Abstract
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.
Highlights
Two-dimensional (2D) digital filters find applications in many areas such as geophysics, robotics, biomedicine, image processing, and prospecting for oil [1, 2]
A rotated filter is designed by rotating a stable 1D analog filter and using the double bilinear transformation to obtain the corresponding digital filter
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 valid for a general 2D polynomial, it is shown in this paper that the denominator polynomials of the 2D discrete transfer functions of the rotated filters belong to a specific class of 2D polynomials for which the planar least-square inverse (PLSI)-based stabilization method can be applied
Summary
Two-dimensional (2D) digital filters find applications in many areas such as geophysics, robotics, biomedicine, image processing, and prospecting for oil [1, 2]. A new method is proposed for realizing stable 2D rotated GIC digital filters using planar least-square inverse (PLSI) polynomials [10,11,12,13,14] It is shown [10,11,12,13,14] 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 valid for a general 2D polynomial, it is shown in this paper that the denominator polynomials of the 2D discrete transfer functions of the rotated filters belong to a specific class of 2D polynomials for which the PLSI-based stabilization method can be applied
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
