Elliptic analog lowpass filter prototype
Frequency Response of Elliptic Lowpass Filter
Design a 6th-order elliptic analog lowpass filter with 5 dB of ripple in the passband and 50 dB of stopband attenuation.
[z,p,k] = ellipap(6,5,50);
Convert the zero-pole-gain filter parameters to transfer function form and display the frequency response of the filter.
[b,a] = zp2tf(z,p,k); freqs(b,a)
n — Filter order
positive integer scalar
Filter order, specified as a positive integer scalar.
Rp — Passband ripple
Passband ripple, specified as a positive scalar in decibels.
Rs — Stopband attenuation
Stopband attenuation down from the peak passband value, specified as a positive scalar in decibels.
ellipap function uses the algorithm outlined in . It
ellipke to calculate the complete elliptic
integral of the first kind and
ellipj to calculate Jacobi elliptic functions.
The function sets the passband edge angular frequency ω0 of the
elliptic filter to 1 for a normalized result. The passband edge angular
frequency is the frequency at which the passband ends and the filter has a
magnitude response of 10-Rp/20.
The transfer function in factored zero-pole form is
Elliptic filters offer steeper rolloff characteristics than Butterworth and Chebyshev filters, but they are equiripple in both the passband and the stopband. Of the four classical filter types, elliptic filters usually meet a given set of filter performance specifications with the lowest filter order.
 Parks, T. W., and C. S. Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.
C/C++ Code Generation
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Usage notes and limitations:
All inputs must be constants. Expressions or variables are allowed if their values do not change.
Introduced before R2006a