Linear Phase FIR Digital Filters Research Articles

Minimax Design of Graph Filter Using Chebyshev Polynomial Approximation

In this brief, the minimax design problem of graph filter using Chebyshev polynomial approximation (CPA) is studied. First, conventional CPA graph filter design is investigated to show that it does not provide the minimax design, so the peak error of the spectral response of the designed filter is not minimized. Then, a spectral transformation is used to convert the minimax design problem of CPA graph filter into the one of the type-I linear-phase FIR digital filter such that the Parks-McClellan method can be employed to obtain the optimal filter coefficients of minimax design. Next, using the recurrence relation of Chebyshev polynomials, an implementation structure of CPA graph filter with low computational complexity is presented. Finally, a graph signal denoising application example is illustrated to show the usefulness of the proposed CPA graph filter.

Convergence properties of a class of exact penalty methods for semi-infinite optimization problems

In this paper, a new class of unified penalty functions are derived for the semi-infinite optimization problems, which include many penalty functions as special cases. They are proved to be exact in the sense that under Mangasarian–Fromovitz constraint qualification conditions, a local solution of penalty problem is a corresponding local solution of original problem when the penalty parameter is sufficiently large. Furthermore, global convergence properties are shown under some conditions. The paper is concluded with some numerical examples proving the applicability of our methods to PID controller design and linear-phase FIR digital filter design.

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.

SPEECH SIGNAL ANALYSIS FOR LINEAR FILTER BANKS OF DIFFERENT ORDERS

In speech signal processing using of filter banks is very important. The critical requirement is the sum of all the frequency responses of the band-pass filters of the filter bank i.e. composite frequency response be flat with linear phase. This paper deals with design and implementation of linear-phase FIR digital filters based filter bank flat with flat composite frequency response. The design is based on special properties of FIR filters by which excellent frequency response can be achieved. Keyword: Speech signal, FIR Filter, Composite frequency response. -------------------------------------------------------------------***------------------------------------------------------------------

Implementation of Biorthogonal Wavelet Transform Using Windowed APDF Based on DCT

All phase digital filter (APDF) is a new type of linear phase FIR digital filter that was proposed in recent years. Firstly, the theory of biorthogonal wavelet transform and windowed APDF based on DCT is expounded and the relationship between them is discussed. Secondly, a novel algorithm is proposed to implement biorthogonal wavelet transform by using windowed APDF based on DCT. As an important application of biorthogonal wavelet transform, multi-resolution analysis of 2-D image signal could be used to test the feasibility and applicability of the proposed algorithm. Finally, the simulation results using MATLAB tool are shown in this paper and the analysis indicates that the proposed method performs well.

Eigenfilter design of linear-phase FIR digital filters using neural minor component analysis

This paper proposes a minor component analysis-based neural learning algorithm for designing linear-phase finite impulse response digital filters. The objective function to be minimized in the least-squares design can be formulated as the eigenvalue problem for solving an appropriate real, symmetric, and positive-definite matrix. To achieve the eigenfilter design, an alternative neural learning rule based on the minor component analysis algorithm is exploited. The optimal filter coefficients corresponding to the eigenvector of the smallest eigenvalue of the positive-definite matrix can be achieved in an iterative manner, avoiding the complex computation of eigenvalue decomposition. Furthermore, the learning step parameter that affects the convergence performance is investigated empirically. The simulation results indicate that the proposed neural-based approach can be applied to eigenfilter design and yields a lower computational complexity compared with traditional matrix algebraic-based approaches.

Area-Efficient VLSI Implementation for Parallel Linear-Phase FIR Digital Filters of Odd Length Based on Fast FIR Algorithm

Based on fast FIR algorithms (FFAs), this brief proposes new parallel FIR filter architectures, which are beneficial to symmetric convolutions of odd length in terms of the hardware cost. The proposed parallel FIR architectures exploit the inherent nature of symmetric coefficients reducing half the number of multipliers in the subfilter section at the expense of increase in adders in preprocessing and postprocessing blocks. Exchanging multipliers with adders is advantageous because adders weigh less than multipliers in terms of silicon area, and in addition, the overhead from the increase in adders in preprocessing and postprocessing blocks stay fixed, not increasing along with the length of the FIR filter, whereas the number of reduced multipliers increases along with the length of the FIR filter. For example, for a three-parallel 81-tap filter, the proposed structure saves 26 multipliers at the expense of five adders, whereas for a three-parallel 591-tap filter, the proposed structure saves 196 multipliers at the expense of five adders still. Overall, the proposed parallel FIR structures can lead to significant hardware savings for symmetric convolution in odd length from the existing FFA parallel FIR filter, particularly when the length of the filter is large.

An efficient closed-form approach to the design of linear-phase FIR digital filters with variable-bandwidth characteristics

This paper deals with the design of variable-bandwidth linear-phase FIR digital filters. Such filters are implemented as a linear combination of fixed-coefficient linear-phase filters and the variable bandwidth characteristics are provided by a tuning parameter embedded in the filter structure. These filters are designed in a least-square sense by formulating an error function reflecting the difference between the desired variable bandwidth filter and the practical filter represented as a linear combination of fixed-coefficient filters in a quadratic form. The filter coefficients are obtained by solving a system of linear equations comprising of a block-symmetric positive-definite matrix in which each block is a Toeplitz-plus-Hankel matrix. Consequently, a significant reduction in computational complexity can be achieved in obtaining the entries of this matrix. Moreover, closed-form expressions are provided for both the block-symmetric matrix as well as the vector involved in the system of linear equations.

Designing linear phase FIR digital filters with flat passband and equiripple stopband characteristics

AbstractIt is known that linear phase FIR digital filters fall into four types considering the symmetry of impulse response. For example, filters of type 2 can be used at the time of partitioning and reconstruction of signals in multirate signal processing, and other types have similar special applications. Moreover, the linear phase FIR digital filters with flat passband and equiripple stopband characteristics are very important filters in practice because they have better time domain characteristics and less ringing than Chebyshev filters with equiripple stopband and passband characteristics. However, conventional design methods are restricted to type 1. In this paper, we therefore propose a method of design of linear phase FIR digital filters with flat passband and equiripple stopband characteristics for all four types. The proposed function is composed of two functions, one with a flat characteristic in the passband and the second with equiripple characteristics in the stopband. The latter function is obtained by using the well‐known Remez algorithm only for the stopband. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(4): 89–95, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1148

Minimax design of 2-D linear-phase FIR filters with continuous and powers-of-two coefficients

This paper deals with the minimax design problem of two-dimensional (2-D) linear-phase FIR digital filters with continuous and powers-of-two (POT) coefficients. First, the minimax continuous-coefficient design problem is formulated as a linear programming problem with inequality constraints. We present a method based on a variant of Karmarkar's algorithm to solve the resulting design problem. During each iteration, the main computing cost required for finding the filter coefficients is to solve a set of linear equations. Based on the obtained continuous coefficients, an efficient method is presented for designing a minimax 2-D FIR filter with POT coefficients in the spatial domain. Simulation results are provided for illustration and comparison.

Realization of FIR Hilbert Transformers as Taylor Structures

Design of maximally flat Hilbert Transformers is proposed. Taylor configuration is suggested to realize a linear phase FIR digital filter. This approach is comparatively simpler than the other known ones. Four relations (two recursive and two explicit) for computation of weights required in the design are derived. The paper also brings out relation between digital Hilbert Transformers and digital differentiators as well as with digital notch filters. Applications of the suggested design are also given.

A method for synthesizing multiplierless FIR digital filters with narrow transition widths

In this paper, a method for synthesizing multiplierless linear-phase FIR digital filters with narrow transition widths is presented. The proposed method is developed based on the structure of interconnecting the identical subfilters by using a few tap coefficients (Saramäki, 1987). In the proposed method, the subfilter's coefficients and the tap coefficients are searched in the discrete powers-of-two coefficient space, respectively, to make the whole filter structure become multiplierless. A simulation example shows that a sharp-cutoff multiplierless filter with tight specification on the maximum allowable ripples can be easily designed using the proposed design technique.

Description of FIR digital filters in the form of parallel connection of linear phase FIRs

The authors aim to show that FIR digital filters can be described in the form of parallel connection of linear phase FIR digital filters. This representation method may be applicable to FIR digital filter design problems, reducing it to linear phase FIR digital filter design problems.

Design of linear phase FIR filters with a maximally flat passband

The design of linear phase FIR digital filters having symmetric or antisymmetric impulse response is formulated as a constrained minimization problem. The constraints express the maximal flatness of the frequency response at the origin in the case of a low-pass filter or at an arbitrary frequency in the passband in the case of a bandpass filter. The objective function, which is a quadratic form in the filter coefficients, is formed as a convex combination of two objective functions representing the energy of the error between the frequency response of the designed filter and a scaled version of the frequency response of the ideal filter in both the stop and passbands.

Fast design of 2-D linear-phase complex FIR digital filters by analytical least squares method

Two-dimensional full-plane and half-plane filters are more general, and much better frequency responses can be obtained than the quarter-plane filters. In this correspondence, the analytical least squares method is generalized and extended for designing 2-D full-plane and half-plane linear phase complex FIR digital filters. The 2-D filter's coefficients can be effectively determined by use of a closed-form transformation matrix and some simple element functions. The unique advantage of this technique is that it is very fast without employing iterative optimization procedures and matrix inversions. Design examples are presented to illustrate the simplicity and efficiency of the proposed method.

General form for designing two-dimensional quadrantally symmetric linear-phase FIR digital filters by analytical least-squares method

The analytical least-squares method has been generalized and extended for designing 16 types of two-dimensional FIR filters with quadrantally symmetric or antisymmetric frequency responses. By means of a closed-form transformation matrix, this fast design method can determine the filter's coefficients very effectively without a recourse to an iterative optimization technique or matrix inversion. Design examples are presented to illustrate the simplicity and efficiency of the proposed method.

Use of finite wordlength FIR digital filter structures with improved magnitude and phase characteristics for reduction of muscle noise in EEG signals.

One of the main disturbances in EEG signals is EMG artefacts generated by muscle movements. In the paper, the use of a linear phase FIR digital low-pass filter with finite wordlength precision coefficients is proposed, designed using the compensation procedure, to minimise EMG artefacts in contaminated EEG signals. To make the filtering more effective, different structures are used, i.e. cascading, twicing and sharpening (apart from simple low-pass filtering) of the designed FIR filter. Modifications are proposed to twicing and sharpening structures to regain the linear phase characteristics that are lost in conventional twicing and sharpening operations. The efficacy of all these transformed filters in minimising EMG artefacts is studied, using SNR improvements as a performance measure for simulated signals. Time plots of the signals are also compared. Studies show that the modified sharpening structure is superior in performance to all other proposed methods. These algorithms have also been applied to real or recorded EMG-contaminated EEG signal. Comparison of time plots, and also the output SNR, show that the proposed modified sharpened structure works better in minimising EMG artefacts compared with other methods considered.

McClellan transform based design techniques for two-dimensional linear-phase FIR filters

This paper considers the design problem of two-dimensional (2-D) linear-phase FIR digital filters through the use of the McClellan transform method. We present two methods for determining the coefficients of the McClellan transform when designing 2-D linear-phase FIR digital filters with continuous and powers-of-two coefficients, respectively. Based on the proposed methods, the contour approximation for 1-D (one-dimensional) to 2-D digital filter transformation and finding the band-edge frequencies of the corresponding 1-D FIR digital filter can be achieved simultaneously. This results in that the required complexity of the designed 2-D digital filter satisfying the design specifications can be minimized. Moreover, the proposed methods allow us to employ the McClellan transform with order more than one for enhancing the capability of the original McClellan transform. Considering the determination of the McClellan transform coefficients and the band-edge frequencies for the design, we formulate the design problem as a linear programming optimization problem. Then, an efficient design procedure is presented to avoid the use of time consuming simplex algorithms. For the powers-of-two coefficient design, a discrete design procedure is presented to avoid the use of time-consuming mixed integer linear programming algorithms. Computer simulations for showing the effectiveness of the proposed design techniques are also presented.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A unified approach to the design of quadrantally symmetric linear-phase two-dimensional FIR digital filters by eigenfilter approach

Instead of the design procedures restricted to same special filter types, a unified approach is proposed to design sixteen possible cases for quadrantally symmetric linear-phase 2-D FIR filters. The original forms of the sixteen possible cases are formulated properly such that the eigenfilter method can design them with the same approach. The conversions between the filter coefficients are tabulated in a complete table. Also two numerical examples are shown to demonstrate the usefulness and flexibility of the present approach.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Systolic realisation of delayed two-path linear phase FIR digital filters

A new method for high speed realisation of 1-dimensional (ID) linear phase FIR digital filter is presented. The method makes use of pipelining in systolic arrays to reduce the minimum clock cycle time, the delayed two-path structure to increase processing speed, and the symmetry of coefficients in a linear phase FIR digital filter to reduce multiplications. The resultant systolic delayed two-path digital filter structure is consisted of four systolic arrays built from one type of basic cells with nearest neighbour interconnections. The method is optimal in terms of the number of multiplications. Both input and output of the proposed filter structure can also be systolised to form an overall pure systolic structure. The proposed digital filter structure can provide a speed improvement of 32 times as compared to that of a direct realisation of the same filter using a single processor. The proposed method is attractive for high speed adaptive and nonadaptive digital filtering