Design Of Finite Impulse Response Digital Filters Research Articles

A weighted least squares algorithm for quasi-equiripple FIR and IIR digital filter design

It has been demonstrated by several authors that if a suitable frequency response weighting function is used in the design of a finite impulse response (FIR) filter, the weighted least squares solution is equiripple. The crux of the problem lies in the determination of the necessary least squares frequency response weighting function. A novel iterative algorithm for deriving the least squares frequency response weighting function which will produce a quasi-equiripple design is presented. The algorithm converges very rapidly. It typically produces a design which is only about 1 dB away from the minimax optimum solution in two iterations and converges to within 0.1 dB in six iterations. Convergence speed is independent of the order of the filter. It can be used to design filters with arbitrarily prescribed phase and amplitude response.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A method for accelerating the design of optimal linear-phase FIR digital filters

A simple method is presented for reducing the execution time of the McClellan-Parks-Rabiner (1973) FIR (finite impulse response) digital filter design program on computers with a floating-point processor. It is found that 80% to 90% of the execution time of this program involves only four lines of the program code. By efficiently implementing these four lines of code in assembly language it is possible to significantly reduce the execution time. Examples of this method are given for personal computers based on both 8086-family and 68000-family microprocessors with a corresponding math coprocessor. It is found that for these computers the method reduces execution time by a factor of 1.6 to 1.9.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A generalized Remez method for the design of FIR digital filters

A generalized Remez method for the design of finite impulse response (FIR) filters is proposed. The method is based on a new problem formulation which largely eliminates certain difficulties brought about by an undetermined approximating polynomial. The new method can be used to design maximal-ripple (MR), extra-ripple (ER), and weighted-Chebyshev filters satisfying prescribed specifications, and, with the addition of some simple techniques, filters can be designed that are free from transition region anomalies. The method incorporates a new initialization strategy and a selective search technique to reduce the amount of computation needed to carry out a design. Extensive experimental results show that the new method is robust and at least as efficient as existing methods for the design of weighted-Chebyshev filters. For MR as well as ER filters, the new method is both robust and very efficient. >

Design of linear-phase direct-form FIR digital filters with quantized coefficients using error spectrum shaping

A generalization of the statistical approach of D.S.K. Chan and L.R. Rabiner (IEEE Trans. Audio Electroacoust., vol.AU-21; p.354-66, Aug. 1973) for predicting the effects of quantized coefficients in direct-form finite-impulse response (FIR) filters is presented. The analysis is used on more sophisticated quantizing procedures involving linear feedback of rounding errors. It is shown that the expected disturbance filter frequency response due to quantization can be controlled. The effect is concentrated in tolerant frequency bands and significantly reduced in critical ones. The price paid is an increase of overall expected disturbance. The method is demonstrated in a practical filter design. A low-pass filter for factor 2 decimation that has greater margins for quantization effects in the passband than in the stopband is specified.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Very fast method for the design of FIR digital filters with linear phase

A simple but very fast method for the design of linear-phase FIR (finite-impulse response) digital filters is presented. A comparison of design times required for the proposed method and for the well-known Parks-McClellan algorithm is given to show the superiority in speed of the proposed method. Other merits of the algorithm are also indicated.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

On the design of optimal equiripple FIR digital filters for data transmission applications

An improved linear programming algorithm is required for the design of finite impulse response (FIR) digital filters. This algorithm avoids the numerical ill-conditioning problems which commonly occur due to the necessity to sample the frequency response on a very dense grid of points for high-order filters. This technique is applied to the design of equiripple FIR Nyquist filters and equiripple FIR transmit and receive matched-filters for data transmission applications. The use of linear programming insures that the designs are optimal in the sense that they achieve the maximum possible stopband attenuation for a given filter order and stopband edge frequency. The design algorithm for the matched filters consists of a two-stage process of linear programming to design a Nyquist filter with a nonnegative frequency response followed by standard spectral factorization techniques to extract the nonlinear-phase transmit and receive filters. The design software consists primarily of commonly available FORTRAN subroutine packages for linear programming and polynomial factorization, and is numerically well behaved and very accurate.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Design of Multiplierless FIR Digital Filters With Two to the N th Power Coefficients

A new method of multiplierless finite impulse response (FIR) digital filter design by using two to the N th power coefficients is presented. This method is based on the cascading, local correlation and windowing. The basic structure of these FIR filters is discussed, and several results of such filter design are presented in this paper.

Generalization of the window method for FIR digital filter design

A generalization of the conventional window method for the design of finite impulse response (FIR) digital filters is presented by including nonequal passband and stopband ripple specifications in the design process. Typically, this results in a savings of up to 30 percent in filter length in comparison to the conventional approach.

Finite Precision Design of Linear-Phase FIR Filters

The FIR (finite impulse response) filter is an essential tool for a large number of applications in communication. In this paper we consider the design of linear-phase FIR digital filters with finitely precise coefficients. Coefficient inaccuracy is known to degrade the frequency response of band-select FIR filters, especially in the stopband region. We derive a bound on the attainable stopband attenuation, and we also develop techniques for designing FIR filters with finitely precise coefficients. Mixed-integer programming algorithms are presented to select finitely precise coefficients for a filter that best approximates an arbitrary magnitude characteristic in the minimax sense. Our method generates a number of possible solutions including that of simple rounding or truncation and then selects the best finitely precise coefficients from this set. In this way, significant improvement in the filter performance is gained over methods that simply round or truncate the infinitely precise coefficients. We also show how integer programming can be used to design filters with powers of two coefficients. Such filters are easier to mechanize since they do not require multipliers.

A comparison of algorithms for minimax design of two-dimensional linear phase FIR digital filters

Linear programming algorithms for the design of finite impulse response (FIR), linear-phase digital filters can be extremely time-consuming. Two iterative design techniques using multiple-exchange ascent algorithms have been developed. These are the methods of Kamp and Thiran and Hersey and Mersereau. They are known to be much faster than the linear programming techniques. The mathematical basis for these algorithms is reviewed and differences in the algorithms are noted. Results of empirical efficiency comparisons are presented. A new algorithm for reducing the number of iterations for multiple-exchange ascent algorithms is also presented.