Linear-phase FIR Filters Research Articles

Order Estimation of Linear-Phase FIR Filters for DAC Equalization in Multiple Nyquist Bands

Order Estimation of Linear-Phase FIR Filters for DAC Equalization in Multiple Nyquist Bands

Design of nonlinear phase prototype filter based on coefficients symmetry for UFMC communication system

One of the candidates for short burst communication is universal filtering multicarrier (UFMC), which applies filters in each sub-band to reduce intercarrier interference. Compared with the linear phase FIR filter (LPFF), prototyping a nonlinear phase FIR filter (NLPFF) as the UFMC filter can benefit system performance by improving the filter magnitude response. However, the benefit, namely the tradeoff between phase response and better magnitude, is limited in previous NLPFF designs. Aiming at this problem, this paper has done the following works. First, we propose a new measure called sum of symmetric coefficient differences (SSCD) to represent the phase deviation. Furthermore, we propose a constrained least squares design for NLPFF, where constraints are imposed on the SSCD and squared magnitude. The design can be effectively realized under the second-order cone programming (SOCP) framework. Due to the significantly reduced constraint size and enhanced performance tradeoff area, the proposed SOCP-SSCD approach is the most competitive in effectiveness and efficiency. We have demonstrated this advantage by comparing with previous NLPFF methods. Consequently, by applying this method to design NLPFF as a prototype filter in the UFMC system, we have achieved better power spectral density, symbol error rate (SER), and demodulated constellation than previous prototype filters. For the SER indicator, Fig. 6(a) indicates an SNR gain of 1.2dB@{SER=0.001} between the designed NLPFFs and the previous prototype filters.

Projection-Based Multiple Notch Filtering

A method for multi-frequency notch filtering is described. The approach is based on quadratic programming, which leads to projecting the signal vector onto the orthogonal complement of the subspace spanned by a set of sinusoidal basis vectors, each corresponding to a notch frequency. The projection matrix uses a weighted inner product whose weights are samples of a standard spectral analysis window. An overlap-add method suitable for block processing is also described. The projection-based notch filter (PNF) is compared with linear-phase FIR and IIR multiple notch filters and is found to have improved amplitude and phase distortion.

High throughput and energy efficient linear phase FIR filter architectures

High throughput, low complex and energy efficient linear phase FIR filter structures with low latency are highly desirable for most of the portable signal processing applications. Improving the throughput and energy efficiency while ensuring low latency and complexity is a difficult problem due to the trade-off between performance metrics. To this end, the design of linear phase filter based on the application of retiming and pipelining is proposed. The CPD, PDP, ADP and ELT of the proposed 16-tap linear phase FIR filter is reduced by 64.83%, 80.1%, 61.58%, and 62.49% respectively in comparison with FIR filter using flexible retiming and by 18.29%, 30.99%, 16.56%, and 12.82% respectively in comparison with the recent retiming based high throughput FIR filter. The 16-tap ECG denoising filter developed from the proposed filter structure provides excellent performances in terms of CPD, PDP, ADP and ELT as the algorithmic transformations are applied to an exact multiplier-less linear phase filter structure. It filters out PLI of 50 Hz, its harmonics and high frequency noises while providing improved denoising performances. The CPD, PDP, ADP and ELT of the proposed multiplier-less ECG denoising filter is reduced by 82.44%, 97.55%, 93.51%, and 81.27% respectively in comparison with a typical 17-tap FIR notch filter and by 70.06%, 99.82%, 99.68%, and 98.12% respectively in comparison with a typical Bartlett window based 256-tap FIR notch filter. Structural model VHDL coding is used for developing filters. For synthesis, Cadence software with gpdk 45 nm standard cell library is used and for simulation modelsim is used.

Synthesis of Linear-Phase FIR Filters With a Complex Exponential Impulse Response

In this paper, a novel recursive realization method with word length reduced is proposed to synthesize linear-phase FIR filters for arbitrary bandwidth. By exploring the sparsity in the frequency domain, it constructs the desired impulse response with few complex exponential series (CES) and very sparse additional coefficients (AC) with equal length. The design problem is formulated as a combinatorial optimization problem by confining the frequencies of CES to a finite dictionary. To reduce the computational complexity at optimization, an iterative algorithm is presented, where appropriate frequencies of CES and zero locations of AC can be quickly determined. Thereafter, an efficient parallel structure is introduced to implement the proposed filter. To verify the performance of the proposed method, MATLAB simulation and Field-programmable gate array (FPGA) implementation are made. It shows that the proposed method requires 18bits23bits word length while the existing advanced recursive realization method the piecewise-polynomial-sinusoidal recursiveneeds 59bits59bits for the same filter specifications. Meanwhile, the method can achieve comparable multiplier reduction compared with the state-of-the-art low-complexity techniques but produce a low extra group delay. Moreover, it can realize variable bandedges with a fixed filter structure.

Heuristic Analysis of CIC Filter Design for Next-Generation Wireless Applications

This paper describes a novel multistage CIC filter which plays a vital role in software-defined radio (SDR) applications. In order to operate the baseband signal, wireless networking standards demand different sample rates. As a result, sample rate conversion (SRC) turns out as a pivotal method of SDR. Thus, cascaded integrator comb (CIC) filter is a distinct kind of linear-phase FIR filter which can be used as a decimation filter for SRC operation. The architecture of this filter is multiplierless with low passband droop; hence, it requires less area in contrast to other decimation filters. In this brief, the fundamental structure of CIC filter is examined with various parallel prefix adders and also the significant parameters of the CIC filter for different adders are exemplified. The proposed CIC filter with various parallel prefix adders has been designed in Verilog HDL using Xilinx ISE 14.7 and implemented on Kintex7 FPGA. The schemed CIC filter design is compared with the traditional CIC filter in view of area, speed and power consumption. Based on the obtained results on Kintex7 FPGA, the CIC filter with Brent Kung adder outperforms in terms of LUTs by 41.67% and power by 34.78% compared with the classical CIC filter and among the CIC filters using other parallel prefix adders. The proposed CIC uses new polynomial method which provides 33.33% reduction in passband droop and 41.14% reduction in stopband ripple compared to the existing sharpened CIC.

A Crystal View on the Design of FIR Filter

In audio and video signal processing main element is the FIR filter. This paper presents complete information regarding the FIR filters. It also focuses on the design of FIR filters which provide low-area, energy-delay, low-power consumption, high-speed, low critical path, and low complexity. Implementation of FIR filters with different methods like memory-based VLSI architecture, filters for sampling rate conversion, linear phase FIR filters, optimal hybrid form FIR filters, Nyquist filters, hybrid multiplier less FIR filters, low complexity FIR filters, variable partition hybrid form FIR filters, area efficiency FIR filters are discussed in this paper. The objective of this paper to provide all related information regarding FIR filters at one platform.

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.

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.

Sparse FIR Filter Design via Partial 1-Norm Optimization

In this brief, we consider a sparse linear-phase FIR filter design problem. Recent methods assume that all the coefficients can be nullified and, thus, various 0 or 1-norm-based optimization techniques are applied on each of them. In contrast, the proposed algorithm is based on two important observations: 1) Given design specifications, some coefficients cannot be nullified, otherwise the specifications cannot be satisfied. 2) Impulse responses on neighboring positions of an FIR filter cannot vary dramatically so as to guarantee the smoothness of the corresponding magnitude responses over most of frequencies. In view of these facts, several rules are adopted in the proposed algorithm to select indices of potential zero coefficients to be used in 1-norm optimization. Simulation results have demonstrated the effectiveness of the proposed design algorithm.

Low computation digital down converter using polyphase IIR filter

PurposeThe digital down converter (DDC) is a principal component in modern communication systems. The DDC process traditionally entails quadrature down conversion, bandwidth reducing filters and commensurate sample rate reduction. To avoid group delay, distortion linear phase FIR filters are used in the DDC. The filter performance specifications related to deep stopband attenuation, small in-band ripple and narrow transition bandwidth lead to filters with a large number of coefficients. To reduce the computational workload of the filtering process, filtering is often performed as a two-stage process, the first stage being a down sampling Hoegenauer (or cascade-integrated comb) filter and a reduced sample rate FIR filter. An alternative option is an M-Path polyphase partition of a band cantered FIR filter. Even though IIR filters offer reduced workload to implement a specific filtering task, the authors avoid using them because of their poor group delay characteristics. This paper aims to propose the design of M-path, approximately linear phase IIR filters as an alternative option to the M-path FIR filter.Design/methodology/approachTwo filter designs are presented in the paper. The first approach uses linear phase IIR low pass structure to reduce the filter’s coefficient. Whereas the second approach uses multipath polyphase structure to design approximately linear phase IIR filter in DDC.FindingsThe authors have compared the performance and workload of the proposed polyphase structured IIR filters with state-of-the-art filter design used in DDC. The proposed design is seen to satisfy tight design specification with a significant reduction in arithmetic operations and required power consumption.Originality/valueThe proposed design is an alternate solution to the M-path polyphase FIR filter offering very less number of coefficients in the filter design. Proposed DDC using polyphase structured IIR filter satisfies the requirement of linear phase with the least number of computation cost in comparison with other DDC structure.

An Alternating Variable Technique for the Constrained Minimax Design of Frequency-Response-Masking Filters

The frequency-response-masking (FRM) technique is one of the most efficient approaches to the design of narrow transition band FIR filters. The constrained minimax design of linear-phase FRM FIR filters in the frequency domain is considered in this paper. The corresponding optimization problem is a nonconvex one. To deal with the nonconvex design problem and improve the FRM filter performance, we propose an algorithm to alternately optimize different subsets of the design variables by fixing the remaining ones. In this way, the nonconvex optimization problem is converted into a series of linear programming subproblems defined on different frequency bands, which are then solved alternately and iteratively. Moreover, the new algorithm converges to a better FRM filter than those obtained by several competitive methods and is flexible to incorporate linear constraints in the design. Several design examples are provided to demonstrate the advantages of the proposed algorithm.

Efficient uniform digital filter bank with linear phase and FRM technique for hearing aids

This paper attempts to present an uniform digital filter bank based on linear phase FIR and IIR filters applied for Frequency Response Masking (FRM) technique in hearing aid applications.In the proposed filter bank, nine uniformly spaced sub-bands are formed with the help of half band filters and masking filters. These nine channel FIR filter bank is realized using an interpolated half band linear phase FIR filter and an appropriate number of masking FIR filters. The nine channel IIR filter bank is realized using an interpolated half band approximately linear phase IIR filter and an appropriate number of masking filters. The proposed approximately linear phase IIR half band filter bank is compared with filter bank based on linear phase FIR half band filters in terms of area, power, memory and number of gates needed for implementation. The experiment was carried on various hearing loss cases and the results obtained from these tests proves that, the proposed filter bank achieved the required matching between audiograms and magnitude response of the filter bank at very reasonable range with less computational complexity.

FPGA based Synthesize of PSO Algorithm and its Area-Performance Analysis

Digital filters are the most significant part of signal processing that are used in enormous applications such as speech recognition, acoustic, adaptive equalization, and noise and interference reduction. It would be of great benefit to implement adaptive FIR filter because of self-optimization property, linearity and frequency stability. Designing FIR filter involves multi-modal optimization problems whereas conservative gradient optimization technique is not useful to design the filter. Hence, Particle Swarm Optimization (PSO) algorithm is more flexible and optimization technique based on population of particles in search space and alternative approach for linear phase FIR filter design. PSO improves the solution characteristic by giving a novel method for updating swarm’s position and velocity vector. Set of optimized filter coefficients will be generated by PSO algorithm. In this paper, PSO based FIR Low pass filter is efficiently designed in MATLAB and further Xilinx System Generator tool is used to efficiently design, synthesize and implement FIR filter in FPGA using SPARTEN 3E kit. For an example specifications, output of PSO algorithm is obtained that is set of optimized coefficients whose response is approximating to the ideal response. Hence, functional verification of the proposed algorithm has been performed and the error between obtained filter and ideal filter is minimized successfully. This work demonstrates the effectiveness of the PSO algorithms in parallel processing environment as compared to the Remez Exchange algorithm.

A General Structure of Linear-Phase FIR Filters With Derivative Constraints

In this paper, a general structure of linear-phase finite impulse response filters, whose frequency responses satisfy given derivative constraints imposed upon an arbitrary frequency, is proposed. It is comprised of a linear combination of parallelly connected subfilters, called the cardinal filters , with weighted coefficients being the successive derivatives of the desired frequency response at the constrained frequency. An advantage of such a cardinal filters design is that only the weighted coefficients are relevant to the desired frequency response but not the cardinal filters; hence, a dynamic adjustment of the filter system becomes feasible. The key to derive the coefficients of cardinal filters is the determination of the power series expansion of certain trigonometric-related functions. By showing the elaborately chosen trigonometric-related functions satisfy specific differential equations, recursive formulas for the coefficients of cardinal filters are subsequently established, which make efficient their computations. At last, a simple enhancement of the cardinal filters design by incorporating the mean square error minimization is presented through examples.

A New Cost-Aware Sensitivity-Driven Algorithm for the Design of FIR Filters

Design for low complexity FIR filters has been an area of intensive research over the last two decades. Recent approaches to integrating common subexpression elimination with filter coefficient synthesis are based on single-minded reliance on bit width truncation or common subexpression sharing to fulfill the frequency response specifications. Such biases have a strong tendency to overfit or underfit the response prematurely, and increase the implementation cost. In this paper, a new algorithm is proposed to synthesize finite-precision coefficients with low implementation cost from the frequency response specifications of linear phase FIR filter. Overfitting is overcome by admitting the most sensitive subexpressions followed by isolated nonzero digits according to their sensitivities to the change in frequency response error if they are independently removed. To leverage on adder reuse of common subexpressions, common subexpressions of each length are admitted into the coefficients immediately after their most sensitive member. Trivial nonzero digits piggybacked on the admission of common subexpression are pruned to remove the excess slack from the finally selected least cost finite-precision coefficient set. To avoid underfitting, the filter length and word length of coefficients are not fixed but determined by how much incremental slack in the frequency response can be harvested from each additional tap and expanded bit. The effectiveness of the proposed algorithm in designing low power and area-efficient FIR filters is demonstrated by comparing its logic synthesis and power simulation results with other FIR filter coefficient synthesis algorithms. On average, the proposed algorithm saves about 20.9% to 72.7% of area and power consumptions on various sizes of benchmark FIR filters, and improves the area and power efficiency of a filter bank designed for feature extraction of EEG signals by 33.9% to 54.8% over the competing algorithms.

A Novel Modular Positive-Sequence Synchrophasor Estimation Algorithm for PMUs

A novel modular positive-sequence estimation algorithm for phasor measurement units (PMUs) is described in this paper with a focus on the restrictions imposed by the IEEE C37.118.1–2011 standard. The first stage consists in a three-phase demodulator which allows us to separate the positive-sequence from the negative-sequence signal in the frequency domain and to eliminate the zero-sequence signal. The second stage is a prefilter that mitigates noise and interference, thus relaxing the filtering requirements of the following stage. The suitability of a linear-phase FIR filter is shown and a comparison of single and multistage designs is presented. On the third stage, a digital state-space-based extension of a synchronous reference frame-phase-locked loop is used for tracking of amplitude, phase, frequency, and rate of change of frequency. It is shown that a phase predictor inside the loop is required. The fourth stage is a compensation algorithm which takes into account the narrowband nature of the input signal to perform an accurate compensation of the filter effects on the signal of interest. Analytical properties of the system are then presented, providing insight into the main factors that affect global performance. Finally, a strict evaluation of the system is presented for both M and P class PMU.

Linear-Phase Lattice FIR Digital Filter Architectures Using Stochastic Logic

This paper presents novel architectures for linear-phase FIR digital filters using stochastic computing. Stochastic computing systems require fewer logic gates and are inherently fault-tolerant. Thus, these structures are well suited for nanoscale CMOS technologies. Compared to direct-form linear-phase FIR filters, linear-phase lattice filters require twice the number of multipliers but the same number of adders. The hardware complexities of stochastic implementations of linear-phase FIR filters for direct-form and lattice structures are comparable. This is because multipliers do not require any more area than adders. Two stochastic implementations of lattice FIR filters are proposed in this paper. Using speech signals from ICA ’99 Synthetic Benchmarks, it is shown that, for linear-phase FIR filters, the signal-to-error ratios of stochastic direct-form and stochastic lattice filters are abou the same.

Interference-driven designs of nonlinear-phase FIR filter with application in FBMC system

In the forthcoming 5G systems, new technologies, such as amorphous networks and non-orthogonal filter bank multi-carriers (FBMC), provide an effective way to accommodate high-rate transmissions. Meanwhile, the prototype filter affects the adjacent channel interference, and therefore is important for FBMC systems. Besides, once the amorphous network is taken into account, the requirement for interference control must be much stricter. Accordingly, this paper focuses on the design of prototype filter with better ability of interference controlling, where we exploit the nonlinear phase FIR filter (NLPFF) instead of traditional linear phase FIR filter (LPFF) to achieve more optimization spaces under a small sacrifice of linear phase. In our designs, both the amplitude and phase responses are handled independently to approach the stop-band performance enhancements, in while the nearly perfect reconstruction (NPR) conditions are relaxed by pre-specified thresholds. Computer simulations confirm the effectiveness of the NLPFF designs, and demonstrate the advantages of the proposed NLPFF in FBMC applications.

J peak extraction from non-standard ballistocardiography data: a preliminary study.

In recent years, several advanced algorithms based on clustering, multi-method or data fusion approaches have been proposed to estimate heartbeat intervals from non-standard ballistocardiography (BCG) data. These advanced algorithms generally have higher computational complexity than J-peak based algorithms. This fact motivated us to study the problem of extracting J peaks from non-standard BCG data, because if this extraction can be realized, then a low-complexity J-peak based algorithm can be used to fast estimate heartbeat intervals from non-standard BCG data. We found that most of the energy in J peaks is contained in a relatively narrow frequency band, called J-peak band, and that the heartbeat harmonics outside the J-peak band can cause the non-standard BCG waveform. According to these findings, a FIR linear phase filter with the J-peak band as its pass-band is proposed. The experimental result demonstrates the ability of the proposed filter to extract J peaks from non-standard BCG data.