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Minimum order for elliptic filters

`[`

returns the lowest order, `n`

,`Wn`

] = ellipord(`Wp`

,`Ws`

,`Rp`

,`Rs`

)`n`

, of the digital elliptic filter with no
more than `Rp`

dB of passband ripple and at least `Rs`

dB of attenuation in the stopband. `Wp`

and `Ws`

, are
respectively, the passband and stopband edge frequencies of the filter, normalized from 0 to
1, where 1 corresponds to *π* rad/sample. The scalar (or vector) of
corresponding cutoff frequencies, `Wn`

, is also returned. To design an
elliptic filter, use the output arguments `n`

and `Wn`

as inputs to `ellip`

.

`ellipord`

uses the elliptic lowpass filter order prediction formula
described in [1]. The function performs its
calculations in the analog domain for both the analog and digital cases. For the digital case,
it converts the frequency parameters to the *s*-domain before estimating
the order and natural frequencies, and then converts them back to the
*z*-domain.

`ellipord`

initially develops a lowpass filter prototype by transforming
the passband frequencies of the desired filter to 1 rad/s (for low and highpass filters) and
to –1 and 1 rad/s (for bandpass and bandstop filters). It then computes the minimum order
required for a lowpass filter to meet the stopband specification.

[1] Rabiner, Lawrence R., and B. Gold.
*Theory and Application of Digital Signal Processing*. Englewood
Cliffs, NJ: Prentice Hall, 1975.