Design Of FIR Digital Filters Research Articles

Design of FIR digital filters with specified tolerances—A neural network approach

AbstractThis paper presents a design method for the equal‐ripple, linear‐phase FIR digital filter when the tolerance for the error of magnitude response in the passband or stopband is specified. To realize the design when various constraints are imposed on the transfer function or magnitude response, the design problem is formulated as the optimization problem.A solution method is shown to solve the problem using the constrained neural net. When the lower bound of the magnitude error in the stopband is set as zero in the proposed method, the filter with double zeros in the stopband can easily be designed. Examples of application are shown for the minimum‐phase FIR filter and the matched filter pair with zero intersymbol interference.

Maximum entropy method and the design of linear phase FIR filters

A procedure that makes use of the maximum-entropy method (MEM) for the design of linear-phase FIR digital filters is described. It is shown that by applying MEM to the inverse of the desired gain function or its square root function, it is possible to generate linear phase FIR filters that match the given gain function to any desired degree of accuracy. Further, an iterative algorithm makes the design procedures very efficient, since the higher-order filters can be recursively generated from the lower-order ones. To minimize any residual distortion in the passband region, a final averaging scheme on the lower-order filters generates a class of linear phase FIR filters that are practically distortion free in the passband as well as the stopband. Simulation results that compare the present procedure with other well-known methods are also presented. >

Polynomial interpolation for Remez exchange method

Newton interpolation is proven to work faster when employed in the Remez exchange method. Using Newton interpolation in the method, we can increase the speed of the Remez exchange method which is widely used for the design of linear-phase Chebyshev FIR digital filters.

Computer-aided design of FIR filters

A computer-aided technique for designing FIR digital filters with close to linear phase property is presented. The approach is based on a constrained optimisation problem designed to minimise the mean-square error between a desired response and the filter response over a passband ofinterest subject to a mean-square stopband constraint. Numerical results are presented to illustrate the performance achievable.

A fast perturbation method for the design of linear phase fir digital filters of finite wordlength using single-frequency filters

In this paper a fast perturbation algorithm for the design of linear phase FIR digital filters of finite wordlength is presented. The original set of filter coefficients are obtained using the Parks-McClellan algorithm, then a small perturbation is given to these sets of coefficients. The peak deviations corresponding to the rounded set of coefficients obtained from the original and the perturbed sets are compared and the set of coefficients with the lower value of peak deviation is stored as the best set of coefficients. A further perturbation is given to the infinite precision coefficents and these are rounded to the required wordlength. Comparison is made between these rounded sets and the present best set with respect to peak deviation and the better set is stored as the best set of coefficients. This process is repeated for a finite number of times or until the peak deviation is sufficiently low. To obtain the compensating filter coefficients single-frequency filters are used. Mathematical justification for the single-frequency design is given. Important results for a large number of design examples are presented to illustrate the speed and effectiveness of the algorithm.

Design of FIR digital filters with novel prefilter structures

Two novel prefilter structures, the cascade of cosine functions (CCOSs) and a bandpass function derived by the cascade of cosine functions (BPC), are discussed. The CCOSs and BPCs are FIR functions. The implementation of CCOSs requires no multipliers and few additions, and the implementation of BPCs requires two multipliers and few additions. These prefilters can be combined with an appropriately designed equalizer based on equiripple methods, leading to an efficient FIR digital filter design. Some efficient prefilter structures derived by Adams and Willson using a combination of RRSs and CCOSs are also discussed. The number of multipliers required to implement the prefilter-equaiizer cascade with the prefilter proposed in this paper can be reduced to nearly 35% of that designed by the direct-form minimax method of McClellan and Parks. The BPC is efficient for the design of bandpass filters. By using this function as a prefilter, the number of multipliers of the corresponding equalizer required to satisfy...

Nonrecursive multiple filters on an integer residue ring

AbstractThe finite ring is used for efficient computation of filters. This paper discusses nonrecursive multiple filtering systems on an integer residue ring. The number theoretic transform, which is the Fourier transform on the finite ring, has been used for the design of FIR digital filter on an integer residue ring. A set of filters can be combined to a single filter on a finite ring, using the isomorphism derived from the Chinese remainder theorem. This equivalence is used to compute the outputs of the set of filters efficiently.An efficient algorithm is also presented to find a primitive 2t‐th root of unity which is needed for the construction of the numbers theoretic transform. For filtering multiplicity ranging from two to five, possible choices of moduli are presented. Finally, an example and evaluations of the nonrecursive multiple filter are shown.

On the design of FIR digital data transmission filters with arbitrary magnitude specifications

A simple algorithm is presented for the design of FIR data transmission filters with arbitrary magnitude specifications. The technique involves the iterative solution of a set of linear equations as opposed to the more common approach of applying linear programming to the data transmission filter design problem. The design algorithm can accommodate conventional Nyquist filters or Nyquist filters with a non-negative frequency response that can be subsequently split into matched filter pairs using spectral factorization techniques. The filters can have equiripple stopbands or can be specified to satisfy arbitrary magnitude specifications, which is a common requirement in data transmission applications. Design examples are presented for filters satisfying FCC mask specifications for digital microwave radio channels. >

Design of FIR digital filters using prescribed subfilters

A method for the design of linear-phase digital filters by the tapped cascaded interconnection of identical subfilters is presented. The method is an extension of the method proposed by Saramaki (1987). An example is given to show that the number of distinct multipliers of the filter determined by the proposed method is less than that of filters determined by Saramaki's method (1987). We also consider the case in which the subfilters are determined by multiple use of a single filter. In particular, if we can make the subfilters multiplierless then the number or multiplications per sample required to implement the overall filter is less than that required by the direct-form minimax method. Methods for the design of computationally efficient filters are also developed based on the proposed transformation method. The multiplication rate of the overall filter is the same as that of the prototype filter. It is very low as compared to that designed by the equivalent direct-form minimax method. With the proposed...

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.

Design of two-dimensional FIR digital filters by using the singular-value decomposition

Design of two-dimensional FIR digital filters by using the singular-value decomposition

Improved design of minimum-phase FIR digital filters by cepstrum and fast Hartley transform

An equiripple minimum-phase FIR filter is designed using the cepstrum and the fast Hartley transform (FHT). This fast procedure is performed entirely in the real domain and requires only two short-length FHT computations. This method avoids complicated phase wrapping and greatly reduces the aliasing error.

New algorithm for the design of linear phase FIR filters with +1, −1 and 0 coefficients

This paper describes a new algorithm for the design of digital FIR filters comprised of a transverse section with tap coefficients restricted to +1, 0 and −1 and a simple recursive network. A double accumulator recursive network was chosen since this structure offers a reasonable compromise between filter length and complexity of tap coefficient constraints. An example demonstrating the design of a lowpass filter is given.

FIR digital filter design using non-equispaced frequency sampling

Frequency-sampling design of FIR digital filters is a well established technique. The method would be of even greater utility if the constraint frequencies could be specified to lie at arbitrary points, rather than just on the standard equispaced grid. Here we show how non-equispaced sampling can easily be achieved, and offer an example of a typical filter design using this flexible new approach.

Design of FIR partial response filters with equiripple stopband attenuation (class II, V)

AbstractThis paper considers the design of transmitter and receiver FIR digital filters with partial response of class II and V for data transmission. the filters are required to band‐limit the transmitting and receiving signal, while maintaining the overall impulse response with zero intersymbol interference (ISI). Two cases are considered: 1) the case where the transmitter itself has the zero ISI impulse response; and 2) the case where the transmitter and receiver filters are matched. In the former, the length of the filter is set to be equal to the number of samples between two zero‐cross points, which are at a certain symmetrical distance from the center of the ideal impulse response. Then a linear‐phase transfer function is derived with an equiripple approximation to the ideal amplitude frequency response. In the approxiamtion, the weight in the stopband is set as less than 1, and ISI of less than 1. percent is obtained. In the design of the matched filter pair, the overall order is set in the same way as in the former. Applying the Herrman‐Schuessler design method for the minimum phase‐shift filter in the frequency domain, the transfer function is derived.To realize ISI of less than 1 percent, it suffices to set the weight in the stopband less than 5 times in the passband. Although an effort was made to decrease ISI by successive approximation with the mirror zeros as the parameters, only a slight improvement was obtained. In either case, class V requires approximately a twice higher order than class II to realize the same attenuation and ISI.

Design of multirate FIR digital filters with arbitrary passband

AbstractThis paper proposes a new method of con structing the multirate FIR digital filter with arbitrary passband, using real‐coefficient filters for the decimator and interpolator composing the multirate filter. It is already known that the bandpass filter can easily be realized using the complex‐coefficient filter. In such a construction, however, the processing of the analytic signal is required using Hubert transform, which makes the whole system somewhat complex. From such a viewpoint, this paper pre sents a method of constructing the multirate bandpass digital filter using the real‐coefficient filter. Another method is also presented, where the muitirate lowpass filter with arbitrary passband can be constructed by combining the complementary response and a lowpass filter. the multirate method is effective in realizing a narrowband response, but may not be useful in realizing a relatively wideband response. By the proposed method, the latter can easily be realized, drastically reducing the number of multiplications. Similar methods can be applied to highpass and bandstop filters.

Circularly symmetric two-dimensional multiplierless FIR digital filter design using an enhanced McClellan transformation

A new analytical approach to the determination of the coefficients of the 1st-order McClellan transformation is presented. The resultant 1st-order expression can then be used to design 2-D (2-dimensional) lowpass/highpass, bandpass/bandstop and multiband digital filters from the corresponding 1-D digital filters with a high accuracy in the circularity of magnitude response along the passband cut-off frequency. On comparing the results with those of the original 1st-order McClellan transformation, it is found that the present analytical approach does improve the effectiveness of the original McClellan transformation for 1-D to 2-D digital filter transformation. Based on the resultant 1st-order expression, the realisation of 2-D FIR structures with sum of powers-of-two coefficients is also presented.

A simple approach to the design of linear phase fir digital filters with variable characteristics

A class of linear phase digital filters is discussed for which the filter coefficients are simple functions of the parameters determining the desired frequency response. In the case of lowpass or highpass filters, the 6 dB cutoff frequency is the parameter considered here. Bandpass and bandstop filters are characterized by the center frequency and the bandwidth measured from the 6 dB cutoff frequencies. Notch filters with a first-order zero at the notch frequency are also discussed. The filters are variable over nearly the whole frequency range from zero to half the sampling frequency. Due to direct control of filter coefficients, the length of the filter does not change when it is made variable.

Effects of Shaped Piezo-Rubber Hydrophones on Directional Patterns

In this paper, aperture functions, originally applied to the design of optimum FIR digital filters, are shown to also be successfully used for suppression of side lobes in acoustics. Test hydrophones have been constructed by shading a flexible piezo-rubber sheet in the form of the aperture functions. Experimental results of Hanning, Hamming and Hamming like Kaiser aperture functions have verified the theoretical predictions on suppression of side lobes. In addition, the fact that a curved Hanning-hdrophone functions as a constant beam width hydrophone over a wide frequency range is discussed.

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.