Change cutoff frequency for lowpass analog filter
Design an 8th-order Chebyshev Type I analog lowpass filter prototype with 3 dB of ripple in the passband.
[z,p,k] = cheb1ap(8,3);
Convert the prototype to transfer function form and display its magnitude and frequency responses.
[b,a] = zp2tf(z,p,k); freqs(b,a)
Transform the prototype to a lowpass filter with a cutoff frequency of 30 Hz. Specify the cutoff frequency in rad/s. Display the magnitude and frequency responses of the transformed filter.
Wo = 2*pi*30; [bt,at] = lp2lp(b,a,Wo); freqs(bt,at)
a— Prototype numerator and denominator coefficients
Prototype numerator and denominator coefficients, specified as row vectors.
a specify the coefficients of the
numerator and denominator of the prototype in descending powers of
D— Prototype state-space representation
Prototype state-space representation, specified as matrices. The state-space matrices relate the state vector x, the input u, and the output y through
Wo— Cutoff angular frequency
Cutoff angular frequency, specified as a scalar. Express
units of rad/s.
at— Transformed numerator and denominator coefficients
Transformed numerator and denominator coefficients, returned as row vectors.
Dt— Transformed state-space representation
Transformed state-space representation, returned as matrices.
lp2lp transforms an analog lowpass filter prototype with a cutoff
angular frequency of 1 rad/s into a lowpass filter with any specified cutoff angular
frequency. The transformation is one step in the digital filter design process for the
lp2lp is a highly accurate
state-space formulation of the classic analog filter frequency transformation. If a lowpass
filter has cutoff angular frequency ω0, the standard
s-domain transformation is
The state-space version of this transformation is
lp2lp function can perform the transformation on two different
linear system representations: transfer function form and state-space form. See
lp2bp for a
derivation of the bandpass version of this transformation.
Usage notes and limitations:
The input transfer function coefficients,
den, must be real.