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lp2hp() - Signal Processing

lp2hp transforms analog lowpass filter prototypes
with a cutoff angular frequency of 1 rad/s into highpass
filters with desired cutoff angular frequency. The transformation
is one step in the digital filter design process for the butter, cheby1, cheby2, and ellip functions.The lp2hp 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] = lp2hp(b,a,Wo) transforms an analog
lowpass filter prototype given by polynomial coefficients into a highpass
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. The frequency transformed filter is returned
in row vectors bt and at.State-Space Form[At,Bt,Ct,Dt] = lp2hp(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 highpass filter with cutoff angular frequency Wo.
The highpass filter is returned in matrices At, Bt, Ct, Dt.


[bt,at] = lp2hp(b,a,Wo)[At,Bt,Ct,Dt] = lp2hp(A,B,C,D,Wo)


At = Wo*inv(A);
Bt = -Wo*(A\B);
Ct = C/A;
Dt = D - C/A*B;

Output / Return Value


Alternatives / See Also