Minimum stopband attenuation of Cauer filters without elliptic functions and integrals

A simplified design of some Cauer filters without Jacobian elliptic functions

“…This mixed phase information is available in the higher order statistics (HOS), like the triple correlation sequence (TCS) or bispectrum and tricovariance or trispectrum [ 11. In the quest of an accurate complete characterization of a non-Gaussian process, the AR model has been introduced to the field of HOS [2]. The existence and uniqueness of such an AR modeling have been discussed and a method for arriving at a unique AR model that involves solution of a system of nonlinear equations has been proposed [3].…”

“…To check whether the eight-order modified function can satisfy the assigned specifications we start with the generalized form of the characteristic function By means of (15), (16), and [2], the stopband frequency may be determined…”

“…It originates from a relation between rational Chebyshev characteristic functions of the elliptic filters of different orders, which is a counterpart of a similar expression between Chebyshev polynomials [l]. This relation was already used in discussing some specific aspects of the design of Cauer filters [2].…”