A practical method for designing FIR digital filters in the complexdomain

A new method is presented for the design of FIR fillers in the complex domain. The method converts the complex approximation problem into an equivalent real nonlinear optimization problem, which is solved by successive linearization using an effective geometrical linearization technique. The method converges rapidly, and the solution has a guaranteed accuracy. It also has the flexibility of allowing addition of extra constraints such as constant group delay constraints and transition-band magnitude overshoot constraints. Numerical examples are presented to illustrate the performance of the method     

Design of 2-D FIR filters by nonuniform frequency sampling

A method for the frequency-sampling design of two-dimensional FIR filters with nonuniformly spaced samples is presented. By imposing some mild constraints on sample location in the 2-D frequency plane, the method always provides a unique design solution. Important characteristics of the method are design flexibility through the use of nonuniform samples and computational efficiency. This method is compared with the uniform sampling, inverse discrete Fourier transform (DFT) approach and also with a general method for filter design called arbitrary sampling. The method presented is shown to require much less computation than the arbitrary sampling approach, which may lead to possible degenerate cases where there is no unique solution for the filter. The method proposed does not lead to such degeneracies and possesses more flexibility than the uniform sampling method. Examples are given in order to compare the new method with the uniform sampling method     

A recursive frequency-sampling method for designing zero-phase FIRfilters by nonuniform samples

A novel frequency-sampling method for designing zero-phase FIR filters from nonuniform samples is presented. The method is fast, simple, recursive and can be used in the design of 1D or 2D zero-phase FIR filters by imposing some mild constraints on sample locations in the 2D frequency plane. Based on a novel Newton representation of the filter transfer function the proposed method guarantees real results, saves a number of operations and produces accurate solutions even in cases of designing high-order filters or when the interpolation matrix is ill-conditioned. In the progressive case when the next sample appears, the design parameters are evaluated by updating the old ones with correction terms that could be used as indicators for convergence, approximation, or filter reduction. The method can be used in mD filter design, in LU-factorization or in inversion of cosine matrices     

A novel common-subexpression-elimination method for synthesizing fixed-point FIR filters

We propose a common-subexpression-elimination (CSE) method for the synthesis of fixed-point finite-impulse response (FIR) filters. The proposed CSE algorithm considers both the redundancy among the canonic-signed-digit (CSD) filter coefficients and the length of the critical path in the multiplier block of a transposed-form FIR filter. Therefore, the proposed CSE method can perform tradeoff designs between complexity and the throughput rate. The number of adders synthesized by our method is commensurate with that by the graph-dependence algorithms. On the other hand, our method can synthesize a high-order complicated FIR filter in a few seconds.     

A polynomial-time algorithm for designing FIR filters withpower-of-two coefficients

This paper presents a polynomial-time algorithm for designing digital filters with coefficients expressible as sums of signed power-of-two (SPT) terms. Our proposal is based on an observation that under certain circumstances, the realization cost of a filter with SPT coefficients depends only on the total number of SPT terms, regardless of how the terms distribute among the coefficients. Therefore, the number of SPT terms for each coefficient is not necessarily limited to a fixed number. Instead, they should be allowed to vary subject to a given number of total SPT terms for the filter. This provides the possibility of finding a better set of coefficients. Our algorithm starts with initializing all the quantized coefficient values to zero. It chooses one SPT term at a time and allocates it to the currently most deserving coefficient to minimize the L^∞ distance between the SPT coefficients and their corresponding infinite wordlength values. This process of allocating the SPT terms is repeated until the total number of SPT terms for the filter is equal to a prescribed number. For each filter gain, the time complexity is a second-order polynomial in the number of coefficients to be optimized and is a first-order polynomial in the filter wordlength     

Iterative procedure for designing two-dimensional FIR filters

We describe a new iterative method to design two-dimensional linear-phase FIR filters with arbitrary magnitude characteristic. The procedure is simple and can be used easily in designing filters of large order. This method is based on the use of the method of projection on to convex sets and can be implemented using the FFT algorithm.     

Frequency sampling method for designing 2-D FIR real-coefficientdigital filters using Hermite interpolation

A novel frequency-sampling method for designing 2-D real-coefficient FIR filters, given the values and slope estimates of the desired frequency response at each of the node points of a rectangular grid, is presented. Based on a new class of bivariate Hermite-type polynomials suitable for interpolating at complex conjugate points, and using Kronecker products, the original 2-D filter design problem is reduced to the solution of two 1-D systems of linear equations. Additional advantages of the method are the securing of the existence and uniqueness of the solution of the design problem, computational efficiency, the use of simple and recursive 1-D algorithms; the guarantee of real accurate results; and the inherent parallelism. The method is also applied to design 2-D symmetric FIR filters and can be extended to m-D design problems     

A computationally efficient nonuniform FIR digital filter bank for hearing aids

A computationally efficient nonuniform digital FIR filter bank is proposed for hearing aid applications. The eight nonuniform spaced subbands are formed with the help of frequency-response masking technique. Two half-band finite-impulse response (FIR) filters are employed as prototypes resulting in significant improvements in the computational efficiency. We show, by means of example, that an eight-band nonuniform FIR filter bank with stopband attenuation of 80 dB can be implemented with 15 multipliers. The performance of the filter bank is enhanced by optimizing the gains for each subband. The tests on various hearing loss cases suggest that the proposed filter achieves reasonable good matching between audiograms and magnitude responses of the filter bank at very low computational cost.     

A class of high-pass digital MTI filters with nonuniform PRF

A class of digital feed-forward filters is developed, satisfying the requirement of a maximally flat stopband characteristic at zero frequency if the pulse-repetition frequency is modulated. A simple algorithm is given to obtain the filter coefficients. Some properties are summarized.     

Complex Chebyshev approximation for FIR digital filters

An adaptive approach to FIR (finite impulse response) filter design is applied to a fully general complex specification, showing it to be capable of giving an optimum Chebyshev solution. It is thought to be one of the first practical approaches to achieve this in the case of a complex function. Design examples include a bandpass filter with nearly linear phase and all-pass filters with general shaping phase. Comparisons are drawn with equivalent results from other algorithms     

A new structure and design method for variable fractional-delay 2-D FIR digital filters

In this paper, a new structure and design method are proposed for variable fractional-delay (VFD) 2-D FIR digital filters. Basing on the Taylor series expansion of the desired frequency response, a prefilter–subfilter cascaded structure can be derived. For the 1-D differentiating prefilters and the 2-D quadrantally symmetric subfilters, they can be designed simply by the least-squares method. Design examples show that the required number of independent coefficients of the proposed system is much less than that of the existing structure while the performance of the designed VFD 2-D filters is still better under the cost of larger delays.     

A WISE method for designing IIR filters

The problem of designing optimal digital IIR filters with frequency responses approximating arbitrarily chosen complex functions is considered. The real-valued coefficients of the filter's transfer function are obtained by numerical minimization of carefully formulated cost, which is referred here to as the weighted integral of the squared error (WISE) criterion. The WISE criterion linearly combines the WLS criterion that is used in the weighted least squares approach toward filter design and some time-domain components. The WLS part of WISE enforces the quality of the frequency response of the designed filter, while the time-domain part of the WISE criterion restricts the positions of the filter's poles to the interior of an origin-centred circle with arbitrary radius. This allows one not only to achieve stability of the filter but also to maintain some safety margins. A great advantage of the proposed approach is that it does not impose any constraints on the optimization problem and the optimal filter can be sought using off-the-shelf optimization procedures. The power of the proposed approach is illustrated with filter design examples that compare favorably with results published in research literature     

Method for designing recursive digital filters with short wordlength

With specified passband ripple, stopband ripple and cutoff frequencies, this method employs Crochiere's 2-parameter optimisation to equalise the passband and stopband statistical wordlengths before optimising coefficients in a multi-dimensional discrete space. Better design can be obtained by investing more computational time. This method is applicable to any recursive digital filters.     

An improved design method based on polyphase components for digital FIR filters

This paper presents an efficient design of digital finite impulse response (FIR) filter, based on polyphase components and swarm optimisation techniques (SOTs). For this purpose, the design problem is formulated as mean square error between the actual response and ideal response in frequency domain using polyphase components of a prototype filter. To achieve more precise frequency response at some specified frequency, fractional derivative constraints (FDCs) have been applied, and optimal FDCs are computed using SOTs such as cuckoo search and modified cuckoo search algorithms. A comparative study of well-proved swarm optimisation, called particle swarm optimisation and artificial bee colony algorithm is made. The excellence of proposed method is evaluated using several important attributes of a filter. Comparative study evidences the excellence of proposed method for effective design of FIR filter.     

Two-dimensional FIR digital filters with maximally flat magnitude

Generation of a class of maximally flat magnitude two-dimensional FIR functions employing McClellan transformation is described and their properties are discussed.     

Phase constraints on FIR digital filters

The letter shows how FIR digital filters can be designed to meet a specific nonlinear phase response in the transition region, although the gain of the filter is not specified in this region.     

Improved design procedure for multiplierless FIR digital filters

An algorithm is presented for the design of finite impulse response filters, yielding filter coefficients that are either single powers of two, or sums or differences of two powers of two. In all cases tried this algorithm gives simpler realisations compared both to conventional design methods and to other multiplierless design algorithms.<>     

Design of digital FIR notch filters

A new procedure for designing digital FIR notch filters for a specified notch frequency ω_d and 3-dB rejection bandwidth Δω has been proposed. Design formulae for computing the required weights and the length N for the filter have been derived. Illustrative examples confirming the new approach are also given     

A design algorithm for optimal low-pass nonlinear phase FIR digital filters

The transfer function of the low-pass nonlinear phase finite impulse response (NLPFIR) digital filter is decomposed into a nonlinear phase part and a linear phase part. An algorithm is proposed to iteratively design the magnitude of the linear phase part and the squared magnitude of the nonlinear phase part by directly calling the Remez algorithm of McClellan, et al. [1]. In the design of the nonlinear phase part, we assume that the linearity constraint on the phase is dropped but the phase response is not specified. A scheme is incorporated into our algorithm so that it can design the filter with the desired ripple ratio. This approach also leads to a method for finding the minimum ripple ratio for the given orders of the two parts and band edges of the filters. The filters with ripple ratio larger than this minimum value can be designed by our algorithm and neither passband nor stopband ripples are required to be prescribed. Analysis of roundoff noise reveals that the cascade filter implementation usually needs higher wordlengths than its direct for counterpart for the same roundoff noise performance.