n-1 derivatives of the squared magnitude response are zero at 
= 0. The squared magnitude response function is
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buttap
Butterworth analog lowpass filter prototype.
[z,p,k] = buttap(n)
[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
0 is always 1/sqrt(2), regardless of the filter order. buttap sets 0 to 1 for a normalized result.
z = []; p = exp(sqrt(-1)*(pi*(1:2:2*n-1)/(2*n)+pi/2)).'; k = real(prod(-p));