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cheb1ap

Chebyshev Type I analog lowpass filter prototype

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Syntax

[z,p,k] = cheb1ap(n,Rp)

Description

example

[z,p,k] = cheb1ap(n,Rp)returns the poles and gain of an ordernChebyshev Type I analog lowpass filter prototype withRpdB of ripple in the passband.

Examples

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Open Live Script

Design a 6th-order Chebyshev Type I analog lowpass filter with 3 dB of ripple in the passband. Display its magnitude and phase responses.

[z,p,k] = cheb1ap(6,3);% Lowpass filter prototype[num,den] = zp2tf(z,p,k);% Convert to transfer function formfreqs(num,den)% Frequency response of analog filter

Figure contains 2 axes objects. Axes object 1 contains an object of type line. Axes object 2 contains an object of type line.

Input Arguments

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Filter order, specified as an integer.

Data Types:single|double

Passband ripple, specified as a scalar in decibels.

Data Types:single|double

Output Arguments

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Zeros of the filter, returned as a matrix.

Poles of the filter, returned as ann-length column vector.

Gain of the filter, returned as a scalar.zis an empty matrix because no zeros exist for this filter design.

Algorithms

Chebyshev Type I filters are equiripple in the passband and monotonic in the stopband. The poles are evenly spaced about an ellipse in the left half plane. The Chebyshev Type I passband edge angular frequencyω0is set to 1.0 for a normalized result. This value is the frequency at which the passband ends. The filter has a magnitude response of 10–Rp/20.

The transfer function is given by

H ( s ) = z ( s ) p ( s ) = k ( s − p ( 1 ) ) ( s − p ( 2 ) ) … ( s − p ( n ) ) .

References

[1] Parks, Thomas W., and C. Sidney Burrus.Digital Filter Design. New York: John Wiley & Sons, 1987.

Extended Capabilities

Version History

Introduced before R2006a

See Also

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