Filters approximating ideal amplitude and arbitrary phase characteristics

by: J Rhodes

Circuits Theory, IEEE Transactions on [legacy, pre - 1988], Vol. 20, No. 2. (1973), pp. 120-124.

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Abstract

The closed-form solution is derived for the scattering transfer function<tex>S_12(p)</tex>of a resistively terminated lossless reciprocal two-port prototype network of degree<tex>2n</tex>which satisfies the following constraints:<tex>|S_12(jomega) | leq 1</tex><tex>|S_12(pmjomega_i) | = 1 , i = 1 rightarrow n</tex><tex>arg S_12(pmjomega_i) = pm psi(omega_i), i = 1 rightarrow n</tex>where the<tex>omega_i</tex>are arbitrary and<tex>psi(omega)</tex>is any odd function. The solution is obtained in terms of the arbitrary phase polynomials of the first and second kinds, which are capable of being generated through simple recurrence formulas.

@article{citeulike:2776189, abstract = {The closed-form solution is derived for the scattering transfer function<tex>S\_{12}(p)</tex>of a resistively terminated lossless reciprocal two-port prototype network of degree<tex>2n</tex>which satisfies the following constraints:<tex>|S\_{12}(jomega) | leq 1</tex><tex>|S\_{12}({pm}j{omega}\_i) | = 1 , i = 1 rightarrow n</tex><tex>arg S\_{12}({pm}j{omega}\_i) = pm psi({omega}\_i), i = 1 rightarrow n</tex>where the<tex>omega\_i</tex>are arbitrary and<tex>psi(omega)</tex>is any odd function. The solution is obtained in terms of the arbitrary phase polynomials of the first and second kinds, which are capable of being generated through simple recurrence formulas.}, author = {Rhodes, J. }, booktitle = {Circuits Theory, IEEE Transactions on [legacy, pre - 1988]}, citeulike-article-id = {2776189}, journal = {Circuits Theory, IEEE Transactions on [legacy, pre - 1988]}, keywords = {filter, phase}, number = {2}, pages = {120--124}, posted-at = {2008-05-09 16:45:41}, priority = {2}, title = {Filters approximating ideal amplitude and arbitrary phase characteristics}, url = {http://ieeexplore.ieee.org/xpls/abs\_all.jsp?arnumber=1083626}, volume = {20}, year = {1973} }

RIS record

TY - JOUR ID - citeulike:2776189 L3 - citeulike-article-id:2776189 TI - Filters approximating ideal amplitude and arbitrary phase characteristics T2 - Circuits Theory, IEEE Transactions on [legacy, pre - 1988] JF - Circuits Theory, IEEE Transactions on [legacy, pre - 1988] VL - 20 IS - 2 SP - 120 EP - 124 N2 - The closed-form solution is derived for the scattering transfer function<tex>S_{12}(p)</tex>of a resistively terminated lossless reciprocal two-port prototype network of degree<tex>2n</tex>which satisfies the following constraints:<tex>|S_{12}(jomega) | leq 1</tex><tex>|S_{12}({pm}j{omega}_i) | = 1 , i = 1 rightarrow n</tex><tex>arg S_{12}({pm}j{omega}_i) = pm psi({omega}_i), i = 1 rightarrow n</tex>where the<tex>omega_i</tex>are arbitrary and<tex>psi(omega)</tex>is any odd function. The solution is obtained in terms of the arbitrary phase polynomials of the first and second kinds, which are capable of being generated through simple recurrence formulas. KW - filter KW - phase AU - Rhodes, J PY - 1973/// UR - http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1083626 ER -

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