# buttord

Butterworth filter order and cutoff frequency

## Description

`[`

returns the lowest order, `n`

,`Wn`

] = buttord(`Wp`

,`Ws`

,`Rp`

,`Rs`

)`n`

, of the digital Butterworth
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 a Butterworth filter, use the output arguments `n`

and `Wn`

as inputs to `butter`

.

## Examples

## Input Arguments

## Output Arguments

## Algorithms

`buttord`

’s order prediction formula operates in the analog domain
for both analog and digital cases. For the digital case, it converts the frequency
parameters to the *s*-domain before estimating the order and natural
frequency. The function then converts back to the *z*-domain.

`buttord`

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

## References

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

## Extended Capabilities

## Version History

**Introduced before R2006a**