lp2lp() - Signal Processing

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.Transfer Function Form (Polynomial)[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.B(s)A(s)=b(1)sn+⋯+b(n)s+b(n+1)a(1)sm+⋯+a(m)s+a(m+1)Scalar Wo specifies the cutoff angular frequency
in units of radians/second. lp2lp returns the frequency
transformed filter in row vectors bt and at.State-Space Form[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 belowx˙=Ax+Buy=Cx+Duinto a lowpass filter with cutoff angular frequency Wo. lp2lp returns
the lowpass filter in matrices At, Bt, Ct, Dt.

Syntax

[bt,at] = lp2lp(b,a,Wo)[At,Bt,Ct,Dt] = lp2lp(A,B,C,D,Wo)

Example

At = Wo*A;
Bt = Wo*B;
Ct = C;
Dt = D;

Output / Return Value

Limitations

Alternatives / See Also

Reference