Linear Phase Finite Impulse Response Research Articles

A New Order Tracking Method for Fault Diagnosis of Gearbox under Non-Stationary Working Conditions Based on In Situ Gravity Acceleration Decomposition

Rotational speed measuring is important in order tracking under non-stational working conditions. However, sometimes, encoders or coded discs are not easy to mount due to the limited measurement environment. In this paper, a new in situ gravity acceleration decomposition method (GAD) is proposed for rotational speed estimation, and it is applied in the order tracking scene for fault diagnosis of a gearbox under non-stationary working conditions. In the proposed method, a MEMS accelerometer is locally embedded on the rotating shaft or disc in the tangential direction. The time-varying gravity acceleration component is sensed by the in situ accelerometer during the rotation of the shaft or disc. The GAD method is established to exploit the gravity acceleration component based on the linear-phase finite impulse response (FIR) filter and complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) methods. Then, the phase signal of time-varying gravity acceleration is derived for rotational speed estimations. A motor–shaft–disc experimental setup is established to verify the correctness and effectiveness of the proposed method in comparison to a mounted encoder. The results show that both the estimated average and instantaneous rotational speed agree well with the mounted encoder. Furthermore, both the proposed GAD method and the traditional vibration-based tacholess speed estimation methods are applied in the context of order tracking for fault diagnosis of a gearbox. The results demonstrate the superiority of the proposed method in the detection of tooth spalling faults under non-stationary working conditions.

Enhanced FPGA linear phase FIR filter with amalgam multiplier

ABSTRACT Designing high-performance integrated circuits that balance area, speed, and power is increasingly challenging. This study optimises hardware implementation of FIR filters using an innovative Amalgam Multiplier, minimising resource use without compromising performance. The key challenge in designing signal processing hardware is the multiplier design, which significantly affects efficiency. This study explores integrated circuit optimisation, addressing the delicate balance between area utilisation, speed, and power consumption. Focusing on hardware implementation of Finite Impulse Response (FIR) filters in signal processing, the article starts with a conventional FIR filter design using a standard array multiplier which consumed 1.790 W, with 8 s real-time completion. Then, Linear Phase FIR (LP-FIR) filter is designed using Braun and Dadda Multiplier. LP-FIR filter with Braun multiplier consumed 1.436 W power and 26 s of completion time whereas LP-FIR with Dadda multiplier consumed 1.363 W power and 23 s of completion time. Finally, the implementation of novel LP-FIR enhanced by Amalgam multiplier consumed 0.302 W power and 10.29 s of completion time, marking a significant advancement in integrated circuit design.

To Bag or Not to Bag? How AudioMoth-Based Passive Acoustic Monitoring Is Impacted by Protective Coverings

Bare board AudioMoth recorders offer a low-cost, open-source solution to passive acoustic monitoring (PAM) but need protecting in an enclosure. We were concerned that the choice of enclosure may alter the spectral characteristics of recordings. We focus on polythene bags as the simplest enclosure and assess how their use affects acoustic metrics. Using an anechoic chamber, a series of pure sinusoidal tones from 100 Hz to 20 kHz were recorded on 10 AudioMoth devices and a calibrated Class 1 sound level meter. The recordings were made on bare board AudioMoth devices, as well as after covering them with different bags. Linear phase finite impulse response filters were designed to replicate the frequency response functions between the incident pressure wave and the recorded signals. We applied these filters to ~1000 sound recordings to assess the effects of the AudioMoth and the bags on 19 acoustic metrics. While bare board AudioMoth showed very consistent spectral responses with accentuation in the higher frequencies, bag enclosures led to significant and erratic attenuation inconsistent between frequencies. Few acoustic metrics were insensitive to this uncertainty, rendering index comparisons unreliable. Biases due to enclosures on PAM devices may need to be considered when choosing appropriate acoustic indices for ecological studies. Archived recordings without adequate metadata may potentially produce biased acoustic index values and should be treated cautiously.

Ultrasonic defect detection of high-density polyethylene pipe materials using FIR filtering and block-wise singular value decomposition

Condition monitoring of high-density polyethylene (HDPE) pipes used for fluid and gas transfer is important for the safety of energy conservation and the environment. Ultrasonic phased array imaging methods provide a solution to detect and assess defects in HDPE pipes. However, ultrasonic bulk waves propagating in these viscoelastic media are strongly attenuated, resulting in reduced signal amplitude. In this study, a linear-phase Finite Impulse Response (FIR) filter is used to remove unwanted frequency components from the measured ultrasonic signals to improve the signal-to-noise ratio before applying the imaging algorithm of the total focusing method (TFM). Building upon this, a block-wise singular value decomposition (SVD) technique, which can adaptively determine the singular value cutoff threshold based on each block in the whole TFM image, is used to enhance the obtained TFM image quality. The performance of the combination of FIR filtering and block-wise SVD technique is validated by experimental data of HDPE pipe materials. Results demonstrate that the proposed approach generates good images to provide the detection and characterization of side-drilled holes in HDPE pipe materials.

Multiplication and Accumulation Co-Optimization for Low Complexity FIR Filter Implementation

In multiplierless finite impulse response (FIR) filters, the product accumulation block (PAB) could be the major contributor to hardware complexity, especially for high-order filters. In this paper, an optimization scheme where the constant multiplication block and the PAB are jointly optimized at the bit-level is proposed to minimize the hardware complexity. In the proposed joint optimization, the multiple constant multiplications (MCM) block is rearranged into several MCM sub-blocks. The products are summed locally before accumulation to reduce the word-length of the structural adders. It is shown that the symmetric property of linear phase FIR filters can be utilized in some cases to further reduce the complexity of the constant multiplications. Quantitative analyses are also presented to study the relationship between the optimum group size and the coefficient values as well as the filter orders. It is shown that there is no fixed optimum structure for filters with different coefficient word-lengths and filter orders, and each filter needs to be optimized specifically to achieve the minimum hardware complexity. Implementation results are presented to validate the effectiveness of the proposed method.

Design and Analysis of Linear Phase Finite Impulse Response Filter Using Water Strider Optimization Algorithm in FPGA

Design and Analysis of Linear Phase Finite Impulse Response Filter Using Water Strider Optimization Algorithm in FPGA

Epileptic Spike Detection Using Neural Networks With Linear-Phase Convolutions

To cope with the lack of highly skilled professionals, machine learning with proper signal processing is key for establishing automated diagnostic-aid technologies with which to conduct epileptic electroencephalogram (EEG) testing. In particular, frequency filtering with the appropriate passbands is essential for enhancing the biomarkers-such as epileptic spike waves-that are noted in the EEG. This paper introduces a novel class of neural networks (NNs) that have a bank of linear-phase finite impulse response filters at the first layer as a preprocessor that can behave as bandpass filters that extract biomarkers without destroying waveforms because of a linear-phase condition. Besides, the parameters of the filters are also data-driven. The proposed NNs were trained with a large amount of clinical EEG data, including 15833 epileptic spike waveforms recorded from 50 patients, and their labels were annotated by specialists. In the experiments, we compared three scenarios for the first layer: no preprocessing, discrete wavelet transform, and the proposed data-driven filters. The experimental results show that the trained data-driven filter bank with supervised learning behaves like multiple bandpass filters. In particular, the trained filter passed a frequency band of approximately 10-30 Hz. Moreover, the proposed method detected epileptic spikes, with the area under the receiver operating characteristic curve of 0.967 in the mean of 50 intersubject validations.

A novel approach for optimal design of digital FIR filter using grasshopper optimization algorithm

The idea behind designing digital filters is to compute the optimal filter coefficients such that the magnitude response of the designed matches the ideal frequency response using optimization algorithms. The proposed work employed a recently proposed swarm-based optimization technique, namely, a grasshopper optimization algorithm (GOA) to design a linear phase finite impulse response (FIR) low pass, high pass, band pass , and band stop filters. This proposed algorithm models the behaviour of grasshoppers while seeking food sources to solve optimization problems. For the designing of the FIR filter, an absolute error difference fitness function is used, which is minimized using GOA to obtain optimal filter coefficients. The performance comparison of the proposed work is done with already existing algorithms such as cuckoo search, particle swarm optimization, artificial bee colony to prove its superiority and consistency. It is found that GOA based filter meets the objective efficiently with reduced ripples in pass band and higher attenuation in stop band with least execution time.

Comprehensive Survey of FIR-Based Sample Rate Conversion

Sample rate conversion (SRC) is ubiquitous and critical function of software defined radio and other signal processing systems (speech coding and synthesis, computer simulation of continuous-time systems, etc..). In this paper, we present a survey on linear phase finite impulse response (FIR) based sampling rate conversion. Many different FIR-based SRC solutions exist, such as classical FIR, polyphase, Farrow, cascaded-integrator-comb, and Newton structures. Each one of these solutions is presented differently in the literature, and SRC reference books introducing the subject are often missing hardware implementation aspects. The main objective of this paper is to provide a simple and comprehensive overview of main FIR-based SRC techniques from theoretical to hardware implementation aspects. The state of the art of FIR-based SRC filters is summed-up through a concise derivation of the different solutions from a common root: linear phase FIR filters. Each SRC solution is presented from both theoretical and practical implementation points of view. The paper provides a succinct tutorial that introduces SRC, and helps identifying and implementing the appropriate FIR-based SRC architecture for any given applications.

Least squares linear phase FIR filter design and its VLSI implementation

In this work we present least squares (LS) approach to design linear phase Finite Impulse Response (FIR) filter. Since the design of FIR digital filters is non-analytic, we aim at ideal zero-phase magnitude response and minimize the weighted error in passband and stopbands. The problem of least squares can then be solved non-iteratively by solving system of linear equations. Solution of which yields impulse response that is both real and symmetric. Frequency response of the proposed LS FIR filter shows a flat passband, and higher stop-band attenuation than traditional window based FIR design and comparable attenuation with Parks–McClellan method of the same order. In addition we have implemented LS FIR filter on FPGA based VLSI architectures. Performance evaluation of proposed LS FIR design on VLSI architecture shows comparable throughput, area and power consumption compared to classical filter design approaches.

Optimal maximally decimated <i>M</i>-channel mirrored paraunitary linear phase FIR filter bank design via norm relaxed sequential quadratic programming

It is worth noting that the conventional maximally decimated M-channel mirrored paraunitary linear phase finite impulse response condition is defined in the frequency domain. As the frequency domain is a continuous set, it is expressed as a matrix functional (a continuous function of the frequency) equation. On the other hand, this paper expresses the condition as a finite number of discrete (a set of functions of the sampled frequencies) equations. Besides, this paper proposes to sample the magnitude responses of the filters with the total number of the sampled frequencies being more than the filter lengths. Hence, the frequency selectivities of the filters can be controlled more effectively. This filter bank design problem is formulated as an optimization problem in such a way that the total mirrored paraunitary linear phase error is minimized subject to the specifications on the magnitude responses of the filters at these sampling frequencies. However, this optimization problem is highly nonconvex. To address this difficulty, a norm relaxed sequential quadratic programming approach is applied for finding its local optimal solution. By iterating the above procedures using different initial conditions, a near global optimal solution is obtained. Computer numerical simulation results show that our proposed design outperforms the existing designs.

Type II, III, and IV Linear-Phase FIR Structures Based on Cardinal Filters

Novel structures of type II, III, and IV linear-phase finite impulse response (FIR) systems are proposed. It is constituted of a linear combination of basic sub-filters, called cardinal filters , with weighting coefficients equal to the derivatives of the system amplitude response at a prescribed frequency. Since the cardinal filters can be synthesized via recursive closed-form expressions, regardless of the desired system amplitude response, the proposed structure provides a universal design for arbitrary derivative-constrained linear-phase FIR filters. Design examples of maximally flat filters show that further improvement by combining derivative constraints with the least squared error optimization technique can be obtained.

Sparse Finite Impulse Response Low Pass Filter Design using Improved Firefly Algorithm

In this work, optimal sparse linear phase Finite impulse response filters are designed using swarm intelligence-based Firefly optimization algorithm. Filters are designed to meet the desired specification with fixed and variable sparsity. The objective function is formulated consisting of three parameters, i. e., maximum passband ripple, maximum stopband ripple and stopband attenuation. The effectiveness of the proposed method is evaluated in two stages. In first stage, the designed filters have been compared with non- sparse in terms of deviation in their specification. The Comparative analysis depicts that the proposed approach of sparse linear phase FIR filter design method performs better than the conventional methods without significantly deviating from the desired specification. The proposed designed filter is then implemented on xilinx ISE14.7(Vertex7) design environment and their performance is compared in terms of time delay, resource utilizaion and frequency of operation. In the second stage, designed sparse FIR filters are compared with earlier state of art sparse FIR filters design techniques.

Design of Pipelined IIR Filters Using Two-Stage Frequency-Response Masking Technique

A pipelined, high-speed infinite impulse response (IIR) filter based on the frequency-response masking (FRM) technique has been proposed by Johansson and Wanhammar. In their method, the bandedge shaping filters are a pair of IIR power complementary filters whose ${z}$ -transform functions are functions of ${z} ^{M}$ and the masking filters are linear phase finite impulse response (FIR) filters. The IIR bandedge shaping filters have $M$ delays in the feedback loop and can be pipelined by ${M}$ stages. In this brief, we present a two-stage FRM method for reducing the number of multipliers of the pipelined IIR filter proposed by Johansson and Wanhammar for a given magnitude response specification and a given number of pipeline stages in the feedback loop. In our design, all the subfilters are optimized jointly. We show that our two-stage masking design requires fewer multipliers if the number of pipeline stages in the feedback loop is larger than four.

Variant of the charged system search algorithm for the design of optimal linear phase finite impulse response filters

ABSTRACT Digital signal filtering is one of the prime area which is frequently used in practical applications. In the class of digital filters, the prominent filters include – filters with finite impulse response (FIR) and filters with infinite impulse response (IIR). Low pass, high pass, band pass and band stop filters are the different types of filters that are currently employed for carrying out filtering actions. Filters are used for practical applications to reduce the noise incurred while processing the signals received, whether it may be an audio signal, video signal, bio-medical signal and so on. The key features for the design of filters include the optimization of coefficients and in turn the design of coefficients is based on attaining maximum stop band attenuation with less ripple rates. This paper proposes the soft computing based wavelet concept being introduced in the charged system search algorithm at the updation process. The scaling factor in the updation equation is implemented with a wavelet introduced to improve the exploration and exploitation capability of the algorithm. This introduction of wavelet into the algorithm results in faster convergence of the algorithm and proves its effectiveness in comparison with that of the other approaches as available in the literature.

Design of Sparse FIR Filters With Reduced Effective Length

In this paper, an exchange algorithm is proposed to design sparse linear phase finite impulse response (FIR) filters with reduced effective length. The sparse FIR filter design problem is formally an ${l} _{0}$ -norm minimization problem. This original design problem is re-formulated by encoding the filter coefficients using a binary encoding vector, which represents the locations of the zero and non-zero filter coefficients. An iterative 0-1 exchange process with proper direction control is proposed to propel the minimax approximation error toward the specified upper bound of error for sparsity maximization. The effective length is optimized with a lower priority than sparsity in the proposed algorithm. Simulation results show that the proposed algorithm is superior to the existing algorithms in terms of both sparsity and/or effective length in most cases.

Area- and Power-Efficient Nearly-Linear Phase Response IIR Filter by Iterative Convex Optimization

Low complexity infinite impulse response (IIR) filter design with nearly-linear phase response has attracted considerable attention in recent years due to the substantially high area and power consumption of linear phase finite impulse response (FIR) filter. Compared with the FIR filter, designing an IIR filter with the minimized group delay deviation and low power cost is a challenging topic. In this paper, the non-convex group delay deviation minimization problem for IIR filter design is reformulated into an iterative optimization problem to achieve lower group delay deviation. The hardware complexity of the solution is iteratively reduced by approximating the IIR filter coefficients to maximize the number of eliminable common subexpressions. The headroom for the coefficient adjustment is governed by the gradient of group delay deviation between iterations. Using our proposed design algorithm, a high-order lowpass filter with a minimum stopband attenuation of 60dB can be implemented by a 13-tap IIR filter with a group delay deviation of 0.002 only, as opposed to two linear-phase FIR filters designed by two recent and competitive FIR filter design algorithms with tap number of 51 and 57, respectively. Logic synthesis shows that the proposed IIR design saves 39.4% of the area and 41.8% of power consumption over the FIR solutions. Comparing with the latest nearly-linear phase IIR filter design algorithms, the group delay deviation of the solutions generated by our proposed algorithm are on average 25.5% lower, along with an average area and power savings of 20.5% and 18.4%, respectively, from the logic synthesis results.

Exploiting Coefficient Symmetry in Conventional Polyphase FIR Filters

The conventional polyphase architecture for linear-phase finite impulse response (FIR) filter loses its coefficient symmetry property due to the inefficient arrangement of the filter coefficients among its subfilters. Although, existing polyphase structures can avail the benefits of coefficient symmetry property, at the cost of versatility and complex subfilters arrangement of the conventional polyphase structure. To address these issues, in this paper, we first present the mathematical expressions for inherent characteristics of the conventional polyphase structure. Thereafter, we use these expressions to develop a generalized mathematical framework which exploits coefficient symmetry by retaining the direct use of conventional FIR filter coefficients. Further, the transfer function expressions for the proposed Type-1/transposed Type-1 polyphase structures using coefficient symmetry are derived. The proposed structures can reduce the requirement of multiplier units in polyphase FIR filters by half. We also demonstrate the decimator design using the proposed Type-1 polyphase structure and the interpolator design using the proposed transposed Type-1 polyphase structure. Moreover, the phase and magnitude characteristics of the proposed Type-1/transposed Type-1 polyphase structures are presented. It is revealed via numerical examples that all subfilters of the proposed symmetric polyphase structure possess linear-phase characteristics.

Learning Front-end Filter-bank Parameters using Convolutional Neural Networks for Abnormal Heart Sound Detection.

Automatic heart sound abnormality detection can play a vital role in the early diagnosis of heart diseases, particularly in low-resource settings. The state-of-the-art algorithms for this task utilize a set of Finite Impulse Response (FIR) band-pass filters as a front-end followed by a Convolutional Neural Network (CNN) model. In this work, we propound a novel CNN architecture that integrates the front-end band-pass filters within the network using time-convolution (tConv) layers, which enables the FIR filter-bank parameters to become learnable. Different initialization strategies for the learnable filters, including random parameters and a set of predefined FIR filter-bank coefficients, are examined. Using the proposed tConv layers, we add constraints to the learnable FIR filters to ensure linear and zero phase responses. Experimental evaluations are performed on a balanced 4-fold cross-validation task prepared using the PhysioNet/CinC 2016 dataset. Results demonstrate that the proposed models yield superior performance compared to the state-of-the-art system, while the linear phase FIR filter-bank method provides an absolute improvement of 9.54% over the baseline in terms of an overall accuracy metric.

Design of Digital Differentiator Using the $$L_1$$ L 1 -Method and Swarm Intelligence-Based Optimization Algorithms

In this paper, a novel approach to design the digital linear-phase finite impulse response (FIR) differentiator is introduced. First, the differentiator design problem is formulated using the $$L_1$$ -method. Then, the $$L_1$$ optimality criterion is applied using the Bat algorithm (BA) and Particle swarm optimization (PSO) to further optimize the differentiator design. A novel fitness function is developed based on the $$L_1$$ -error norm which is unique and is liable to produce a flat response. These techniques are developed in order to minimize the non-differentiable fitness function. Finally, the simulation results have been presented for 5th-, 7th- and 11th-order FIR differentiator using the $$L_1$$ -method, PSO- $$L_1$$ and BA- $$L_1$$ . The magnitude response of the designed differentiators is analyzed for different frequency bands on the basis of relative magnitude error computed with respect to the ideal response. All the reported techniques contribute toward superior results, when compared with the traditional gradient-based optimizations, such as the window method, minimax and least-squares approach. In addition, the $$L_1$$ -method yields better results for higher-order designs. Furthermore, the proposed designs are tested on two input signals for their efficient response.