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FACTA UNIVERSITATIS (NI S) SER.: ELEC. ENERG. vol. 19, no. 1, April 2006, 143-146

SER.: ELEC. ENERG. vol. 19, no. 1, April 2006, 143-146
Al-Alaoui Operator and the -Approximation for
Discretization of Analog Systems
Mohamad Adnan Al-Alaoui
Abstract: The -approximation for discretization of analog systems was recently in-
troduced. In this paper it is shown that the -approximation is exactly the same as the
parameterized Al-Alaoui operator.
Keywords: Al-Alaoui operator, discretization, digital filters.
1 Introduction
A popular method for designing IIR digital filters is to map the transfer function of
a corresponding analog filter using an s-to-z transformation [1]-[6]. It is desirable
that the mapping procedures have the following two properties: 1) they should map
the left half of the s-plane to the interior of the unit circle in the z-plane which
would insure that stable analog filters map into stable digital filters, and 2) the
imaginary axis of the s-plane should be mapped onto the unit circle circumference
in the z-plane.
The bilinear transform meets the above requirements. However, it introduces a
warping effect due to its nonlinearity, albeit it can be ameliorated somewhat by a
pre-warping technique. The backward difference transform satisfies the first con-


Source: Al-Alaoui, Mohamad Adnan - Faculty of Engineering and Architecture, American University of Beirut, Lebanon


Collections: Engineering