Finite Impulse Response Notch Filter Research Articles

Eigen-Approach for Designing Selective Notch Filters

An innovative method of obtaining the weights for a Finite Impulse Response (FIR) notch filter using the Eigen-approach is proposed. The Eigen-approach was used to identify the frequencies of the source signals by determining the eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix. The FIR notch filter was constructed by shifting the root corresponding to the desired signal, which filtered out all other undesired signals. The obtained results indicate that using the Eigen-approach to generate a selective FIR notch filter is a viable solution.

A Modified DFT-Based Phasor Estimation Algorithm Using an FIR Notch Filter

Accurate and fast extraction of the fundamental parameters of fault signals is a critical issue in the overall performance of protective relays. The decaying DC terms (DDTs) in the fault current challenge the discrete Fourier transform (DFT), the reference algorithm for phasor estimation. To meet this challenge, a new modification for half and full-cycle DFT algorithms is proposed in this paper. In the first step, a finite impulse response (FIR) notch filter designed for fundamental frequency is applied to the output of the DFT algorithm. After that, the outcome of the FIR notch filter and its complex conjugate make it possible to extract error terms. Finally, the estimated phasors are emptied from DDTs error. The ability of the proposed method for estimating phasor and tolerating disturbances was assessed using practical simulated signals. The results perform that the proposed method is much more robust, accurate, and faster than previous methods and enhances the efficiency of the DFT algorithm faced by multiple DDTs.

A Comparison Study for Cardiac Arrhythmias Noise Cancellation Techniques

The electrocardiogram (ECG), which represents the electrical activity of the heart, is always chosen as the basic signal for diagnosing cardiac abnormalities and detecting the patient's states. Generally, the various filters are applied (preprocessing) to denoise the artifacts from ECG signal. This step makes the decision making and diagnosis simpler and faster. The most common noise sources are power line interference and baseline wandering. This article discusses different filtering techniques used to denoise the ECG signals. Electrocardiogram signals were downloaded from the MIT-BIH Arrhythmia Database. The MIT-BIH Database was the first set of standard test materials that is generally available to evaluate arrhythmia detection. To remove baseline wander, 4 filters were designed. The filters are a fourth-order high-pass Butterworth filter, a second-order finite impulse response Hamming window, an finite impulse response rectangular window with length L, and an finite impulse response Hanning window. To extract the power line interference (60 Hz), 4 filters were designed: a second-order digital bandpass Butterworth filter, a second-order finite impulse response filter, a Chebyshev filter, and an finite impulse response notch filter with Hanning window. Finally, 5 parameters were used to evaluate filter performance; the parameters are frequency response, phase response, average filter delay (group delay), phase delay, and signal-to-noise ratio. The results show that, for baseline wander filters, a fourth-order high-pass Butterworth filter removes more noise and has no time delay. Power line interference filters have the same signal-to-noise ratio approximately.

A new design method for FIR notch filter using Fractional Derivative and swarm intelligence

In this paper, a new design method for the finite impulse response (FIR) notch filters using fractional derivative (FD) and swarm intelligence technique is presented. The design problem is constructed as a minimization of the magnitude response error w.r.t. filter coefficients. To acquire high accuracy of notch filter, fractional derivative (FD) is evaluated, and the required solution is computed using the Lagrange multiplier method. The fidelity parameters like passband error, notch bandwidth, and maximum passband ripple vary non-linearly with respect to FD values. Moreover, the tuning of appropriate FD value is computationally expensive. Therefore, modern heuristic methods, known as the constraint factor particle swarm optimization (CFI-PSO), which is inspired by swarm intelligence, is exploited to search the best values of FDs and number of FD required for the optimal solution. After an exhaustive analysis, it is affirmed that the use of two FDs results in 21% reduction in passband error, while notch bandwidth is slightly increased by 2% only. Also, it has been observed that, in the proposed methodology, at the most 66 iterations are required for convergence to optimum solution. To examine the performance of designed notch filter using the proposed method, it has been applied for removal of power line interference from an electrocardiography (ECG) signal, and the improvement in performance is affirmed.

DFT-Based Phasor Estimation for Removal of the Effect of Multiple DC Components

A current sampled signal in a faulted transmission line can contain multiple dc components, namely a primary decaying dc component (DDC), a secondary DDC, an auxiliary DDC, and a bias DDC, and these may be due to a faulted line, current transformer, internal transformer, and analog-to-digital converter in the numerical relay, respectively. The intensity of the primary DDC is much higher than those of other DDCs. The elimination of the phasor-estimation error due to the primary DDC is the main issue in numerical relays, where the presence of other DDCs can deteriorate the phasor-estimation accuracy. This paper proposes a discrete Fourier transform (DFT)-based method using a second-order finite-impulse response (FIR) notch filter to combine multiple DDCs as a certain DDC through DFT. The FIR notch filter is designed to minimize the calculation complexity of the identification. Phasor-estimation errors that are due to the multiple DDCs are corrected by identifying the combined DDC. The proposed method can be applied for both full-cycle DFT (FCDFT) and half-cycle DFT. The feasibility of the proposed FCDFT-based method is compared with those of conventional FCDFT-based methods using simulations on DDCs, harmonics, noise, and a faulted transmission line.

Digital Finite Impulse Response Notch Filter with Non-Zero Initial Conditions, Based on an Infinite Impulse Response Prototype Filter

Abstract In this paper a concept of finite impulse response (FIR) narrow band-stop (notch) filter with non-zero initial conditions, based on infinite impulse response (IIR) prototype filter, is proposed. The filter described in this paper is used to suppress power line noise from ECG signals. In order to reduce the transient response of the proposed FIR notch filter, optimal initial conditions for the filter have been determined. The algorithm for finding the length of the initial conditions vector is presented. The proposed values of the length of initial conditions vector, for several ECG signals and interfering frequencies, are calculated. The proposed filters are tested using various ECG signals. Computer simulations demonstrate that the proposed FIR filters outperform traditional FIR filters with initial conditions set to zero.

Highly narrow rejection bandwidth finite impulse response notch filters for communication

Design of finite impulse response (FIR) notch filters (NFs) with highly narrow rejection bandwidth (RBW) is suggested. RBW is the distance between 3 dB points on the response. Reduction in the RBW is achieved progressively in three stages. In the first stage, an FIR NF is designed from a second order infinite impulse response (IIR) prototype filter. For a given length L of the NF, the authors choose maximum permissible value of ` r ' (the pole length of IIR prototype filter) to achieve very narrow RBW of the FIR filter. In the next stage, by using an amplitude change function (ACF): H ( z )(2 - H ( z )), the designed filter is sharpened. Consequently, the RBW of the resulting NF is reduced to almost half of the earlier value. This reduction of bandwidth makes the resulting NF of length 2 L . In the next stage, RBW can be further reduced by the repeated sharpening of the filter by the same ACF.

Indirect frequency estimation based on second-order adaptive FIR notch filter

This paper deals with estimating the frequency of sinusoidal signal buried in broad band noise. The simple unbiased indirect frequency estimation (IFE) algorithm is proposed for a second-order adaptive finite impulse response (FIR) notch filter with constrained zeros. The technique of estimating input noise variance is employed to remove the bias existing in the estimated filter parameter. Also, the difference equation for the convergence of the expectation of the estimated parameter and the closed-form of steady state estimation mean square error (MSE) are derived. In addition, extensive simulations are conducted to corroborate the efficiency of the proposed estimator with the theoretical analysis.

Direct frequency estimation based adaptive algorithm for a second-order adaptive FIR notch filter

This work deals with the problem of the frequency estimation of a sinusoidal signal corrupted by broad-band noise. The direct frequency estimation based adaptive algorithm for a second-order adaptive finite impulse response (FIR) notch filter (AFNF) is thus proposed. The proposed algorithm employs the bias removal technique to remove the bias existing in the estimated parameter. The performances including the rate of convergence and the mean square error (MSE) can be easily controlled by using only one parameter, i.e., step size parameter. Moreover, the proposed filter is simple to implement and suitable for real-time applications. In addition, the difference equations for the convergence in the mean and mean square, and the closed form expressions for the steady-state estimation bias and MSE are also carried out. Finally, the simulation results are provided to confirm the theoretical analysis.

Fast algorithms for designing variable FIR notch filters

AbstractThe paper presents fast algorithms for designing finite impulse response (FIR) notch filters. The aim is to design a digital FIR notch filter so that the magnitude of the filter has a deep notch at a specified frequency, and as the notch frequency changes, the filter coefficients should be able to track the notch fast in real time. The filter design problem is first converted into a convex optimization problem in the autocorrelation domain. The frequency response of the autocorrelation of the filter impulse response is compared with the desired filter response and the integral square error is minimized with respect to the unknown autocorrelation coefficients. Spectral factorization is used to calculate the coefficients of the filter. In the optimization process, the computational advantage is obtained by exploiting the structure of the Hessian matrix which consists of a Toeplitz plus a Hankel matrix. Two methods have been used for solving the Toeplitz‐plus‐Hankel system of equations. In the first method, the computational time is reduced by using Block–Levinson's recursion for solving the Toeplitz‐plus‐Hankel system of matrices. In the second method, the conjugate gradient method with different preconditioners is used to solve the system. Comparative studies demonstrate the computational advantages of the latter. Both these algorithms have been used to obtain the autocorrelation coefficients of notch filters with different orders. The original filter coefficients are found by spectral factorization and each of these filters have been tested for filtering synthetic as well as real‐life signals. Copyright © 2007 John Wiley & Sons, Ltd.

Closed-form unbiased frequency estimation of a noisy sinusoid using notch filters

In this note, the problem of the frequency estimation of a sinusoid embedded in white noise is considered. The approach used herein is the minimization of the sample variance of the output of constrained notch filters fed by the noisy sinusoid. In particular, this note focuses on closed-form expressions of the frequency estimate, which can be obtained using notch filters having an all-zeros finite-impulse response (FIR) structure. The results presented in this note are as follows: 1) it is shown that the FIR notch filters obtained from standard second-order infinite-impulse response (IIR) filters are inadequate; 2) a new second-order IIR notch filter is proposed, which provides an unbiased estimate of the frequency; 3) the FIR filter obtained from the new IIR filter provides a closed-form unbiased frequency estimate; and 4) the closed-form frequency estimate obtained using the new FIR notch filter asymptotically converges toward the Pisarenko harmonic decomposition estimator and the Yule-Walker estimator.

Chebyshev Design of a Class Of FIR Filters With Frequency EquationConstraints

This paper considers the design of finite impulse response (FIR) filters with equation constraints in the frequency domain and proposes a design algorithm. The design problem is formulated as Chebyshev approximation subject to equation constraints. The optimal filter is proved to have a characteristic property that there exists a set of frequencies including extremal frequencies where the weighted error takes a maximum value, and constraint frequencies where the response takes a given magnitude. According to this property, an orthogonal projection-based Remez exchange algorithm is proposed to solve the constrained Chebyshev design problem. As its application, the algorithm is applied to the design of FIR lowpass filters and notch filters. Simulation examples demonstrate the effectiveness and good performance of the proposed algorithm.