Change cutoff frequency for lowpass analog filter
[bt,at] = lp2lp(b,a,Wo)
[At,Bt,Ct,Dt] = lp2lp(A,B,C,D,Wo)
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 butter,
cheby1,
cheby2,
and ellip
functions.
The lp2lp function can perform the
transformation on two different linear system
representations: transfer function form and
state-space form. In both cases, the input system
must be an analog filter prototype.
[bt,at] = lp2lp(b,a,Wo)
transforms an analog lowpass filter prototype
given by polynomial coefficients into a lowpass
filter with cutoff angular frequency
Wo. Row vectors
b and a
specify the coefficients of the numerator and
denominator of the prototype in descending powers
of s.
Scalar Wo specifies the
cutoff angular frequency in units of rad/s.
lp2lp returns the frequency
transformed filter in row vectors
bt and
at.
[At,Bt,Ct,Dt] = lp2lp(A,B,C,D,Wo)
converts the continuous-time state-space lowpass
filter prototype in matrices A,
B, C,
D below
into a lowpass filter with cutoff angular
frequency Wo.
lp2lp returns the lowpass
filter in matrices At,
Bt, Ct,
Dt.
lp2lp is a highly accurate
state-space formulation of the classic analog
filter frequency transformation. If a lowpass
filter is to have cutoff angular frequency
ω0, the standard
s-domain transformation
is
The state-space version of this transformation is
At = Wo*A; Bt = Wo*B; Ct = C; Dt = D;
See lp2bp for a derivation of the
bandpass version of this transformation.