Chebyshev Type II filter order
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs)
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs,'s')
cheb2ord
calculates the minimum order of
a digital or analog Chebyshev Type II filter required
to meet a set of filter design specifications.
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs)
returns the lowest order n
of
the Chebyshev Type II filter that loses no more than Rp
dB in the passband and has at least Rs
dB of attenuation in the stopband. The scalar (or vector)
of corresponding cutoff frequencies Ws
, is also
returned. Use the output arguments n
and Ws
in cheby2
.
Choose the input arguments to specify the stopband and passband according to the following table.
Description of Stopband and Passband Filter Parameters
Use the following guide to specify filters of different types.
Filter Type Stopband and Passband Specifications
Filter Type | Stopband and Passband Conditions | Stopband | Passband |
---|---|---|---|
|
|
| |
Highpass |
|
|
|
Bandpass | The interval specified by |
|
|
Bandstop | The interval specified by |
|
|
If your filter specifications call for a bandpass or bandstop filter with unequal ripple in each of the passbands or stopbands, design separate lowpass and highpass filters according to the specifications in this table, and cascade the two filters together.
[n,Ws] = cheb2ord(Wp,Ws,Rp,Rs,'s')
finds the minimum order n
and
cutoff frequencies Ws
for an analog Chebyshev Type
II filter. You specify the frequencies Wp
and Ws
similar
to those described in the Description of Stopband and Passband Filter Parameters table
above, only in this case you specify the frequency in radians per
second, and the passband or the stopband can be infinite.
Use cheb2ord
for lowpass, highpass, bandpass,
and bandstop filters as described in the Filter Type Stopband and Passband Specifications table above.
cheb2ord
uses the Chebyshev lowpass filter
order prediction formula described in [1]. The function performs its calculations in the analog
domain for both analog and digital cases. For the digital case, it
converts the frequency parameters to the s-domain
before the order and natural frequency estimation process, and then
converts them back to the z-domain.
cheb2ord
initially develops a lowpass filter
prototype by transforming the stopband 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 passband specification.
[1] Rabiner, Lawrence R., and Bernard Gold. Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.