Signal Processing Toolbox

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)
  [...] = 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 (approx. -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.

[...] = maxflat(n,m,Wn,'design_flag') enables you to monitor the filter design, where '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

• n = 10; na = 2; Wn = 0.2;
  [b,a,b1,b2] = maxflat(n,m,Wn,'plots')
  
  
  

Algorithm

The method consists of the use of formulae, polynomial root finding, and a transformation of polynomial roots.

See Also

butter, filter, freqz

References

[1] Selesnick, I.W., and C.S. Burrus, "Generalized Digital Butterworth Filter Design," Proceedings of the IEEE Int. Conf. Acoust., Speech, Signal Processing, Vol. 3 (May 1996).

lsf2poly

medfilt1