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Chebyshev Type II filter design (stopband ripple)
[z,p,k] = cheby2(n,R,Wst)
[z,p,k] = cheby2(n,R,Wst,'ftype')
[b,a] = cheby2(n,R,Wst)
[b,a] = cheby2(n,R,Wst,'ftype')
[A,B,C,D] = cheby2(n,R,Wst)
[A,B,C,D] = cheby2(n,R,Wst,'ftype')
[z,p,k] = cheby2(n,R,Wst,'s')
[z,p,k] = cheby2(n,R,Wst,'ftype','s')
[b,a] = cheby2(n,R,Wst,'s')
[b,a] = cheby2(n,R,Wst,'ftype','s')
[A,B,C,D] = cheby2(n,R,Wst,'s')
[A,B,C,D] = cheby2(n,R,Wst,'ftype','s')
cheby2 designs lowpass, highpass, bandpass, and bandstop digital and analog Chebyshev Type II filters. Chebyshev Type II filters are monotonic in the passband and equiripple in the stopband. Type II filters do not roll off as fast as type I filters, but are free of passband ripple.
[z,p,k] = cheby2(n,R,Wst) designs an order n lowpass digital Chebyshev Type II filter with normalized stopband edge frequency Wst and stopband ripple R dB down from the peak passband value. It returns the zeros and poles in length n column vectors z and p and the gain in the scalar k.
Normalized stopband edge frequency is the beginning of the stopband, where the magnitude response of the filter is equal to -R dB. For cheby2, the normalized stopband edge frequency Wst is a number between 0 and 1, where 1 corresponds to half the sample rate. Larger values of stopband attenuation R lead to wider transition widths (shallower rolloff characteristics).
If Wst is a two-element vector, Wst = [w1 w2], cheby2 returns an order 2*n bandpass filter with passband w1 < ω < w2.
[z,p,k] = cheby2(n,R,Wst,'ftype')designs a highpass, lowpass, or bandstop filter, where the string 'ftype' is one of the following:
'high' for a highpass digital filter with normalized stopband edge frequency Wst
'low' for a lowpass digital filter with normalized stopband edge frequency Wst
'stop' for an order 2*n bandstop digital filter if Wst is a two-element vector, Wst = [w1 w2]. The stopband is w1 < ω < w2.
With different numbers of output arguments, cheby2 directly obtains other realizations of the filter. To obtain the transfer function form, use two output arguments as shown below.
Note: See Limitations below for information about numerical issues that affect forming the transfer function. |
[b,a] = cheby2(n,R,Wst) designs an order n lowpass digital Chebyshev Type II filter with normalized stopband edge frequency Wst and stopband ripple R dB down from the peak passband value. It returns the filter coefficients in the length n+1 row vectors b and a, with coefficients in descending powers of z.
[b,a] = cheby2(n,R,Wst,'ftype') designs a highpass, lowpass, or bandstop filter, where the string 'ftype' is 'high', 'low', or 'stop', as described above.
To obtain state-space form, use four output arguments as shown below.
[A,B,C,D] = cheby2(n,R,Wst) or
[A,B,C,D] = cheby2(n,R,Wst,'ftype') where A, B, C, and D are
and u is the input, x is the state vector, and y is the output.
[z,p,k] = cheby2(n,R,Wst,'s') designs an order n lowpass analog Chebyshev Type II filter with angular stopband edge frequency Wst rad/s.. It returns the zeros and poles in length n or 2*n column vectors z and p and the gain in the scalar k.
Angular stopband edge frequency is the frequency at which the magnitude response of the filter is equal to -R dB. For cheby2, the angular stopband edge frequency Wst must be greater than 0 rad/s.
If Wst is a two-element vector Wst = [w1 w2] with w1 < w2, then cheby2(n,R,Wst,'s') returns an order 2*n bandpass analog filter with passband w1 < ω< w2.
[z,p,k] = cheby2(n,R,Wst,'ftype','s') designs a highpass, lowpass, or bandstop filter, where the string 'ftype' is 'high', 'low', or 'stop', as described above.
With different numbers of output arguments, cheby2 directly obtains other realizations of the analog filter. To obtain the transfer function form, use two output arguments as shown below:
[b,a] = cheby2(n,R,Wst,'s') designs an order n lowpass analog Chebyshev Type II filter with angular stopband edge frequency Wst rad/s.. It returns the filter coefficients in the length n+1 row vectors b and a, with coefficients in descending powers of s, derived from the transfer function.
[b,a] = cheby2(n,R,Wst,'ftype','s') designs a highpass , lowpass, or bandstop filter, where the string 'ftype' is 'high', 'low', or 'stop', as described above.
To obtain state-space form, use four output arguments as shown below:
[A,B,C,D] = cheby2(n,R,Wst,'s') or
[A,B,C,D] = cheby2(n,R,Wst,'ftype','s') where A, B, C, and D are
and u is the input, x is the state vector, and y is the output.