Design of Stable Circularly Symmetric Two-Dimensional GIC Digital Filters Using PLSI Polynomials
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Research Article Design of Stable Circularly Symmetric Two-Dimensional GIC Digital Filters Using PLSI Polynomials Ezra Morris Abraham Gnanamuthu,1 C. Eswaran,2 and K. Ramar1 1 Faculty 2 Faculty
of Engineering, Multimedia University, Cyberjaya 63100, Selangor, Malaysia of Information Technology, Multimedia University, Cyberjaya 63100, Selangor, Malaysia
Received 5 December 2005; Accepted 24 May 2007 Recommended by Ricardo Merched A method for designing stable circularly symmetric two-dimensional digital filters is presented. Two-dimensional discrete transfer functions of the rotated filters are obtained from stable one-dimensional analog-filter transfer functions by performing rotation and then applying the double bilinear transformation. The resulting filters which may be unstable due to the presence of nonessential singularities of the second kind are stabilized by using planar least-square inverse polynomials. The stabilized rotated filters are then realized by using the concept of generalized immittance converter. The proposed method is simple and straight forward and it yields stable digital filter structures possessing many salient features such as low noise, low sensitivity, regularity, and modularity which are attractive for VLSI implementation. Copyright © 2007 Ezra Morris Abraham Gnanamuthu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Two-dimensional (2D) digital filters find applications in many areas such as geophysics, robotics, biomedicine, image processing, and prospecting for oil [1, 2]. A special class of 2D infinite impulse response (IIR) digital filters whose magnitude responses are approximately circularly symmetric can be realized by cascading a number of elementary filters known as rotated filters [3, 4]. A rotated filter is designed by rotating a stable 1D analog filter and then using the double bilinear transformation to obtain the corresponding digital filter. However, the stability of these rotated digital filters is not guaranteed due to the presence of nonessential singularities of the second kind [5, 6]. To overcome this problem, a new type of rotated filters known as pseudorotated filters has been proposed in [7]. Methods for realizing rotated and pseudorotated digital filters by using the concept of generalized immittance converter (GIC) have been reported in [8, 9]. In this paper, a new method is proposed for realizing stable 2D rotated GIC digital filters using planar least-square inverse (PLSI) polynomials [10–14]. It is shown [10–14] that an unstable 2D IIR digital filter can be stabilized by replacing its denominator polynomial, say B(z1 , z2 ), by a new polynomial B (z1 , z2 ) which is the double PLSI polynomial of
B(z1 , z2 ) and the magnitude response of the resulting stable filter would be approximately equal to that of the original unstable filter. Though this approach is not va
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