SUMMARYPolynomial approximations are extensively used in analog and IIR digital filter design. In this paper, a comprehensive filter design and an optimization procedure are presented explicitly using a filter-appropriate modified Pascal polynomial. The so-designed all-pole Pascal filters exhibit non-equiripple passband and monotonic transition and stopband responses. The order of the new Pascal filters is calculated from the order inequality which, although it cannot be analytically solved, leads to a nomograph that has been created and is presented here. Inevitably, the mathematical complexity introduced by the nature of the Pascal polynomials makes the analytical expression of the poles of the transfer function unfeasible and for that reason poles are given by means of appropriate tables. The design method is demonstrated in several detailed examples and Pascal filters are compared with their all-pole counterparts, Butterworth and Chebyshev, over which they reveal certain advantages and disadvantages. Copyright POLYNOMIAL APPROXIMATIONSThe ideal normalized lowpass gain response is approximated within the tolerances imposed by magnitude specifications given in terms of plain gain, logarithmic gain in dB or attenuation, as shown in Figures 1(a)-(c), respectively. Reference level H o is usually taken equal to 1 (i.e. a o = 0 dB) without loss of generality and therefore filter requirements are determined by three numbers:S and {H C H S } or {a max a min } where a max = 20 log(H o /H C ) and a min = 20 log(H o /H S ) Since a linear system of order N is described by a linear differential equation of degree N , the corresponding transfer function H N (s) is a rational function of s, and the gain takes the form:

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This paper aims at an investigation of factors of differentiation of basic social and economic characteristics of foreign immigrants in the Region of Western Greece. The paper explores whether the thesis of urban-rural divide is relevant for the differentiation of immigrants’ socio-economic characteristics in a typical Region of Greece, where there is a strong interplay between major urban centers and large rural areas. Findings show that spatial factors play a very limited role in the differentiation of socio-economic characteristics of immigrants and indicate that other factors are more important. Thus, and as regards socio-economic characteristics of immigrants, the overall picture is that of urban-rural continuum rather than divide.