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Change cutoff frequency for lowpass analog filter



[bt,at] = lp2lp(b,a,Wo) transforms an analog lowpass filter prototype given by polynomial coefficients (specified by row vectors b and a) into a lowpass filter with cutoff angular frequency Wo. The input system must be an analog filter prototype.

[At,Bt,Ct,Dt] = lp2lp(A,B,C,D,Wo) converts the continuous-time state-space lowpass filter prototype (specified by matrices A, B, C, and D) to a lowpass filter with cutoff angular frequency Wo. The input system must be an analog filter prototype.


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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);

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);

Input Arguments

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Prototype numerator and denominator coefficients, specified as row vectors. b and a specify the coefficients of the numerator and denominator of the prototype in descending powers of s:


Data Types: single | double

Prototype state-space representation, specified as matrices. The state-space matrices relate the state vector x, the input u, and the output y through


Data Types: single | double

Cutoff angular frequency, specified as a scalar. Express Wo in units of rad/s.

Data Types: single | double

Output Arguments

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Transformed numerator and denominator coefficients, returned as row vectors.

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 butter, cheby1, cheby2, and ellip functions.

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





The 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.

Extended Capabilities

Version History

Introduced before R2006a