Compute the transfer function coefficients of a Cauer analog filter.
ncauer(Rp, Rs, n)A list of class Zpg with the following list elements:
complex vector of the zeros of the model
complex vector of the poles of the model
gain of the model
dB of passband ripple.
dB of stopband ripple.
filter order.
Paulo Neis, p_neis@yahoo.com.br.
Conversion to R Tom Short,
adapted by Geert van Boxtel, G.J.M.vanBoxtel@gmail.com.
Cauer filters have equal maximum ripple in the passband and the stopband. The Cauer filter has a faster transition from the passband to the stopband than any other class of network synthesis filter. The term Cauer filter can be used interchangeably with elliptical filter, but the general case of elliptical filters can have unequal ripples in the passband and stopband. An elliptical filter in the limit of zero ripple in the passband is identical to a Chebyshev Type 2 filter. An elliptical filter in the limit of zero ripple in the stopband is identical to a Chebyshev Type 1 filter. An elliptical filter in the limit of zero ripple in both passbands is identical to a Butterworth filter. The filter is named after Wilhelm Cauer and the transfer function is based on elliptic rational functions.Cauer-type filters use generalized continued fractions.[1]
[1] https://en.wikipedia.org/wiki/Network_synthesis_filters#Cauer_filter
Zpg, filter, ellip
zpg <- ncauer(1, 40, 5)
freqz(zpg)
zplane(zpg)
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