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
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
Choose the input arguments to specify the stopband and passband according to the following table.
Description of Stopband and Passband Filter Parameters
Stopband corner frequency
Passband ripple, in decibels. This value is the maximum permissible passband loss in decibels.
Stopband attenuation, in decibels. This value is the number of decibels the stopband is down from the passband.
Use the following guide to specify filters of different types.
Filter Type Stopband and Passband Specifications
Stopband and Passband Conditions
The interval specified by
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
Ws for an analog Chebyshev Type
II filter. You specify the frequencies
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.
cheb2ord for lowpass, highpass, bandpass,
and bandstop filters as described in the Filter Type Stopband and Passband Specifications table above.
For data sampled at 1000 Hz, design a lowpass filter with less than 3 dB of ripple in the passband defined from 0 to 40 Hz, and at least 60 dB of attenuation in the stopband defined from 150 Hz to the Nyquist frequency.
Wp = 40/500; Ws = 150/500; Rp = 3; Rs = 60; [n,Ws] = cheb2ord(Wp,Ws,Rp,Rs)
n = 4
Ws = 0.3000
[b,a] = cheby2(n,Rs,Ws); freqz(b,a,512,1000) title('n = 4 Chebyshev Type II Lowpass Filter')
Design a bandpass filter with a passband of 60 Hz to 200 Hz, with less than 3 dB of ripple in the passband, and 40 dB attenuation in the stopbands that are 50 Hz wide on both sides of the passband:
Wp = [60 200]/500; Ws = [50 250]/500; Rp = 3; Rs = 40; [n,Ws] = cheb2ord(Wp,Ws,Rp,Rs)
n = 7
Ws = 1×2 0.1000 0.5000
[b,a] = cheby2(n,Rs,Ws); freqz(b,a,512,1000) title('n = 7 Chebyshev Type II Bandpass Filter')
cheb2ord uses the Chebyshev lowpass filter
order prediction formula described in . 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.
 Rabiner, Lawrence R., and Bernard Gold. Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975.
Usage notes and limitations:
All inputs must be constants. Expressions or variables are allowed if their values do not change.