maxflat
Generalized digital Butterworth filter design
Syntax
[b,a] = maxflat(n,m,Wn)
b = maxflat(n,'sym',Wn)
[b,a,b1,b2] = maxflat(n,m,Wn)
[b,a,b1,b2,sos,g] = maxflat(n,m,Wn)
[...] = maxflat(n,m,Wn,'design_flag')
Description
[b,a] = maxflat(n,m,Wn) is a lowpass Butterworth
filter with numerator and denominator coefficients b and a of
orders n and m, respectively. Wn is
the normalized cutoff frequency at which the magnitude response of
the filter is equal to (approximately
–3 dB). Wn must be between
0 and 1, where 1 corresponds to the Nyquist frequency.
b = maxflat(n,'sym',Wn) is
a symmetric FIR Butterworth filter. n must be even,
and Wn is restricted to a subinterval of [0,1].
The function raises an error if Wn is specified
outside of this subinterval.
[b,a,b1,b2] = maxflat(n,m,Wn) returns two polynomials b1 and b2 whose
product is equal to the numerator polynomial b (that
is, b = conv(b1,b2)). b1 contains all the zeros at z = -1, and b2 contains
all the other zeros.
[b,a,b1,b2,sos,g] = maxflat(n,m,Wn) returns the second-order
sections representation of the filter as the filter matrix sos and
the gain g.
[...] = maxflat(n,m,Wn, enables
you to monitor the filter design, where 'design_flag')'design_flag' is
'trace'for a textual display of the design table used in the design'plots'for plots of the filter's magnitude, group delay, and zeros and poles'both'for both the textual display and plots
Examples
Generalized Butterworth Filter
Design a generalized Butterworth filter with normalized cutoff frequency rad/s. Specify a numerator order of 10 and a denominator order of 2. Visualize the frequency response of the filter.
n = 10; m = 2; Wn = 0.2; [b,a] = maxflat(n,m,Wn); fvtool(b,a)
Algorithms
The method consists of the use of formulae, polynomial root finding, and a transformation of polynomial roots.
References
[1] Selesnick, Ivan W., and C. Sidney Burrus. “Generalized Digital Butterworth Filter Design.” IEEE® Transactions on Signal Processing. Vol. 46, Number 6, 1998, pp. 1688–1694.