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Elliptic Filters

Module by: Richard Baraniuk

Summary: Briefly describes Elliptic filters.

Compared with the other filters, Butterworth and Chebyshev, Elliptic filters have the most rapid transition (narrow transition band). However, this does not come without a price. Elliptic filters have rippling in both the passband and stopband. This is the result of a pole-zero configuration that consists of both poles and zeros.

Figure 1: The magnitude plot of the transfer function of an Elliptic filter demonstrates the equal ripple in both the passband and stopband. It also displays the most rapid transition of the three most common filters.
Figure 1 (elliptic1.png)

The magnitude of the transfer function is

Hⅈω=11+ε2 R n 2ω H ω 1 1 ε 2 R n ω 2 (1)
where R n ω R n ω is the nnth order Chebyshev rational function.

As with Butterworth and Chebyshev filters, the most reasonable way to design Elliptic filters is with the assistance of a table or Matlab. In this case, the relevant Matlab command is ellipap.

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