Documentation Center |
Chebyshev Type I filter design (passband ripple)
[z,p,k] = cheby1(n,R,Wp)
[z,p,k] = cheby1(n,R,Wp,'ftype')
[b,a] = cheby1(n,R,Wp)
[b,a] = cheby1(n,R,Wp,'ftype')
[A,B,C,D] = cheby1(n,R,Wp)
[A,B,C,D] = cheby1(n,R,Wp,'ftype')
[z,p,k] = cheby1(n,R,Wp,'s')
[z,p,k] = cheby1(n,R,Wp,'ftype','s')
[b,a] = cheby1(n,R,Wp,'s')
[b,a] = cheby1(n,R,Wp, 'ftype','s')
[A,B,C,D] = cheby1(n,R,Wp,'s')
[A,B,C,D] = cheby1(n,R,Wp,'ftype','s')
cheby1 designs lowpass, bandpass, highpass, and bandstop digital and analog Chebyshev Type I filters. Chebyshev Type I filters are equiripple in the passband and monotonic in the stopband. Type I filters roll off faster than type II filters, but at the expense of greater deviation from unity in the passband.
[z,p,k] = cheby1(n,R,Wp) designs an order n Chebyshev lowpass digital Chebyshev filter with normalized passband edge frequency Wp and R dB of peak-to-peak ripple in the passband. It returns the zeros and poles in length n column vectors z and p and the gain in the scalar k.
[z,p,k] = cheby1(n,R,Wp,'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 passband edge frequency Wp
'low' for a lowpass digital filter with normalized passband edge frequency Wp
'stop' for an order 2*n bandstop digital filter if Wp is a two-element vector, Wp = [w1 w2]. The stopband is w1 < ω < w2.
Normalized passband edge frequency is the frequency at which the magnitude response of the filter is equal to -R dB. For cheby1, the normalized passband edge frequency Wp is a number between 0 and 1, where 1 corresponds to half the sample rate, π radians per sample. Smaller values of passband ripple R lead to wider transition widths (shallower rolloff characteristics).
If Wp is a two-element vector, Wp = [w1 w2], cheby1 returns an order 2*n bandpass filter with passband w1 < ω < w2.
With different numbers of output arguments, cheby1 directly obtains other realizations of the filter. To obtain the transfer function form, use two output arguments as shown below.
Note: See Limitations for information about numerical issues that affect forming the transfer function. |
[b,a] = cheby1(n,R,Wp) designs an order n Chebyshev lowpass digital Chebyshev filter with normalized passband edge frequency Wp and R dB of peak-to-peak ripple in the passband. It returns the filter coefficients in the length n+1 row vectors b and a, with coefficients in descending powers of z.
[b,a] = cheby1(n,R,Wp,'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] = cheby1(n,R,Wp,'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] = cheby1(n,R,Wp,'s') designs an order n lowpass analog Chebyshev Type I filter with angular passband edge frequency Wp 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 passband edge frequency is the frequency at which the magnitude response of the filter is -R dB. For cheby1, the angular passband edge frequency Wp must be greater than 0 rad/s.
If Wp is a two-element vector Wp = [w1 w2] with w1 < w2, then cheby1(n,R,Wp,'s') returns an order 2*n bandpass analog filter with passband w1 < ω< w2.
[z,p,k] = cheby1(n,R,Wp,'ftype','s') designs a highpass, lowpass, or bandstop filter, where the string 'ftype' is 'high', 'low', or 'stop', as described above.
You can supply different numbers of output arguments for cheby1 to directly obtain other realizations of the analog filter. To obtain the transfer function form, use two output arguments as shown below.
[b,a] = cheby1(n,R,Wp,'s') designs an order n lowpass analog Chebyshev Type I filter with angular passband edge frequency Wp rad/s. It returns the filter coefficients in length n+1 row vectors b and a, in descending powers of s, derived from the transfer function
[b,a] = cheby1(n,R,Wp, '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] = cheby1(n,R,Wp,'s') or
[A,B,C,D] = cheby1(n,R,Wp,'ftype','s') where A, B, C, and D are defined as
and u is the input, x is the state vector, and y is the output.