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Ripple-pass function

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The well-known relation for an all-pass function is generalized by the introduction of two parameters k_{a} and k_{b} making F(s)=frac{EvP(s)-k_{a}OdP(s)}{EvP(s)+k_{b}OdP(s)} where P(s) is a Hurwitz polynomial, while EvP(s) and OdP(s) are its even and odd parts, respectively. It is shown that the amplitude, phase, and group delay of such a generalized all-pass function ripple, and that the ripples are dependent on the two introduced parameters and their ratio K = k_{a}/k_{b} . Thus the name "ripple-pass function." Some interesting and important features of the discussed function have been considered here. The ripple-pass function is suitable for practical applications such as amplitude, phase, and/or delay equalization, or for design of narrow-bandpass or bandstop (notch) filters. The ripple-pass function can be easily realized by using simple passive and active networks.

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IEEE Transactions on Circuits and Systems  (Volume:21 ,  Issue: 6 )