidth (Δω), the Hamming window has a narrower bandwidth than the Blackman window, making it more appropriate to use in this FIR filter design. This type of filter is important for analyzing the different types of signals that are essential in a world where digital filters play a major role in DSP applications. This research paper offers a Matlab-based low-pass FIR digital filter that uses Hamming window functions. Keywords: FIR filters, Hamming window, Blackman window Hanning window, Matlab. DOI: 10.7176/CEIS/11-2-04 Publication date: February 29th 202

Sparse Filter Design Under a Quadratic Constraint: Low-Complexity Algorithms

This paper considers three problems in sparse filter design, the first involving a weighted least-squares constraint on the frequency response, the second a constraint on mean squared error in estimation, and the third a constraint on signal-to-noise ratio in detection. The three problems are unified under a single framework based on sparsity maximization under a quadratic performance constraint. Efficient and exact solutions are developed for specific cases in which the matrix in the quadratic constraint is diagonal, block-diagonal, banded, or has low condition number. For the more difficult general case, a low-complexity algorithm based on backward greedy selection is described with emphasis on its efficient implementation. Examples in wireless channel equalization and minimum-variance distortionless-response beamforming show that the backward selection algorithm yields optimally sparse designs in many instances while also highlighting the benefits of sparse design.Texas Instruments Leadership University Consortium Progra

Synthesis methods for linear-phase FIR filters with a piecewise-polynomial impulse response

his thesis concentrates on synthesis methods for linear-phase finite-impulse response filters with a piecewise-polynomial impulse response. One of the objectives has been to find integer-valued coefficients to efficiently implement filters of the piecewise-polynomial impulse response approach introduced by Saram¨aki and Mitra. In this method, the impulse response is divided into blocks of equal length and each block is created by a polynomial of a given degree. The arithmetic complexity of these filters depends on the polynomial degree and the number of blocks. By using integer-valued coefficients it is possible to make the implementation of the subfilters, which generates the polynomials, multiplication-free. The main focus has been on finding computationally-efficient synthesis methods by using a piecewise-polynomial and a piecewise-polynomial-sinusoidal impulse responses to make it possible to implement high-speed, low-power, highly integrated digital signal processing systems. The earlier method by Chu and Burrus has been studied. The overall impulse response of the approach proposed in this thesis consists of the sum of several polynomial-form responses. The arithmetic complexity depends on the polynomial degree and the number of polynomial-form responses. The piecewise-polynomial-sinusoidal approach is a modification of the piecewise-polynomial approach. The subresponses are multiplied by a sinusoidal function and an arbitrary number of separate center coefficients is added. Thereby, the arithmetic complexity depends also on the number of complex multipliers and separately generated center coefficients. The filters proposed in this thesis are optimized by using linear programming methods

Automatic Tuning of Silicon Photonics Millimeter-Wave Transceivers Building Blocks

Today, continuously growing wireless traffic have guided the progress in the wireless communication systems. Now, evolution towards next generation (5G) wireless communication systems are actively researched to accommodate expanding future data traffic. As one of the most promising candidates, integrating photonic devices in to the existing wireless system is considered to improve the performance of the systems. Emerging silicon photonic integrated circuits lead this integration more practically, and open new possibilities to the future communication systems. In this dissertation, the development of the electrical wireless communication systems are briefly explained. Also, development of the microwave photonics and silicon photonics are described to understand the possibility of the hybrid SiP integrated wireless communication systems. A limitation of the current electrical wireless systems are addressed, and hybrid integrated mm-wave silicon photonic receiver, and silicon photonic beamforming transmitter are proposed and analyzed in system level. In the proposed mm-wave silicon photonic receiver has 4th order pole-zero silicon photonic filter in the system. Photonic devices are vulnerable to the process and temperature variations. It requires manual calibration, which is expensive, time consuming, and prone to human errors. Therefore, precise automatic calibration solution with modified silicon photonic filter structure is proposed and demonstrated. This dissertation demonstrates fully automatic tuning of silicon photonic all-pass filter (APF)-based pole/zero filters using a monitor-based tuning method that calibrates the initial response by controlling each pole and zero individually via micro-heaters. The proposed tuning approach calibrates severely degraded initial responses to the designed elliptic filter shapes and allows for automatic bandwidth and center frequency reconfiguration of these filters. This algorithm is demonstrated on 2nd- and 4th-order filters fabricated in a standard silicon photonics foundry process. After the initial calibration, only 300ms is required to reconfigure a filter to a different center frequency. Thermal crosstalk between the micro-heaters is investigated, with substrate thinning demonstrated to suppress this effect and reduce filter calibration to less than half of the original thick substrate times. This fully automatic tuning approach opens the possibility of employing silicon photonic filters in real communication systems. Also, in the proposed beamforming transmitter, true-time delay ring resonator based 1x4 beamforming network is imbedded. A proposed monitor-based tuning method compensates fabrication variations and thermal crosstalk by controlling micro-heaters individually using electrical monitors. The proposed tuning approach successfully demonstrated calibration of OBFN from severely degraded initial responses to well-defined group delay response required for the targeted radiating angle with a range of 60◦ (-30◦ to 30◦ ) in a linear beamforming antenna array. This algorithm is demonstrated on OBFN fabricated in a standard silicon photonics foundry process. The calibrated OBFN operates at 30GHz and provide 2GHz bandwidth. This fully automatic tuning approach opens the possibility of employing silicon OBFN in real wideband mm-wave wireless communication systems by providing robust operating solutions. All the proposed photonic circuits are implemented using the standard silicon photonic technologies, and resulted in several publications in IEEE/OSA Journals and Conferences

Sparse equalizer filter design for multi-path channels

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2012.Cataloged from PDF version of thesis.Includes bibliographical references (p. 81-82).In this thesis, sparse Finite Impulse Response (FIR) equalizers are designed for sparse multi-path channels under a pre-defined Mean Squared Error (MSE) constraint. We start by examining the intrinsic sparsity of the Zero Forcing equalizers and the FIR Minimum MSE (MMSE) equalizers. Next the equalization MSE is formulated as a quadratic function of the equalizer coefficients. Both the Linear Equalizer (LE) and the Decision Feedback Equalizer (DFE) are analyzed. Utilizing the quadratic form, designing a sparse equalizer under a single MSE constraint becomes an 10-norm minimization problem under a quadratic constraint, as described in [2]. Three previously developed methods for solving this problem are applied, namely the successive thinning algorithm, the branch-and-bound algorithm, and the simple linear programming algorithm. Simulations under various channel specifications, equalizer specifications and algorithm specifications are conducted to show the dependency of the sparsity on these factors. The channels include the ideal discrete multipath channels and the Vehicular A multi-path channels in both the Single-Input-Single- Output (SISO) and the Multiple-Input-Multiple-Output scenarios. Additionally, the sparse FIR equalizer is designed for MIMO channels under two MSE constraints. This is formulated as an 10-norm minimization problem under two quadratic constraints. A sub-optimal solution by decoupling the two constraints is proposed.by Xue Feng.S.M

Fir notch filter design: a review

Notch filters are invariably used in communication, control, instrumentation and bio-medical engineering, besides a host of other fields, to eliminate noise and power line interferences. Digital notch filters can be designed as infinite impulse response (IIR) as well as finite impulse response (FIR) structures. As compared to the latter, IIR filters have the advantage that they require lower orders for efficient approximation of a given set of specifications. However, IIR filters are potentially unstable and do not provide linear phase characteristics, in general. FIR filters, on the other hand, are unconditionally stable and can be designed to give exact linear phase characteristics. We, in this review paper, focus our attention to the recent design techniques proposed by us for FIR notch filters. Standard FIR filter design methods, such as windowing, frequency sampling and computer-aided/optimization may be used for designing FIR notch filters. However, most of these methods result in ripples in the passbands. In many situations, maximally at (MF) filters are preferred since they have maximum attenuation in the stopband and hence can yield the best signal-to-noise ratio. A number of methods are available in the literature for designing MF digital filters. We, in this paper, review the design techniques for computing the weights of MF FIR notch filters. A number of design methodologies have been highlighted that lead to either recursive or explicit formulas for the computation of weights of FIR notch filters. Procedures for the design of FIR notch filters with maximal flatness of the amplitude response (in the Butterworth sense) at ω = 0 and ω = p have been given. Empirical formulas for finding the filter length N have also been proposed. By relaxing the linear phase property, it is possible to reduce the filter order required for a given magnitude response specifications. An FIR filter (with non-linear phase) can be derived from a second order IIR notch filter prototype. Explicit mathematical formulas for computing the weights for such FIR notch filters have been given. Design approaches based on the use of (i) Bernstein polynomials, and (ii) lowpass filter design have also been exploited to obtain maximally at FIR notch filters

Design of discrete-time filters for efficient implementation

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2011.Cataloged from PDF version of thesis.Includes bibliographical references (p. 325-333).The cost of implementation of discrete-time filters is often strongly dependent on the number of non-zero filter coefficients or the precision with which the coefficients are represented. This thesis addresses the design of sparse and bit-efficient filters under different constraints on filter performance in the context of frequency response approximation, signal estimation, and signal detection. The results have applications in several areas, including the equalization of communication channels, frequency-selective and frequency-shaping filtering, and minimum-variance distortionless-response beamforming. The design problems considered admit efficient and exact solutions in special cases. For the more difficult general case, two approaches are pursued. The first develops low-complexity algorithms that are shown to yield optimal or near-optimal designs in many instances, but without guarantees. The second focuses on optimal algorithms based on the branch-and-bound procedure. The complexity of branch-and-bound is reduced through the use of bounds that are good approximations to the true optimal cost. Several bounding methods are developed, many involving relaxations of the original problem. The approximation quality of the bounds is characterized and efficient computational methods are discussed. Numerical experiments show that the bounds can result in substantial reductions in computational complexity.by Dennis Wei.Ph.D