Infinite Impulse Response Notch Filter Research Articles

FPGA Implementation of IIR Notch and Anti-Notch Filters With an Application to Localization of Protein Hot-Spots.

In this paper, high-speed second-order infinite impulse response (IIR) notch filter (NF) and anti-notch filter (ANF) are designed and realized on hardware. The improvement in speed of operation for the NF is then achieved by using the re-timing concept. The ANF is designed to specify a stability margin and minimize the amplitude area. Next, an improved approach is proposed for the detection of protein hot-spot locations using the designed second-order IIR ANF. The analytical and experimental results reported in this paper show that the proposed approach provides better hot-spot prediction compared to the reported classical filtering techniques based on the IIR Chebyshev filter and S-transform. The proposed approach also yields consistency in prediction hot-spots compared to the results based on biological methodologies. Furthermore, the presented technique reveals some new "potential" hot-spots. The proposed filters are simulated and synthesized using the Xilinx Vivado 18.3 software platform with Zynq-7000 Series (ZedBoard Zynq Evaluation and Development Kit xc7z020clg484-1) FPGA family.

A robust feedforward hybrid active noise control system with online secondary‐path modelling

In this study, a robust feedforward hybrid active noise control (ANC) system with online secondary-path modelling (SPM) is proposed that is capable of not only effectively suppressing the broadband and narrowband noise components but also tracking the secondary path (SP) variations. An finite impulse response online SPM subsystem as well as an efficient decoupling filter are included in the proposed feedforward hybrid ANC (HANC) system. The decoupling filter is a parallel-form bandpass filter bank that consists of multiple bandpass filters that are derived from the second-order infinite impulse response notch filters. It takes the residual noise as its input and separates the broadband component from the narrowband component, with the former used as not only a desired signal for the SPM but also as an error signal for updating the broadband sub-controller, whereas the latter adapted simultaneously to scale the auxiliary white Gaussian noise and to update the narrowband sub-controller. Extensive simulations are conducted with both the synthetic and real SPs as well as the synthetic and real noise signals that are generated by a large-scale factory cutting machine (strand-cutter) to demonstrate the advantages and effectiveness of the proposed feedforward HANC system. Comparisons are also demonstrated with the original HANC system as well as its directly extended version with an online SPM subsystem.

Single and Multiple Continuous-Wave Interference Suppression Using Adaptive IIR Notch Filters Based on Direct-Form Structure in a QPSK Communication System

The removal filter coefficients in this technique are dependent on the jammer’s power and its Instantaneous Frequency (IF) information, which can both be obtained in the time–frequency domain (adaptive filtering techniques). The dependence of the removing/reducing filter characteristics on the interference power is critical, as it allows an optimal trade-off between removal interference and the amount of self-noise generated by the filter. This trade-off is bounded by the two extreme cases of no notch filter (no self-noise) and full suppression (k1 = 1) for both low- and high-power jammer values. In this paper, a cascade second-order adaptive direct Infinite Impulse Response (IIR) Notch Filter (NF) with a gradient-based algorithm to suppress the Continuous-Wave (CW and MCW) interference is proposed for maximizing the receiver Signal-to-Noise Ratio (SNR) in a Quadrature Phase-Shift Keying (QPSK)-modulated signal. The suppression approach consists of two Adaptive IIR NFs (ANFs) based on a direct-form structure: the Hd1(z) and Hd1(z). The proposal in this work presents a low-complexity Time-Domain (TD) algorithm for controlling the update filter coefficient and notch depth. Simulation results demonstrate that the proposed approach represents an effective method for removing/reducing the impacts of CWI/MCWI, resulting in improved system performance for low- and high-power jammer values when compared with the case of full suppression (k1 = 1); furthermore, it also improves the notch filter’s output SNR for a given Jamming-to-Signal Ratio (JSR) value and Bit Error Ratio (BER) performance. For example, the SNR output of the proposed IIR NF was enhanced by 7 dB versus the case without a filter when Eb/No = 15 dB and JSR = −5 dB. The proposed method can detect and mitigate weak and strong jamming with JSR values ranging from −30 to 40 dB, and can track the hopping frequency interference. Moreover, an improved BER performance is seen as compared to the case without an IIR NF.

Time-Varying IIR Notch Filter with Reduced Transient Response Based on the Bézier Curve Pole Radius Variability

In this paper a concept of the second order digital infinite impulse response narrow band-reject filter with reduced transient response is proposed. In order to suppress the transient response of the considered infinite impulse response (IIR) notch filter its pole radius is temporarily varied in time using the Bézier parametric curve. Computer simulations verifying the effectiveness of the proposed pole-radius-varying notch filter are presented and compared to the performance of the traditional time-invariant filter using ECG signals distorted by unwanted powerline interference.

New GPS anti‐jamming system based on multiple short‐time Fourier transform

In this study, an enhanced short-time Fourier transform (STFT)-based jamming mitigation system which employs several windows to increase time–frequency (t–f) plane resolution is proposed. A technique for employing near-optimum windows is also proposed. It is observed that selection of these windows leads to increasing the resolution of the t–f representation. An infinite impulse-response notch filter is employed for jamming removal process. Performance of the proposed method is evaluated by a set of measured global positioning system data. It is compared with conventional STFT-based algorithms reported in literature.

Real-time estimation of respiratory rate from a photoplethysmogram using an adaptive lattice notch filter

BackgroundMany researchers have attempted to acquire respiratory rate (RR) information from a photoplethysmogram (PPG) because respiration affects the waveform of the PPG. However, most of these methods were difficult to operate in real-time because of their complexity or computational requirements. From these needs, we attempted to develop a method to estimate RR from a PPG with a light computational burden.MethodsTo obtain RR information, we adopt a sequential filtering structure and frequency estimation technique, which extracts a dominant frequency from a given signal. In particular, we used an adaptive lattice notch filter (ALNF) to estimate RR from a PPG along with an additional heart rate that is utilized as an adaptation parameter of our method. Furthermore, we designed a sequential infinite impulse response (IIR) notch filtering system (i.e., harmonic IIR notch filter) to eliminate the cardiac component and its harmonics from the PPG. We compared the proposed method with Burg’s AR modeling method, which is widely used to estimate RR from a PPG, using open-source data and measured data.ResultsBy using a statistical test, it was determined that our adaptive lattice-type respiratory rate estimator (ALRE) was significantly more accurate than Burg’s AR model method (p <0.0001). Furthermore, the ALRE’s tracking performance was better than that of Burg’s method, and the variances of its estimates were smaller than those of Burg’s method.ConclusionsIn short, our method showed a better performance than Burg’s AR modeling method for real-time applications.

Mitigation of Periodic Impulsive Noise in OFDM-Based Power-Line Communications

This paper presents a novel approach to mitigate the periodic impulsive noise before the synchronization of the orthogonal frequency-division multiplexing (OFDM)-based power-line communications (PLC) system. The proposed algorithm is employed to detect the periodic impulsive noise and then suppresses the periodic impulsive noise with an adaptive infinite impulse response (IIR) notch filter before the synchronization of the system, finally compensating the distortion of received signals brought by the IIR notch filter. Subsequently, the periodic impulsive noise mitigation algorithm is simulated and implemented in the PLC receiver's physical layer. Finally, the proposed algorithm is verified in field-programmable gate array and tested in the indoor PLC network. The simulation and field trial results show that the proposed periodic impulsive noise mitigation technique is simple and effective for the narrowband OFDM-based PLC system, such as the application of automatic meter reading.

Time-efficient removal of power-line noise from EMG signals using IIR notch filters with non-zero initial conditions

Power-line interference is always a problem when biopotential signals are recorded. This paper presents a technique for time-efficient power-line interference suppression from EMG signals using digital IIR (Infinite Impulse Response) notch filters with reduced transient response. The reduction of the transient response is obtained by finding optimal non-zero initial conditions for the considered notch filters. Simulations verifying the effectiveness of the proposed technique are presented and compared with the performance of the traditional notch filters with zero initial conditions using EMG signal with unwanted sinusoidal interferences as a study case.

A hybrid approach to the simultaneous eliminating of power-line interference and associated ringing artifacts in electrocardiograms

BackgroundThe second-order, infinite impulse response notch filter is widely used to remove electrical power line noise in electrocardiograms (ECGs). However this filtering process often introduces spurious ringing artifacts in the vicinity of raw signal with sharp transitions. It is challenging to simultaneously remove these two types of noise without losing vital information about cardiac activities.ObjectiveOur objective is to devise a method to remove the power-line interference without introducing artifacts nor losing vital information. To this end we have developed the "hybrid approach" involving two-sided filtration and multi-iterative approximation techniques. The two-sided filtration technique can suppress the interference but some cardiac components are lost. The lost information can be restored using multi-iterative approximation technique.ResultsFor evaluation, four artificial data sets, each including 91 ECGs of different heart rates, were generated by a dynamical model. Four publicly-accessible sets of clinical data (MIT-BIH Arrhythmia, QT, PTB Diagnostic ECG, and T-Wave Alternans Challenge Databases) were also selected. Our new hybrid approach and the existing method were tested with these two types of signal under various pre-determined conditions. In contrast with the existing method, the hybrid approach can provide more than 27.40 dB and 37.77 dB reduction in signal distortion for 95% and 60% of artificial ECGs respectively; it can provide in excess of 11.78 dB and 17.48 dB reduction in distortion for 95% and 60% of these real records respectively.ConclusionsOverall, a significant reduction in signal distortion is demonstrated. These test results indicate that the newly proposed approach outperforms the traditional method assessed on both the artificial and clinical ECGs and suggest it could be of practical use for clinicians in the future.

Pulse compression technique for simultaneous HIFU surgery and ultrasonic imaging: A preliminary study

In an ultrasound image-guided High Intensity Focused Ultrasound (HIFU) surgery, reflected HIFU waves received by an imaging transducer should be suppressed for real-time simultaneous imaging and therapy. In this paper, we investigate the feasibility of pulse compression scheme combined with notch filtering in order to minimize these HIFU interference signals. A chirp signal modulated by the Dolph–Chebyshev window with 3–9MHz frequency sweep range is used for B-mode imaging and 4MHz continuous wave is used for HIFU. The second order infinite impulse response notch filters are employed to suppress reflected HIFU waves whose center frequencies are 4MHz and 8MHz. The prototype integrated HIFU/imaging transducer that composed of three rectangular elements with a spherically con-focused aperture was fabricated. The center element has the ability to transmit and receive 6MHz imaging signals and two outer elements are only used for transmitting 4MHz continuous HIFU wave. When the chirp signal and 4MHz HIFU wave are simultaneously transmitted to the target, the reflected chirp signals mixed with 4MHz and 8MHz HIFU waves are detected by the imaging transducer. After the application of notch filtering with pulse compression process, HIFU interference waves in this mixed signal are significantly reduced while maintaining original imaging signal. In the single scanline test using a strong reflector, the amplitude of the reflected HIFU wave is reduced to −45dB. In vitro test, with a sliced porcine muscle shows that the speckle pattern of the restored B-mode image is close to that of the original image. These preliminary results demonstrate the potential for the pulse compression scheme with notch filtering to achieve real-time ultrasound image-guided HIFU surgery.

BER of OFDM System with Multiple NBI Rejection Cascade Complex Coefficient Adaptive IIR Notch Filter

In this paper, rejection of multiple narrowband interferers in a binary phase shift keying modulated orthogonal frequency division multiplexing (BPSK-OFDM) system is investigated. The BPSK-OFDM system in consideration operates in an additive white Gaussian noise (AWGN) channel. A cascade complex coefficient adaptive infinite impulse response (IIR) notch filter with gradient-based algorithm is used to reject the interferers. Bit error ratio (BER) performance of the system is studied and a general closed-form expression is derived assuming negligible steady-state leakage NBI and by estimating the decision variable as Gaussian distributed based on Central Limit Theorem (CLT). Dependence of the BER performance on the notch bandwidth coefficient is demonstrated by the analysis. Extensive simulation results are included to substantiate accuracy of the analysis.

Design of three-dimensional adaptive IIR notch filters

This paper investigates a realization of a three-dimensional (3-D) adaptive notch filter. The procedures are mainly divided into two parts: frequency-detecting and sinusoidal interference removal. The detections are based on adaptive line enhancer on infinite impulse response (IIR) lattice structure. In the interference removal part, a non-separable version of a 3-D notch filter is effectively applied. The magnitude response of a 3-D adaptive IIR notch filter is illustrated. At the end of the paper, the implementation of an IIR notch filter on a 3-D image is also conducted in order to show how to remove a sinusoidal interference superimposed on a 3-D image.

Closed-form real single-tone frequency estimator based on a normalized IIR notch filter

A novel unbiased frequency estimator for a single real-valued sinusoid in white noise is proposed, which is based on a normalized second-order infinite impulse response (IIR) notch filter, and can be seen as an extension of the Pisarenko harmonic decomposer (PHD) estimator. The new estimator inherits the simplicity of the PHD estimator and the high accuracy and selectivity achieved by an IIR filter. As the coefficient determining the pole angle of the IIR notch filter depends on the unknown frequency value, an iterative scheme is proposed in which this coefficient is computed from the frequency estimate from the previous iteration. An analytic expression for the mean square error at each iteration is derived. Simulation results show that this iterative method can approach the Cramer–Rao lower bound in a few iterations under different signal to noise ratio levels, provided that the data record length is sufficiently large.

Novel adaptive IIR filter for frequency estimation and tracking [DSP Tips&amp;Tricks

In many applications, a sinusoidal signal may be subjected to nonlinear effects in which possible harmonic frequency components are generated. In such an environment, we may want to estimate (track) the signal's fundamental frequency as well as any harmonic frequencies. Using a secondorder notch filter to estimate fundamental and harmonic frequencies is insufficient since it only accommodates one frequency component. On the other hand, applying a higher-order infinite impulse response (IIR) notch filter may not be efficient due to adopting multiple adaptive filter coefficients. In this article, we present a novel adaptive harmonic IIR notch filter with a single adaptive coefficient to efficiently perform frequency estimation and tracking in a harmonic frequency environment. Furthermore, we devise a simple scheme to select the initial filter coefficient to insure algorithm convergence to its global minimum error.

Tracking Analysis of Complex Adaptive IIR Notch Filter for a Linear Chirp Signal

This paper analyzes frequency tracking characteristics of a complex-coefficient adaptive infinite impulse response (IIR) notch filter with a simplified gradient-based algorithm. The input signal to the complex notch filter is a complex linear chirp embedded in a complex zero-mean white Gaussian noise. The analysis starts with derivation of a first-order real-coefficient difference equation with respect to steady-state instantaneous frequency tracking error. Closed-form expression for frequency tracking mean square error (MSE) is then derived from the difference equation. Lastly, closed-form expressions for optimum notch bandwidth coefficient and step size constant that minimize the frequency tracking MSE are derived. Computer simulations are presented to validate the analysis.

Adaptive IIR notch filters based on new error criteria

Modified indirect and direct plain gradient (MIPG and MDPG) algorithms using new error criteria for second-order adaptive IIR (infinite-impulse response) notch filters (ANFs) with constrained poles and zeros are proposed in this paper. The proposed techniques are based on modifying error functions of the standard indirect and direct ANFs. In this work, the proposed error criteria are modified as the mean value of the product of the two signals which are, respectively, produced by the FIR (finite-impulse response) and IIR sections of the ANFs. Due to a non-zero slope straight line-like characteristic of the new cost functions, the gradient based adaptive algorithm rapidly converges to an optimum solution resulting in faster convergence speed than that of the conventional method. The closed form expressions for steady-state estimation bias and mean square error (MSE) of the proposed algorithms are also carried out. In addition, extensive simulations of the proposed algorithms compared to other methods are provided to support the theoretical analyses. Although, there are some limitations in the proposed algorithms, however, the demonstrated results obtained from tested algorithms at the same condition confirm that the proposed MIPG and MDPG algorithms are superior to others in convergent speed.

Adaptive IIR Filters for Single Interference Suppression in a BPSK DS CDMA System In Rayleigh Fading Channel

In this paper, effect of a single narrow-band interference (NBI) on bit error rate (BER) performance for a binary phase shift keying (BPSK) synchronous direct-sequence code-division multiple access (DS CDMA) communication system operating in a frequency nonselective Rayleigh fading channel is analyzed. Second-order adaptive infinite impulseresponse (IIR) notch filters with plain gradient algorithm (GA) for suppression of NBI in the DS CDMA system are proposed. A general closed-form BER expression for the DS CDMA system with NBI suppression second order adaptive IIR notch filters is derived based on the standard Gaussian approximation (SGA) method. BER expressions are then derived for the allpass filter-based adaptive IIR notch filter and adaptive IIR notch filter with constrained poles and zeros, the two structures that are commonly found in literature. It is observed that both adaptive IIR notch filter structures exhibit comparable BER performance. Extensive computer simulation results are presented to verify the accuracy and limitations of the analysis.

Recursive least squares-like algorithms for the adaptive second-order lattice notch filter

Two new adaptive second-order infinite impulse response (IIR) notch filters with fast convergence rate, accurate estimation of notch frequency, and modest realization complexity are proposed in this paper. It is proven that the optimum filter coefficient can be determined by using the minimum output energy (MOE) criterion. Based on it, a simplified equivalent adaptive system is derived, and two recursive least squares (RLS)-like algorithms are presented to adaptively estimate the filter coefficient. Extensive simulations show the effectiveness and robustness of the new adaptive IIR notch filters.

Performance Analyses of Adaptive IIR Notch Filters Using a PSD-Based Approach

In this letter we present steady-state analyses of a gradient algorithm (GA) for second-order adaptive infinite impulse response (IIR) notch filters. A method for deriving more accurate estimation mean square error (MSE) expressions than the recently proposed method is presented. The method is based on the estimation error power spectral density (PSD). Moreover, an expression for the estimation bias for the adaptive IIR notch filter with constrained poles and zeros is shown to be obtained from the estimation MSE expression. Simulations are presented to confirm the validity of the analyses.

Statistical performance of the memoryless nonlinear gradient algorithm for the constrained adaptive IIR notch filter

Gradient-type algorithms for the adaptive infinite-impulse response (IIR) notch filters are very attractive in terms of both performance and computational requirements for various real-life applications. This paper presents, in detail, a statistical analysis of the memoryless nonlinear gradient (MNG) algorithm applied to the well-known second-order adaptive IIR notch filter with constrained poles and zeros. This analysis is based on a proper use of Taylor series expansion and nonlinearization of output signals of the notch and gradient filters. Two difference equations are derived first for the convergence in the mean and mean square senses, respectively. Two closed-form expressions, one for the steady-state estimation bias and the other for the mean-square error, are then derived based on the difference equations, with the former valid for both fast and slow adaptations and the latter valid for slow adaptation only. A closed-form coarse stability bound for the step size parameter of the algorithm is also derived. Extensive simulations are performed to reveal the validity and limitations of the analytical findings. Comparisons between the MNG and the conventional plain gradient algorithm are also made.