buttap (Signal Processing Toolbox)

Butterworth analog lowpass filter prototype.

Syntax

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

Description

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

returns the zeros, poles, and gain of an order n Butterworth analog lowpass filter prototype. It returns the poles in the length n column vector p and the gain in scalar k. z is an empty matrix, because there are no zeros. The transfer function is

Butterworth filters are characterized by a magnitude response that is maximally flat in the passband and monotonic overall. In the lowpass case, the first 2n-1 derivatives of the squared magnitude response are zero at

= 0. The squared magnitude response function is

corresponding to a transfer function with poles equally spaced around a circle in the left half plane. The magnitude response at the cutoff frequency

₀ is always 1/sqrt(2), regardless of the filter order. buttap sets

₀ to 1 for a normalized result.

Algorithm

z = [];
p = exp(sqrt(-1)*(pi*(1:2:2*n-1)/(2*n)+pi/2)).';
k = real(prod(-p));

See Also


`besselap`	Bessel analog lowpass filter prototype.
`butter`	Butterworth analog and digital filter design.
`cheb1ap`	Chebyshev type I analog lowpass filter prototype.
`cheb2ap`	Chebyshev type II analog lowpass filter prototype.
`ellipap`	Elliptic analog lowpass filter prototype.

References

[1] Parks, T.W., and C.S. Burrus. Digital Filter Design. New York: John Wiley & Sons, 1987. Chapter 7.

[ Previous | Help Desk | Next ]