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besselap

Bessel analog lowpass filter prototype

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Syntax

[z,p,k] = besselap(n)

Description

[z,p,k] = besselap(n)returns the poles and gain of an order-nBessel analog lowpass filter prototype.nmust be less than or equal to 25. The function returns the poles in the lengthncolumn vectorpand the gain in scalark.zis an empty matrix because there are no zeros. The transfer function is

H ( s ) = k ( s − p ( 1 ) ) ( s − p ( 2 ) ) ⋯ ( s − p ( n ) )

besselapnormalizes the poles and gain so that at low frequency and high frequency the Bessel prototype is asymptotically equivalent to the Butterworth prototype of the same order[1]. The magnitude of the filter is less than 1 / 2 at the unity cutoff frequency Ωc= 1.

Analog Bessel filters are characterized by a group delay that is maximally flat at zero frequency and almost constant throughout the passband. The group delay at zero frequency is

( ( 2 n ) ! 2 n n ! ) 1 / n

Examples

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Open Live Script

Design a 6th-order Bessel analog lowpass filter. Display its magnitude and phase responses.

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

Algorithms

besselapfinds the filterroots from a lookup table constructed using Symbolic Math Toolbox™ software.

References

[1] Rabiner, L. R., and B. Gold. Theory and Application of Digital Signal Processing. Englewood Cliffs, NJ: Prentice-Hall, 1975, pp. 228–230.

Extended Capabilities

See Also

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Introduced before R2006a

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