Tapio Saramäki

Design of computationally efficient interpolated FIR filters

The number of multipliers required in the implementation of interpolated FIR (Finite-impulse response) filters in the form H(Z)=F(z/sup L/)G(z) is studied. Both single-stage and multistage implementations of G(z) are considered. Optimal decompositions requiring fewest number if multipliers are given for some representative low-pass cases. An efficient algorithm for designing these filters is described. It is based on iteratively designing F(z/sup L/) and G(z) using the Remez multiple-exchange algorithm until the difference between the successive stages is within the given tolerance limits. A novel implementation for G(z) based on the use of recursive running sums is given. The design of this class of filters is converted into another design problem to which the Remez algorithm is directly applicable. The results show that the proposed methods result in significant improvements over conventional multiplier efficient implementations of FIR digital filters. >

Improved technique for design of perfect reconstruction FIR QMF banks with lossless polyphase matrices

A technique is developed for the design of analysis filters in an M-channel maximally decimated, perfect reconstruction, finite-impulse-response quadrature mirror filter (FIR QMF) bank that has a lossless polyphase-component matrix E(z). The aim is to optimize the parameters characterizing E(z) until the sum of the stopband energies of the analysis filters is minimized. There are four novel elements in the procedure reported here. The first is a technique for efficient initialization of one of the M analysis filters, as a spectral factor of an Mth band filter. The factorization itself is done in an efficient manner using the eigenfilters approach, without the need for root-finding techniques. The second element is the initialization of the internal parameters which characterize E(z), based on the above spectral factor. The third element is a modified characterization, mostly free from rotation angles, of the FIR E(z). The fourth is the incorporation of symmetry among the analysis filters, so as to minimize the number of unknown parameters being optimized. The resulting design procedure always gives better filter responses than earlier ones (for a given filter length) and converges much faster. >

Interpolation filters with arbitrary frequency response for all-digital receivers

If the sampling of the received signal is not synchronized to the incoming data symbols, timing adjustment must be done after sampling using interpolation. If the impulse response of the interpolation filter is a polynomial or piecewise polynomial, it can be implemented efficiently using a Farrow structure. The remaining problem is that there exist no good design methods for polynomial-based filters. In this paper we present a new synthesis technique which allows to design polynomial-based interpolation filters with an arbitrary frequency response. This means that we are able to design interpolation filters in the same manner as normal FIR filters. There can be many passbands and stopbands, and for every band we can set the desired amplitude and weight.

On the design of digital filters as a sum of two all-pass filters

The necessary and sufficient conditions are given for a digital filter transfer function to be implementable as a sum of two all-pass filters. The conditions are derived directly in the z -plane. The class of filters satisfying these conditions is shown to be wider than the class of filters obtained via the bilinear transformation from the corresponding conventional analog filters. An example shows that the given conditions enable us to design complementary filter pairs with different numerator and denominator orders directly using magnitude squared functions. These filters compare favorably with the corresponding classical filters.

Optimization and efficient implementation of FIR filters with adjustable fractional delay

An efficient design method is introduced for optimizing polynomial-based FIR filters with adjustable fractional delay. Given the passband region, the filter parameters are optimized to minimize in the passband the worst-case phase delay deviation from the desired value (the maximum deviation for fractional delays between zero and unity) subject to a given worst-case amplitude deviation from unity in the passband. It is shown that the filter with fractional delay equal to half determines the lower limit for the achievable amplitude distortion. Because the filters under consideration are polynomial-based, they can be efficiently implemented using the modified Farrow structure introduced by the authors.

On properties and design of nonuniformly spaced linear arrays (antennas)

The properties of nonuniformly spaced linear arrays (and nonrecursive filters with nonequidistant taps) are studied. It is shown that in many cases the element spacings of the optimal solution are integer multiples of a suitably chosen basic spacing. This significantly simplifies the design procedure since the arrays can be designed as thinned uniformly spaced arrays, thus avoiding complicated nonlinear optimizations. A simple thinning procedure is used. Another design procedure based on Nth-band FIR (finite-impulse response) filter concepts is introduced, making possible the use of standard FIR filter design methods for nonuniformly spaced arrays; illustrative examples are included. The results compare favorably to published results for nonuniformly spaced designs that did not exploit the special properties of uniform or discrete nonuniform arrays. >

A class of window functions with nearly minimum sidelobe energy for designing FIR filters

A class of window functions is introduced for designing FIR filters. These window functions are obtained from the rectangular window by using a simple frequency transformation. The frequency transformation contains an adjustable parameter with which the mainlobe width and, correspondingly, the minimum stopband attenuation of the resulting filter can be controlled. The transition bandwidth of the filter can then be controlled by the filter order. Like the well-known Kaiser window, the proposed windows are close approximations to the discrete prolate functions which minimize the sidelobe energy. The FIR filters obtained by using the new window are slightly better than those obtained by using the Kaiser window. The main advantages of the proposed window compared to the Kaiser window are that the new window possesses analytic expressions in both the time and frequency domains and no power series expansions are required in evaluating the window function. Furthermore, it provides a better approximation to the discrete prolate functions.<<ETX>>

A systematic algorithm for the design of multiplierless FIR filters

A systematic algorithm is proposed for designing multiplierless finite-impulse response (FIR) filters. This algorithm minimizes the number of adders required to implement the overall filter to meet the given amplitude criteria. The optimization is performed in two basic steps. First, a linear programming algorithm is used for determining a parameter space of the infinite-precision coefficients including the feasible space where the filter meets the given amplitude specifications. The second step involves finding the filter parameters in this space such that the resulting filter meets the given criteria with the simplest coefficient representation forms. The efficiency of the proposed algorithm is illustrated by means of several examples taken from the literature.

Recursive implementation of FIR differentiators with optimum noise attenuation

We introduce a computationally efficient recursive implementation of digital finite impulse response (FIR) filters for estimating the rate of change or slope of digitized signals. The proposed FIR differentiator is characterized by the optimal attenuation of white noise and an efficient suppression of upper-band frequencies. The basic structure needs only one multiplier, which becomes a power of two with an appropriate selection of the length of the impulse response. The structure does not need resetting and recovers from any bit errors. For long filters, sampling rate reduction by decimation gives further computational savings.

The synthesis of half-band filter using frequency-response masking technique

An important property of a half-band filter is that half of its coefficient values are trivial. This yields significant advantage in terms of its computational complexity. Nevertheless, the complexity of a half-band filter is still very high if its transition-width is very narrow. In this letter, we introduce a novel method for the synthesis of very sharp half-band filter using the frequency response masking technique. >