Second-order Infinite Impulse Response Research Articles

A Novel Approach for Realizing Loop-Filter in Low-Distortion Noise-Coupled ΣΔ Modulators

This paper presents an innovative general structure for a single-loop Sigma-Delta ([Formula: see text]) modulator that combines low-distortion and noise-coupled techniques to achieve high-resolution for low-power applications. The low-distortion technique adjusts the signal transfer function of the proposed structure to unity, while the noise-coupled technique enhances the order of quantization noise-shaping at the modulator output. These techniques were incorporated into the design to increase the modulator order without requiring additional operational amplifiers during its circuit implementation, resulting in a low-power modulator compared to similar structures. To reduce the number of required amplifiers, a second-order infinite impulse response (IIR) filter was used in the modulator loop filter, in place of two integrators. To assess the proposed structure’s performance, a third-order modulator sample was implemented and simulated for speech recognition applications, specifically, digital hearing aids, using 180[Formula: see text]nm complementary metal oxide semiconductor (CMOS) technology. The results indicate that for a third structure with a sampling rate of 64, an input sine signal of −6[Formula: see text]dBFS and a sampling frequency of 2.56[Formula: see text]MHz, the signal to noise plus distortion (SNDR) was 81.9[Formula: see text]dB, and the dynamic range (DR) was 88[Formula: see text]dB for a 20[Formula: see text]KHz bandwidth. The modulator’s power consumption was 126.9[Formula: see text][Formula: see text]W. Circuit and system-level simulations demonstrate the effectiveness of the proposed method.

Uncertainty Constraint on Headphone Secondary Path Function for Designing Cascade Biquad Feedback Controller with Improved Noise Reduction Performance

The uncertainty in the secondary path of active noise control (ANC) headphones affects the waterbed effect and stability of the feedback system. This study focuses on the uncertainty of the secondary path when real users wear headphones and proposes a new uncertainty constraint based on the measured results of the secondary path transfer function under different wearing conditions of a dummy head and limited subjects. This constraint and a cascaded second-order infinite impulse response filter with fixed coefficients are used to formulate a control strategic function, which is optimized using the Improved Grey Wolf Optimizer (IGWO) algorithm to obtain the optimal controller with better noise reduction performance. The proposed method and simulation model are validated based on the experimental test results. The results demonstrate that the safety factor and waterbed suppressing factor contained in the proposed uncertainty constraint ensure more stable noise reduction and effective suppression of the waterbed effect for new subjects without a priori data.

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.

Real-time notch filtering based on the modified subspace-based high-resolution frequency estimator

This paper presents the real-time notch filtering based on a modified subspace-based high-resolution frequency estimator. The modified subspace-based frequency estimator is proposed based on the propagator using total least squares (TLS) to enhance the robustness to noise, which can be extended to the recursive implementation using data projection method (DPM). In addition, a subspace-based amplitude estimation method is proposed based on the available frequency estimates. For notch filtering, a second-order infinite impulse response (IIR) notch filter is directly designed in the discrete-time domain with given notch frequency and notch bandwidth. The performance of the proposed method is validated through numerical simulations and a real-world example.

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.

Hardware-Aware Design of Multiplierless Second-Order IIR Filters With Minimum Adders

In this work we optimally solve the problem of multiplierless design of second-order Infinite Impulse Response filters with minimum number of adders. Given a frequency specification, we design a stable direct form filter with hardware-aware fixed-point coefficients where all multiplications are replaced by bit shifts and additions. The coefficient design, quantization and implementation, typically conducted independently, are now gathered into one global optimization problem, modeled through integer linear programming and efficiently solved using generic solvers. The optimal filters are implemented within the FloPoCo IP core generator and synthesized for field programmable gate arrays (FPGAs) and application specific integrated circuits (ASICs). With respect to state-of-the-art three-step filter design methods, our one-step design approach achieves, on average, 48% reduction in number of lookup tables, 27% delay reduction and 57% reduction in power on FPGAs. ASICs experiment illustrate similar 48% reduction in circuit area, 27% delay reduction and 65% power reduction for a 14 nm ASIC.

On Minimal Second-order IIR Bandpass Filters with Constrained Poles and Zeros

In this paper, several forms of infinite impulse response (IIR) bandpass filters with constrained poles and zeros are presented and compared. The comparison includes the filter structure, the frequency ranges and a number of controlled parameters that affect computational efforts. Using the relationship between bandpass and notch filters, the two presented filters were originally developed for notch filters. This paper also proposes a second-order IIR bandpass filter structure that constrains poles and zeros and can be used as a minimal parameter adaptive digital second-order filter. The proposed filter has a wider frequency range and more flexibility in the range values of the adaptation parameters.

FPGA-based Implementation of IIR Filter for Real-Time Noise Reduction in Signal

Filtering of unwanted frequencies represents the main aspect of digital signal processing (DSP) in any modern communication system. The main role of the filter is to perform attenuation of certain frequencies and pass only frequencies of interest. In a DSP system, sampled or discrete-time signals are processed by digital filters using different mathematical operations. Digital filters are commonly categorized as Finite Impulse Response (FIR) and Infinite Impulse Response (IIR). This research focuses on the full VHDL implementation of digital second-order lowpass IIR filter for reducing the noisy frequencies on the FPGA board. The initial step is to determine, from continuous time domain function, the transfer function in the complex {s} domain, then map transfer function in complex {z} domain and finally calculate the difference equation in discrete-time domain of the system with adequate coefficients. Prior to the FPGA implementation, the IIR filter is tested in MATLAB using a signal with mixed frequencies and signal with randomly generated noise. The digital implementation is completed by using fixed-point binary vectors and clocked processes.

Personal audio system for neckband headset with low computational complexity.

Personal audio systems have been developed based on various approaches with the goal of synthesizing an isolated sound zone that avoids disturbing others in different locations. In this work, a near-field solution for a neckband headset using three loudspeakers positioned close to each ear is proposed. In particular, it is an attempt to derive a simple multichannel filter for reducing the computational cost in mobile devices. Unlike super-directive beamforming techniques, the controlled radiation pattern is not highly directional but can boost the near-field sound, thereby providing an extra sound level difference between the listener's ear locations and far-field surrounding areas. For this purpose, a multichannel filter is designed using a conventional pressure matching technique for reproducing a target signal at the ear location while suppressing sound radiation to a far-field. It is shown that the optimal filter weights can be successfully approximated in the form of a simple broadside differential array pattern. The simplified filter structure can be realized using only two second-order infinite impulse response filters for driving the middle and two side loudspeakers. Through various simulations and experiments, it is demonstrated that the proposed solution can effectively realize a personal audio system with a minimal loss of sound isolation performance.

General method to mitigate the continuous wave interference and narrowband interference for GNSS receivers

A low-complexity method based on the second-order direct infinite impulse response (IIR) notch and its cascaded form for global navigation satellite systems (GNSSs) is proposed to mitigate the continuous wave interference (CWI) and narrowband interference (NI) as well as their mixed interference. The number of the cascaded stages is selected by the bandwidth of NI as well as that of the second-order direct IIR notch. The parameters of the second-order direct IIR notch and the bandwidth of NI are determined by the fast Fourier transform. To evaluate the performance of the proposed method, the authors conduct the simulation experiment and real-data experiment. In each experiment, the CWI scenario, the NI scenario and the mixed interference of CWI and NI scenarios are verified. The results of experiments depict the effectiveness of the introduced method.

A Systematic Approach via IIR Filters for Enhancing the Robustness of LCL-Type Shunt Active Power Filters to Grid Impedance

A dual-loop current control method (grid current loop and inverter-side current loop) is promising for digitally controlled LCL -type shunt active power filters (APFs), due to its inherent active damping effect for LCL resonance. However, the damping region is only up to one-sixth of the sampling frequency $(f_{s}/ 6)$ , which leads to limited system robustness against grid impedance variation at the point of common coupling (PCC). Hence, in this study, the robustness of such control is discussed through mathematic derivations and diagram analysis, which reveals that both the system delays and PCC voltage feedforward affect the system robustness. On the basis of theoretical analysis, a systematic approach via infinite impulse response (IIR) filters has been proposed for enhancing the robustness of grid impedance. Thereof, a second-order IIR filter-based inverter-side current feedback is proposed to widen the damping region up to almost the Nyquist frequency $(f_{s}/ 2)$ , while a band-stop IIR filter-based PCC voltage feedforward is proposed to achieve the superior stability margins under a large grid impedance in comparison with unit feedforward. Finally, experimental results on a 30-kVA APF prototype have verified the effectiveness of the proposed approach.

Realization of Second-Order Structure of Recursive Algorithm for Discrete Cosine Transform

A computational and hardware-efficient second-order infinite impulse response filter structure is proposed in this paper. It can compute discrete cosine transform (DCT) with improved processing speed and is valid for N = 2r, where N is the length of the input sequence and r > 1. A new algorithm is also proposed in this paper which is an improvement over previously reported algorithms in the literature. The proposed algorithm reduces the total number of real multiplications and additions in comparison with the existing algorithms. Using the suggested algorithm, computational cycles required to compute a DCT coefficient are less which further reduces the truncation error while processing a long length of input data.

IIR Filter Architectures with Truncation Error Feedback for ECG Signal Processing

This work proposes fixed-point hardware architectures for two IIR filters, focusing on design specifications for ECG signal processing, using the truncation error feedback (TEF) to attenuate errors caused by truncation operations inside these recursive structures. The TEF is represented by modulo operation followed by a unit-delay operator and multiplication by a coefficient. In this work, the proposed TEF core consists of a hardware structure based on delay, right-shift and modulo operations. The TEF approach is applied to sequential and parallel IIR filter architectures with fixed and adaptive coefficients. The first structure comprises a first-order high-pass filter applied to attenuate low frequencies of the electrocardiogram (ECG) signal. The second one is a second-order infinite impulse response (IIR) adaptive notch filter used to attenuate power line interference signals. All dedicated architectures were described and simulated using VHDL and synthesized in Cadence environment using the 45 nm Nangate Open Cell Library to verify the results of the area, delay and power metrics. A simulated ECG signal was used as input to check the functionality of the filters. Our results indicate that the TEF approach was useful for both high-pass filter (HPF) and adaptive notch filter (ANF), and it can be a significant strategy to meet design specifications and dynamic performance of fixed-point digital filters. For the synthesis analysis, both HPF and ANF sequential filters had lower power and cell area figures but presented higher normalized power per sample and delay. In summation, the TEF approach enabled the use of fixed-point filters for ECG filtering without degrading their dynamic performance or increasing noise caused by truncation.

Улучшение синхронизации параллельного активного силового фильтра с питающей сетью

The paper reviews the features of the synchronization system for three-phase shunt active power filters. It suggests an improved more stable design of a synchronization system with. The synchronization system has been improved by introducing bandpass filters in order to filter the input signals of a conventional phase-locked loop synchronization system. The design of the second-order infinite impulse response bandpass filter has been elaborated. The simulation of the three-phase shunt active power filter with the proposed synchronization system was carried out. The simulation results were verified by the laboratory prototype of a three-phase active power filter.

Modified second-order nonlinear infinite impulse response (IIR) filter for equalizing frequency response and compensating nonlinear distortions of electrodynamic loudspeaker

In this paper, we propose a modified second-order nonlinear infinite impulse response (IIR) filter for equalizing the frequency response and compensating nonlinear distortions of an electrodynamic loudspeaker. A problem of electrodynamic loudspeakers is the generation of nonlinear distortions, which degrade the sound quality. One of the approaches to reducing nonlinear distortions is to use a second-order nonlinear IIR filter. This filter is based on an equivalent circuit model of an electrodynamic loudspeaker and its coefficients are determined by physical parameters. However, it is difficult to compensate nonlinear distortions when a loudspeaker has a high Q factor at the lowest resonance frequency, at which the displacement of the diaphragm and nonlinear distortions become large. The Q factor determines the linear frequency response of the electrodynamic loudspeaker. Although it is necessary to compensate the Q factor of the loudspeaker, a nonlinear IIR filter cannot compensate the Q factor because it does not have a linear filtering feature. In this paper, we propose a modified second-order nonlinear IIR filter that can not only compensate the nonlinear distortions caused by the nonlinearities of the force factor and stiffness but also equalize the frequency response by employing the linear characteristics of the loudspeaker with the desired Q factor. Experimental results show that the proposed filter can compensate the linear and nonlinear distortions more effectively than a conventional filter.

Ultra-wideband microwave photonic filter with a high Q-factor using a semiconductor optical amplifier.

An ultra-wideband microwave photonic filter (MPF) with a high quality (Q)-factor based on the birefringence effects in a semiconductor optical amplifier (SOA) is presented, and the theoretical fundamentals of the design are explained. The proposed MPF along orthogonal polarization in an active loop operates at up to a Ku-band and provides a tunable free spectral range from 15.44 to 19.44 GHz by controlling the SOA injection current. A prototype of the equivalent second-order infinite impulse response filter with a Q-factor over 6300 and a rejection ration exceeding 41 dB is experimentally demonstrated.

Modified 2nd-order nonlinear infinite impulse response (IIR) filter for compensating sharpness and nonlinear distortions of electrodynamic loudspeakers

Electrodynamic loudspeakers generate the nonlinear distortions and degrade the sound quality. This is because the nonlinearity of electrodynamic loudspeaker is caused by the large displacement of the diaphragm, in particular, around the lowest resonance frequency. One of the compensation methods for the nonlinear distortions is using mirror filter. This filter is derived from the linear and nonlinear differential equations and designed by second-order nonlinear IIR filter or third-order nonlinear IIR filter. The coefficients of these filters are determined by the physical parameters of the loudspeaker. However, it is difficult to compensate the nonlinear distortions when the sharpness of the loudspeaker is high at the lowest resonance frequency because of large displacement of the diaphragm. Although it is required to compensate the sharpness of the loudspeaker, second-order nonlinear IIR filter cannot compensate the sharpness because of the compensation principle, i.e., this filter adds the nonlinear signal into the input signal and does not include the linear filtering. This paper proposes a modified second-order nonlinear IIR filter that can compensate not only the sharpness but also the lowest resonance frequency. The difference between the conventional and proposed filter structures is only coefficients. Experimental results show the effectiveness of the proposed filter.

Configurable Folded IIR Filter Design

This brief proposes an efficient very-large-scale integration architecture for folded configurable infinite-impulse response (IIR) filter design, which is used in modern real-time digital signal processing applications such as loudspeaker equalization. The proposed configurable sixth-order IIR filter is designed with three cascaded second-order IIR filters, and the same is used to perform one sixth-order or three second-order or one fourth-order and one second-order IIR filter operations in parallel, where floating-point multiply–accumulate circuit (MAC) is used to design each second-order IIR filter. The proposed sixth-order IIR filter achieves a 58.4% reduction in energy per operation compared with conventional MAC-based architecture using 45-nm technology.

Complex conjugate poles implementation in discrete‐time charge‐domain filters

A discrete-time charge-domain filter is proposed, which can realise complex conjugate poles in the transfer function of the filter. By employing a second transconductance in the feedback path of a second-order infinite impulse response charge-domain filter, it is proved that the filter topology is capable of implementing complex poles. This method makes charge-sampling filters more efficient in designing frequency-domain filters where they can be used to synthesise any type of filter structures such as Butterworth, Chebyshev and so on.

Design of GPS Anti-Jamming Systems Using Adaptive Notch Filters

Continuous wave interferences (CWIs) can reduce the positioning accuracy of a Global Positioning System (GPS) receiver and even paralyze its normal operation. Therefore, we have designed a low-cost anti-jamming system to combat CWIs for GPS receivers. The anti-jamming system comprises cascaded CWI-detectable adaptive notch filter (ANF) modules, and each module is able to mitigate one CWI. The ANF module is composed of a second-order infinite-impulse response (IIR) filter with a lattice structure. The proposed ANF detects the existence of the CWI and estimates its power by exploiting the statistic value and internal state associated with the IIR filter, respectively. The impact of the ANF module on the acquisition and tracking loops is analyzed. Properly controlling the $-$ 3-dB bandwidth of the ANF module allows its impact to be neglected. Moreover, more modules can be cascaded to deal with multiple CWIs. We have also designed an adaptation algorithm for the ANF modules and proven that the module can adaptively notch the strongest CWI at its input. This merit enables us to notch the primary CWIs with a limited number of ANF modules. Simulation results show that our approach considerably outperforms related works in both CWI detection and rejection capabilities.