Design Of Finite Impulse Response Digital Filters Research Articles

FIR digital filter design based on improved artificial bee colony algorithm

The traditional swarm intelligence optimization algorithm is prone to fall into local optimal solutions in finite impulse response (FIR) digital filter design and has slow convergence speed. In order to optimize the design of FIR filter, a FIR digital filter design method based on improved bee colony (ABC) algorithm is proposed. This improved ABC algorithm can adaptively adjust the step size of the selected neighborhood of nectar source location. At the same time, the information of the global optimal solution is used to guide the search of candidate solution, which improves the global search ability of the algorithm. The improved ABC algorithm can balance the conflict between local search ability and global search ability, so it can achieve better optimization effect. The time and space complexity of the algorithm is analyzed in detail. Then, the improved ABC algorithm is used to design three typical FIR digital filters, namely low-pass, band-pass and band-stop filter. The performance of the designed filter is tested by simulation experiments. The experimental results show that compared with other state-of-the-art optimization algorithms, the proposed FIR filter design method has achieved better effect and performance. Meanwhile, the proposed design method has shorter optimization time. The superiority of the proposed method is verified.

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.

Designing digital filter banks using wavelets

In digital filters theory, filtering techniques generally deal with pole-zero structures. In this context, filtering schemes, such as infinite impulse response (IIR) filters, are described by linear differential equations or linear transformations, in which the impulse response of each filter provides its complete characterization, under filter design specifications. On the other hand, finite impulse response (FIR) digital filters are more flexible than the analog ones, yielding higher quality factors. Since many approaches to the circuit synthesis using the wavelet transform have been recently proposed, here we present a digital filter design algorithm, based on signal wavelet decomposition, which explores the energy partitioning among frequency sub-bands. Exploring such motivation, the method involves the design of a perfect reconstruction wavelet filter bank, of a suitable choice of roots in the Z-plane, through a spectral factorization, exploring the orthogonality and localization property of the wavelet functions. This approach resulted in an energy partitioning across scales of the wavelet transform that enabled a superior filtering performance, in terms of its behavior on the pass and stop bands. This algorithm presented superior results when compared to windowed FIR digital filter design, in terms of the intended behavior in its transition band. Simulations of the filter impulse response for the proposed method are presented, displaying the good behavior of the method with respect to the transition bandwidth of the involved filters.

Design and Realization of FIR Digital Filter for Optical IM/DD-OFDM System Using FPGA

We present a finite impulse response (FIR) filter by using field programmable gate array (FPGA). It is designed in MATLAB, and we get filter coefficient from it. The implementation results showed decent performance in filtering.

Design and implementation of an efficient FIR digital filter

AbstractDigital signal processing (DSP) circuits are extremely important in computing and communications areas. One application of DSP is a Finite impulse response (FIR) filter. The principle objective of this exploration is to present a methodology for an upgraded framework of a FIR digital filter from software level to the hardware level. It includes the selection of design method, structure and cost effective hardware utilization. Theoretical and experimental results performed FIR band pass filter suggests that the window design method is relatively simple and easy to use because of the availability of well-defined equation. Comparison presented that Kaiser window gives the minimum main-lobe width and a sharp cut-off which means this window has less transition width and the study showed that the Direct-Form structure approach is simpler and offers a better performance than other common filter structures. It results in low cost, reduced area and more robust to withstand the quantization errors. For effi...

FIR Digital Filter Design by Sampled-Data*H∞ Discretization

FIR (finite impulse response) digital filter design is a fundamental problem in signal processing. In particular, FIR approximation of analog filters (or systems) is ubiquitous not only in signal processing but also in digital implementation of controllers. In this article, we propose a new design method of an FIR digital filter that optimally approximates a given analog filter in the sense of minimizing the H∞ norm of the sampled-data error system. By using the lifting technique and the KYP (KalmanYakubovichPopov) lemma, we reduce the H∞ optimization to a convex optimization described by an LMI (linear matrix inequality). We also extend the method to multi-rate and multi-delay systems. A design example is shown to illustrate the effectiveness of the proposed method.

New Approach to Look-Up-Table Design and Memory-Based Realization of FIR Digital Filter

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> Distributed arithmetic (DA)-based computation is popular for its potential for efficient memory-based implementation of finite impulse response (FIR) filter where the filter outputs are computed as inner-product of input-sample vectors and filter-coefficient vector. In this paper, however, we show that the look-up-table (LUT)-multiplier-based approach, where the memory elements store all the possible values of products of the filter coefficients could be an area-efficient alternative to DA-based design of FIR filter with the same throughput of implementation. By operand and inner-product decompositions, respectively, we have designed the conventional LUT-multiplier-based and DA-based structures for FIR filter of equivalent throughput, where the LUT-multiplier-based design involves nearly the same memory and the same number of adders, and less number of input register at the cost of slightly higher adder-widths than the other. Moreover, we present two new approaches to LUT-based multiplication, which could be used to reduce the memory size to half of the conventional LUT-based multiplication. Besides, we present a modified transposed form FIR filter, where a single segmented memory-core with only one pair of decoders are used to minimize the combinational area. The proposed LUT-based FIR filter is found to involve nearly half the memory-space and <formula formulatype="inline"> <tex Notation="TeX">$(1/N)$</tex></formula> times the complexity of decoders and input-registers, at the cost of marginal increase in the width of the adders, and additional <formula formulatype="inline"><tex Notation="TeX">$\sim(4N\times W)$</tex></formula> AND-OR-INVERT gates and <formula formulatype="inline"> <tex Notation="TeX">$\sim(2N\times W)$</tex></formula> NOR gates. We have synthesized the DA-based design and LUT-multiplier based design of 16-tap FIR filters by Synopsys Design Compiler using TSMC 90 nm library, and find that the proposed LUT-multiplier-based design involves nearly 15% less area than the DA-based design for the same throughput and lower latency of implementation. </para>

An Analytical Approach for Design of Nth-band FIR Digital Filters with Equi-Ripple Passband

In FIR (Finite Impulse Response) filter applications, Nth-band FIR digital filters are known to be important due to their reduced computational requirements. The conventional methods for de- signing FIR filters use iterative approaches such as the well-known Parks-McClellan algorithm. The Parks-McClellan algorithm is also used to design Nth-band FIR digital filters after Mintzer's research. However, a disadvantage of the Parks-McClellan algorithm is that it needs a large amount of design time. This paper describes a direct design method for Nth-band FIR Filters using Chebyshev polyno- mials, which provides a reduced design time over indirect methods such as the Parks-McClellan algo- rithm. The response of the resulting filter is equi-ripple in passband. Our proposed method produces a passband response that is equi-ripple to within a minuscule error, comparable to that of Mintzer's de- sign method which uses the Parks-McClellan algorithm.

FIR, Allpass, and IIR Variable Fractional Delay Digital Filter Design

This paper presents two-step design methodologies and performance analyses of finite-impulse response (FIR), allpass, and infinite-impulse response (IIR) variable fractional delay (VFD) digital filters. In the first step, a set of fractional delay (FD) filters are designed. In the second step, these FD filter coefficients are approximated by polynomial functions of FD. The FIR FD filter design problem is formulated in the peak-constrained weighted least-squares (PCWLS) sense and solved by the projected least-squares (PLS) algorithm. For the allpass and IIR FD filters, the design problem is nonconvex and a global solution is difficult to obtain. The allpass FD filters are directly designed as a linearly constrained quadratic programming problem and solved using the PLS algorithm. For IIR FD filters, the fixed denominator is obtained by model reduction of a time-domain average FIR filter. The remaining numerators of the IIR FD filters are designed by solving linear equations derived from the orthogonality principle. Analyses on the relative performances indicate that the IIR VFD filter with a low-order fixed denominator offers a combination of the following desirable properties including small number of denominator coefficients, lowest group delay, easily achievable stable design, avoidance of transients due to nonvariable denominator coefficients, and good overall magnitude and group delay performances especially for high passband cutoff frequency ( ges 0.9pi) . Filter examples covering three adjacent ranges of wideband cutoff frequencies [0.95, 0.925, 0.9], [0.875, 0.85, 0.825], and [0.8, 0.775, 0.75] are given to illustrate the design methodologies and the relative performances of the proposed methods.

An iterative algorithm for optimal design of non-frequency-selective FIR digital filters

This paper proposes a novel iterative algorithm for optimal design of non-frequency-selective Finite Impulse Response (FIR) digital filters based on the windowing method. Different from the traditional optimization concept of adjusting the window or the filter order in the windowing design of an FIR digital filter, the key idea of the algorithm is minimizing the approximation error by successively modifying the design result through an iterative procedure under the condition of a fixed window length. In the iterative procedure, the known deviation of the designed frequency response in each iteration from the ideal frequency response is used as a reference for the next iteration. Because the approximation error can be specified variably, the algorithm is applicable for the design of FIR digital filters with different technical requirements in the frequency domain. A design example is employed to illustrate the efficiency of the algorithm.

Minimax Design of Variable Fractional-Delay FIR Digital Filters by Iterative Weighted Least-Squares Approach

In this letter, an iterative weighted least-squares (LS) approach is proposed for the design of variable fractional-delay (VFD) finite impulse response (FIR) digital filters in minimax sense. For deriving the elements of relevant matrices, there is no need for numerical integration or closed-form formulation and they obey given specifications. Comparing with the existing method, the proposed method does not lead to a misleading problem, and the performance of convergence is also better. Especially, it is found that the used LS weighting function is only dependent on the frequency, not on the tunable parameter, which makes it easier for the minimax design of VFD FIR digital filters.

Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming

This paper studies the design of digital finite impulse response (FIR) filters with prescribed flatness and peak design error constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is utilized in this study for the optimal minimax and least squares design of linear-phase and low-delay (LD) FIR filters with prescribed magnitude flatness and peak design error. The proposed approach offers more flexibility than traditional maximally-flat approach for the tradeoff between the approximation error and the degree of design freedom. Using these results, new LD specialized filters such as digital differentiators, Hilbert Transformers, Mth band filters and variable digital filters with prescribed magnitude flatness constraints can also be derived.

Design and parallel implementation of FIR digital filters with simultaneously variable magnitude and non-integer phase-delay

Variable fractional-delay digital filters are useful in various signal processing applications. To perform both fractional-delay filtering and signal frequency selecting, variable fractional-delay filters must also have variable magnitude characteristics. This paper proposes a method for designing variable finite-impulse response (FIR) filters with both variable magnitude and variable noninteger phase-delay. First, the coefficients of a variable FIR filter are expressed as different 2-variable polynomials of a pair of spectral parameters; one is for varying magnitude response, and the other is for varying noninteger phase-delay. Then the optimal coefficients of the 2-variable polynomials are found by minimizing the total weighted squared error of the variable frequency response. Since the coefficients of the obtained variable FIR filter are the polynomials of the two spectral parameters, we can yield variable magnitude and variable noninteger phase-delay simultaneously or independently by substituting different spectral parameter values to the 2-variable polynomial coefficients. Finally, we show that the resulting variable FIR filter can be implemented in a parallel form, which is suitable for high-speed signal processing.

On the design and implementation of FIR and IIR digital filters with variable frequency characteristics

This paper studies the design and implementation of finite-impulse response (FIR) and infinite-impulse response (IIR) variable digital filters (VDFs), whose frequency characteristics can be controlled continuously by some control or tuning parameters. A least squares (LS) approach is proposed for the design of FIR VDFs by expressing the impulse response of the filter as a linear combination of basis functions. It is shown that the optimal LS solution can be obtained by solving a system of linear equations. By choosing the basis functions as piecewise polynomials, VDFs with larger tuning range than that of ordinary polynomial based approach results. The proposed VDF can be efficiently implemented using the familiar Farrow structure. Making use of the FIR VDF so obtained, an Eigensystem Realization Algorithm (ERA)-based model reduction technique is proposed to approximate the FIR VDF by a stable IIR VDF with lower system order. The advantages of the model reduction approach are: 1) it is computational simple which only requires the computation of the singular value decomposition of a Hankel matrix; 2) the IIR VDF obtained is guaranteed to be stable; and 3) the frequency response such as the phase response of the FIR prototype is well preserved. Apart from the above advantages, the proposed IIR VDF does not suffer from undesirable transient response during parameter tuning found in other approaches based on direct tuning of filter parameters. For frequency selective VDFs, about 40% of the multiplications can be saved using the IIR VDFs. The implementation of the proposed FIR VDF using sum-of-powers-of-two (SOPOT) coefficient and the multiplier block (MB) technique are also studied. Results show that about two-third of the additions in implementing the multiplication of the SOPOT coefficients can be saved using the multiplier block, which leads to significant savings in hardware complexity.

Design of discrete coefficient FIR and IIR digital filters with prefilter-equalizer structure using linear programming

Optimal methods for designing multiplierless finite-impulse response (FIR) and infinite-impulse response (IIR) filters with cascaded prefilter-equalizer structures are proposed. Assuming that an FIR filter consists of a cyclotomic polynomial (CP) prefilter and an interpolated second order polynomial (ISOP) equalizer, in the proposed method, the prefilter and equalizer are simultaneously designed using mixed integer linear programming (MILP). The resulting filter is a cascaded filter with minimal complexity. For IIR filters, all-pole IIR equalizers consisting of inverse of interpolated first order polynomials (IIFOP's) are introduced, and a CP-prefilter cascaded with this type of equalizer is designed. Design examples demonstrate that the proposed methods produce a more efficient cascaded prefilter-equalizer than existing methods.

An algorithm for solving the Toeplitz systems of equations in FIR digital filter design problems

An algorithm is presented for solving the Toeplitz systems of equations that occur in finite impulse response (FIR) digital filter and window design problems. The proposed algorithm is an extension of the algorithms in a paper by Jain (1979) and a paper by Ammar and Gader (1991).

The design of the maximal SNR linear phase FIR digital filters

The gradient algorithm for the design of the maximal signal-to-noise ratio (SNR) finite impulse response (FIR) digital filters is presented. It is noted that the eigenvalue gradient determination cannot lead to the global maximum from any initial point. The properties of the linear phase low-pass, high-pass and band-pass filters designed by the proposed method are considered. The maximal SNR filters provide obtaining a significant filter's profit even when the filter's length is rather small. The filters are preferable for processing a mix of a stationary signal and a stationary noise with the known power spectra.

In the optimum design of the block adaptive FIR digital filter

A general optimum block adaptive (GOBA) algorithm for adaptive FIR (finite impulse response) filtering is presented. In this algorithm, the correction terms for the filter coefficients in each block, instead of the convergence factors, are optimized in a least squares sense. There are no constraints on the block length L and the filter tap number N. It is shown that the GOBA algorithm is reduced to the normalized LMS algorithm when L>or=N. The convergence of the GOBA algorithm can be assured if the correlation matrix of the input signal is positive definite. Computer simulations based on an efficient computing procedure confirm that the GOBA algorithm achieves faster convergence with slightly degraded convergence accuracy in stationary environments and better weight tracking capability in nonstationary environments as compared to existing block adaptive algorithms with no constraints on L and N. >

The design of arbitrary FIR digital filters using the eigenfilter method

The design of finite impulse response (FIR) digital filters for approximating an arbitrary function (in both magnitude and phase) in the least-square sense is studied. The design method is based on the computation of an eigenvector of an appropriate real, symmetric and positive-definite matrix. The design of the complex-coefficient filter is shown to be an extension of the design of the real-coefficient filter. Several design examples, including the constant-group-delay filters and digital phase all-pass filters, are presented. Comparisons to existing methods are made. >

Complex eigenfilter design of arbitrary complex coefficient FIR digital filters

The real eigenfilter approach is extended to complex cases for designing arbitrary complex finite impulse response (FIR) filters. By minimizing a quadratic measure of the error in the passband and stopband, a complex eigenvector of an appropriate complex, Hermitian symmetric, and positive-definite matrix is computed to get the filter coefficients. Several arbitrary magnitude and phase FIR filters, such as multiple passband complex filters and staircase-delay allpass phase equalizers, can be easily designed by this approach. This method can be easily extended to design 2-D complex FIR filters. If an appropriate iterative process is used, equiripple filters in the complex Chebyshev sense can be obtained. Several numerical design examples demonstrate the usefulness of the approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>