# ellipap

Elliptic analog lowpass filter prototype

## Description

## Examples

## Input Arguments

## Output Arguments

## Algorithms

The `ellipap`

function uses the algorithm outlined in [1]. It
employs `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 ω_{0} 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

$$H(s)=\frac{z(s)}{p(s)}=k\frac{(s-{z}_{1})(s-{z}_{2})\dots (s-{z}_{N})}{(s-{p}_{1})(s-{p}_{2})\dots (s-{p}_{M})}$$

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.

## 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**