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ellipap

Elliptic analog lowpass filter prototype

Syntax

[z,p,k] = ellipap(n,Rp,Rs)

Description

[z,p,k] = ellipap(n,Rp,Rs)returns the zeros, poles, and gain of an ordernelliptic analog lowpass filter prototype, withRpdB涟漪的通带和阻带RsdB down from the peak value in the passband. The zeros and poles are returned in lengthncolumn vectorszandpand the gain in scalark. Ifnis odd,zis lengthn-1. The transfer function in factored zero-pole form is

H ( s ) = z ( s ) p ( s ) = k ( s − z 1 ) ( s − z 2 ) … ( s − z N ) ( s − p 1 ) ( s − p 2 ) … ( s − p M )

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.

ellipapsets the passband edge angular frequency ω0of the elliptic filter to 1 for a normalized result. Thepassband edge angular frequencyis the frequency at which the passband ends and the filter has a magnitude response of 10rp / 20.

Algorithms

ellipapuses the algorithm outlined in[1]. It employsellipketo calculate the complete elliptic integral of the first kind andellipjto calculate Jacobi elliptic functions.

References

[1] Parks, T. W., and C. S. Burrus.Digital Filter Design. New York: John Wiley & Sons, 1987, chap. 7.

Extended Capabilities

Version History

Introduced before R2006a

See Also

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