Design Of FIR Research Articles

On the design of two channel perfect construction QMF filters

This paper presents two rapidly convergent methods for the design of two-channel odd degree linear phase FIR banks as well as IIR filter banks. In both cases, zeros of arbitrary multiplicity are assumed at z = −1, to ensure regularity of the generated wavelet basis. It is shown that in the FIR case, the problem reduces to the solution of an eigenvalue problem. A simple minimization method is proposed for its solution to reduce most of the computational complexities of eigenvalue evaluations. In the IIR case, a simple rapidly convergent algorithm is also described for the determination of a perfect as well as pseudo-perfect reconstruction stable IIR function having equiripple pass and stop band responses and with almost constant group delay. It is also shown that the analysis and synthesis banks are of same complexities, and as a result of being expressed as sum of two all-pass functions, they are realized in a lattice form. Therefore, they are immune from quantization effects. Illustrative examples are also given. Copyright © 2000 John Wiley & Sons, Ltd.

Design of biorthogonal FIR linear phase filter banks with structurally perfect reconstruction

Design of biorthogonal FIR linear phase filter banks with structurally perfect reconstruction

Design of optimal symmetric FIR receive filters

A method for designing optimal symmetric odd-length finite impulse response digital receive filters is proposed. The filter jointly minimises the mean power of intersymbol interference and additive noise or interference under the constraint that the filter coefficients are symmetric. The method yields exactly symmetric filters with the same performance as the earlier unconstrained design but with a lower computational complexity.

Design of Frequency Sampling Filters Using Cyclotomic Polynomials

Frequency sampling filters (FSFs) are of interest to designers of filter banks due, in part, to their intrinsic low complexity and linear phase behavior. FSF designs rely on exact pole-zero annihilation and are often found in embedded applications. Exact FSF pole-zero annihilation can be guaranteed by using polynomial filters defined over an integer ring in the residue number system (RNS) along with algebraic integers. An FPGA implementation example is presented which offers an 86% complexity reduction compared with standard nonrecursive FIR designs.

Design of equiripple log FIR and IIR filters using multiple exchange algorithm

In this paper, an efficient design method for linear phase FIR filter with equiripple log magnitude response is first investigated. Then, we extend this method to design a class of IIR filter having equiripple behavior in both log magnitude and group delay response. Both design procedures are mainly based on the multiple exchange algorithm. Also, the log FIR and IIR filters are designed in three cases where the passband and stopband error ratio, or the passband error, or the stopband error are specified. Several design examples for lowpass log filters are presented to demonstrate the effectiveness of the proposed methods.

Frequency domain design of FIR and IIR Laplacian of Gaussian filters for edge detection

This work addresses the design of LoG filters in the frequency domain within a structure formed by the cascade of quasi-Gaussian and discrete Laplacian filters. The main feature of such a structure is that it requires half the number of convolutions of the classical structure in which the LoG transfer function is expressed as the sum of two separable transfer functions of 1-D Gaussian and LoG type. Such a perspective allows one to rephrase the design of IIR and FIR filters for edge detection as a frequency domain approximation problem solvable by standard digital filter design tools. The zero-phase IIR solutions have a good performance at low orders and approximation errors practically independent of the aperture parameter. The characteristics of the nearly linear-phase IIR filters solving the problem suggest the consideration of linear-phase FIR filters with zeros constrained on the unit circle. The use of such filters leads to remarkable computational savings with respect to the filters designed by impulse response sampling. The agreement between the edge values obtained by the filters designed according to the scheme proposed in this work and those obtained by standard techniques is very good.

Linear programming design of FIR raised cosine filterswith >100% excess bandwidth

The authors describe a design method for realising FIR linear phase raised cosine filters with >100% excess bandwidth. Using linear programming, the method approximates the ideal filter response in the frequency domain while ensuring zero intersymbol interference (ISI) in the time domain. It is shown that the method is capable of generating designs closely matching the ideal raised cosine response. As an example, the design of a 21-tap FIR filter with a roll-off factor of 1.2 is included.

The use of model reduction techniques for designing IIR filters with linear phase in the passband

A technique to design IIR filters with linear phase in the passband is presented. This technique is based on model reduction of an FIR prototype using frequency weighting to improve the approximation in the transition region. Filters designed using the proposed technique are compared with linear-phase FIR designs and to IIR phase equalized designs with respect to computational complexity and group delay. It is shown that for highly selective filters, the proposed technique offers a good compromise.

Optimal decorrelating receivers for DS-CDMA systems: a signal processing framework

Code division multiple access (CDMA) schemes allow a number of asynchronous users to share a transmission medium with minimum cooperation among them. However, sophisticated signal processing algorithms are needed at the receiver to combat interference from other users and multipath effects. A discrete-time multirate formulation is introduced for asynchronous CDMA systems, which can incorporate multipath effects. This formulation reveals interesting links between CDMA receivers and array processing problems. In this framework, linear receivers are derived that can completely suppress multiuser interference (decorrelating receivers). A criterion is introduced, which guarantees the decorrelating property, while providing optimal solutions in the presence of noise. Parametric FIR designs as well as nonparametric solutions are delineated, and their performance is analyzed. The proposed receivers are resistant to near-far effects and do not require the estimation of the users' and noise powers.

Design of discrete coefficient FIR digital filters with arbitrary amplitude and phase responses

The design of FIR digital filters with discrete coefficients in the complex frequency domain is considered. A design method based on a recently developed weighted-least-squares (WLS) algorithm is presented. First, FIR filters with continuous coefficients are designed, using the WLS algorithm to meet the desired frequency response specifications in the minimax sense. To avoid the effect of a nonuniformly distributed coefficient grid due to discretization of filter coefficients, a procedure is then performed to obtain an optimal filter gain factor. Finally, utilizing the error weighting function obtained by the WLS algorithm, an efficient discrete optimization process is performed to obtain a discrete solution in the minimax sense. The efficiency of the method is illustrated by the design of discrete-coefficient FIR filters with constant group delay and filter length greater than 60. >

Efficient computational procedure for the design of FIR digital filters using WLS technique

The design of an FIR filter using the weighted least-squares (WLS) technique involves solving a Toeplitz matrix problem. However, if the requirement that the impulse response of the filter must be exactly symmetrical is imposed, the matrix becomes non-Toeplitz. The authors point out that it is Toeplitz-plus-Hankel, and present a method with complexity O(N2) for solving the WLS problem. As exact symmetry is imposed on the impulse response, the number of variables to be solved is reduced by about a factor of two. This results in smaller matrices and, as a consequence, the new method uses less computer time per iteration than the Toeplitz case.

Genetic approach to design of multiplierless FIR filters

The design of multiplierless FIR filters using genetic algorithms is presented. The proposed algorithm uses simple operators (reproduction, crossover, and mutation) to search through the discrete coefficient space of predefined power-of-two coefficients. This approach has proved to be highly effective and outperformed existing multiplierless FIR design techniques.

ON THE USE OF LP TO DESIGN MULTIDIMENSIONAL VIDEO FIR FILTERS

Filter design formulations simultaneously controlling both frequency and space-time behaviour are rather interesting for video applications. An FIR design tool addressing such formulations has been built using standard linear programming packages. The result has been quite satisfactory and the cost was very reasonable both in terms of man-time effort and required computing facilities. The construction of such a CAD tool and its performance are the subject of this paper.

A unified approach to IFIR filter design using B-spline functions

An efficient procedure is presented for the design of interpolated finite impulse response (IFIR) filters with linear phase. The algorithm uses the uniform B-spline function as an interpolator and solves the optimal Chebyshev approximation problem on the appropriate subinterval. The technique can be used for the design of general low-pass, high-pass and bandpass filters. Although the number of multiplications of the IFIR filter is dependent on the bandwidth and the center frequency of the desired filter, this approach nearly always provides a substantial reduction in complexity when compared to other FIR and IFIR design procedures.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Sampling in-phase and quadrature components of band-pass signals

A filtering method for sampling the lowpass equivalent of a bandpass analog signal is introduced. This input is sampled at exactly twice the sampling rate of the in-phase and quadrature components provided at the output. The sampling frequency determination and the lowpass decimator filter design are straightforward. The practical implementation of the sampling method is accomplished by the polyphase realization of the filter; this implementation is particularly suitable for linear phase FIR designs.

N-dimensional symmetries and their applications in digital filters

N-dimensional ( N-D) digital signal processing always results in enormous data processing and numerous parameters to be determined. The use of symmetries existing in the desired frequency specifications largely reduces the independent parameters, and furthermore, reduces the computation in the implementation. N-D digital filter symmetries existing in the frequency domain are developed and are related to numerator and denominator polynomials C( z 1, …, z N ). Constraints for identify magnitude ∥ C( rme jω 1, …, e jω N )∥ symmetries, anti-identity phase θ( ω 1,…, ω N ) symmetries, and conjugate complex frequency response C(e jω 1,…e j ω N symmetries, are developed. The necessary and sufficient conditions for a polynomial C( z 1, …, z N ) to satisfy a certain symmetry constraint are proposed. The newly developed symmetry constraints are used to derive special forms of discrete polynomials C( z 1, …, z N ) possessing these symmetries. The stability constraint is then imposed on the newly derived polynomial forms. These polynomial forms can be used in the design (in the frequency domain) and implementation of FIR and IIR digital filters, and will provide great saving of computation work and simplified hardware architecture.

FIR design by non-uniform sampling in frequency domain

In this paper an expression for H(z) has been derived in terms of N independent samples {Hk }. It has then been used to examine effects of non-uniform frequency sampling on the resultant frequency response of FIR filters. This has been applied first to the non-uniform sampling in both the passband and stopband, of a desired filter, and then to non-uniform sampling in the stopband only. Several lowpass filter designs have been examined by these methods and results discussed.

Maximally Linear FIR Digital Differentiators: A Review

Digital differentiators (DD) are extensively used in various computational systems. An ideal DD has the frequency response given by Hd(w)=jw,—n≤w≤π. The most popular FIR design for the differentiators is the minimax relative error (MRE) approximation, proposed by Rabiner and Schafer [1], The MRE-DDs are, in general, suitable for wideband frequency ranges with moderate accuracy, (say, 100±1%) but are not flexible enough to be efficiently adopted for limited (low, mid or high) frequency bands. Moreover, the required weighting coefficients for these DDs are computed by using an optimization algorithm [2]In this review paper, we discuss a new class of digital differentiators, recently investigated by us, which have maximally linear (ML) frequency response at w=0 or w=π/2 or w=π. Correspondingly, this design yields efficient approximations for low, mid or high frequency ranges, giving extremely low relative errors (RE). A universal digital differentiator has also been obtained, which covers the frequency range 0≤w≤0.90π. Mathematical formulas for computing the exact values of the weighting coefficients have also been given.

Note on FIR design by frequency sampling method

ABSTRACT Expressions for FIR filter weights have been derived for frequency sampled arbitrary magnitude and a linear phase response. This has been done for four cases: samples taken at uniform frequency intervals and then for the samples taken uniformly at midpoints between interval integers; in both cases odd and even number of points, within ( ± π / T) range, have been considered

Design of minimum phase FIR digital filters

Minimum phase FIR filters are known to have certain practical advantages, e.g. minimum group delay, reduced order for given gain specifications, and lower coefficient sensitivity, when compared with the more common linear phase filters. In the paper, a new adaptive method for designing such filters is presented. The algorithm requires a gain specification in a manner identical to the linear phase case. Conditions for optimality are investigated in terms of the zeros' configuration, equiripple characteristics, minimax and LMS criteria. The result is a very flexible minimum phase FIR filter design technique, with the potential to accommodate a number of different filter structures and types. It is thought to be the second, after the transformation of linear to minimum phase approach, able to guarantee optimum Chebyshev solutions.