A technique, based on the residue number system (RNS) with diminished-1 encoded channel, has being used for implementing a finite impulse response (FIR) digital filter. The proposed RNS architecture of the filter consists of three main blocks: forward and reverse converter and arithmetic processor for each channel. Architecture for residue to binary (reverse) convertor with diminished-1 encoded channel has been proposed. Besides, for all RNS channels, the systolic design is used for the efficient realization of FIR filter. A numerical example illustrates the principles of diminished-1 residue arithmetic, signal processing, and decoding for FIR filters.

A new class of continuous-time low-pass filter using a set of Jacobi polynomials, with all transmission zeros at infinity, is described. The Jacobi polynomial has been adapted by using the parity relation for Jacobi polynomials in order to be used as a filter approximating function. The resulting class of polynomials is referred to as a pseudo Jacobi polynomials, because they are not orthogonal. The obtained magnitude response of these filters is more general than the magnitude response of the classical ultraspherical filter, because of one additional degree of freedom available in pseudo Jacobi polynomials. This additional parameter may be used to obtain a magnitude response having either smaller passband ripples or sharper cutoff slope. Monotonic, critical monotonic, or nearly monotonic passband filter approximating functions can be also generated. It is shown that proposed pseudo Jacobi polynomial filter approximation also includes the Chebyshev filter of the first kind, the Chebyshev filter of the second kind, the Legendre filter, and many transitional filter approximations, as its special cases. Several examples are presented, and detailed formulas including the practical suggestions for their efficient implementation are also provided. The proposed nearly monotonic filter is compared with the least-square-monotonic filters, designed as critical monotonic, in details. The advantages of the new filters are discussed.

SUMMARY A new type of filter approximation, which utilizes orthonormal Legendre polynomials, referred to as sum‐of‐squared Legendre polynomials, is presented in this paper. Power transmission coefficient and the group delay of the proposed filter are compared with those of the Butterworth, Legendre–Papoulis, and Halpern filters. In order to illustrate the design of the proposed filter function, sum‐of‐squared Legendre polynomials coefficients and normalized element values of the low‐pass LC (inductor‐capacitor) ladder network prototype are given, up to the 10th degree. For continuous‐time domain filtering, doubly terminated LC ladder network topologies have very low sensitivities to changes of component values. In order to determine the effect of variation of all reactive components on the filter attenuation characteristic, the new sensitivity function has been proposed. Copyright © 2015 John Wiley & Sons, Ltd.

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The aim of this study is to estimate the effects of metal frame glasses on the electric field distribution and Specific Absorption Rate (SAR) inside the model of a human head. The numerical solution of the equations of electromagnetic wave propagation has been used to obtain the electric field distribution and values of SAR in the vicinity of the metal frame glasses, exposed to cell phone radiation at the frequency of the 3G mobile network. The assessment of these effects has been performed during the conversation over a mobile phone. In order to obtain the most accurate results, the realistic 3D model of the human head, as well as the model of metal frame glasses have been created. For evaluating the mentioned effects, a comparative analysis of models with and without glasses has been carried out. Therefore, the obtained results are presented within different biological tissues and organs from which the human head model was made.