Abstract
Analytical methods are developed for choosing the coefficients of the first-order generalized McClellan transformation for the design of 2-D elliptically symmetric digital filters of arbitrary orientation from 1-D filters. Formulas are derived for calculating the coefficients by forcing the lower order significant terms in the power series expansion of the linear error function to zero. Formulas are also presented for calculating the coefficients of the first-order scaling-free generalized McClellan transformation. We consider all the cases of the rotated vertical and horizontal elliptical cutoff contours. The results obtained by using the derived formulas agree very well with the results of the optimization method and other analytical methods, and their accuracy is more than sufficient for many engineering applications. Since all the formulas are extremely simple, they are very useful for real-time adaptive design of 2-D digital filters. Also, the number of multiplications required to implement the designed filters is small and therefore, they are very attractive for real-time digital filtering. The described methods do not have the disadvantages of [10]–[12], and have many advantages.
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References
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Nagamuthu, N., Swamy, M.N.S. (1989). Analytical methods for the design of 2-D elliptically symmetric digital filters of arbitrary orientation using generalized McClellan transformation. In: Porter, W.A., Kak, S.C. (eds) Advances in Communications and Signal Processing. Lecture Notes in Control and Information Sciences, vol 129. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0042732
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DOI: https://doi.org/10.1007/BFb0042732
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