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Determine whether filter is minimum phase


flag = isminphase(b,a)
flag = isminphase(sos)
flag = isminphase(d)
flag = isminphase(...,tol)
flag = isminphase(h)


A filter is minimum phase when all the zeros of its transfer function are on or inside the unit circle, or the numerator is a scalar. An equivalent definition for a minimum phase filter is a causal and stable system with a causal and stable inverse.

flag = isminphase(b,a) returns a logical output, flag, equal to true if the filter specified by numerator coefficients, b, and denominator coefficients, a, is a minimum phase filter.

flag = isminphase(sos) returns true if the filter specified by second order sections matrix, sos, is minimum phase. sos is a K-by-6 matrix, where the number of sections, K, must be greater than or equal to 2. Each row of sos corresponds to the coefficients of a second order (biquad) filter. The ith row of the sos matrix corresponds to [bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)].

flag = isminphase(d) returns true if the digital filter, d, has minimum phase. Use designfilt to generate d based on frequency-response specifications.

flag = isminphase(...,tol) uses the tolerance, tol, to determine when two numbers are close enough to be considered equal. If not specified, tol, defaults to eps^(2/3).

 Details for Fixed-Point Arithmetic

flag = isminphase(h) determines if the dfilt filter object h is minimum phase.


collapse all

Design a sixth-order lowpass Butterworth IIR filter using second order sections. Specify a normalized 3-dB frequency of 0.15. Check if the filter has minimum phase.

[z,p,k] = butter(6,0.15);
SOS = zp2sos(z,p,k);            
min_flag = isminphase(SOS)
min_flag = logical

Redesign the filter using designfilt. Check that the zeros and poles of the transfer function are on or within the unit circle.

d = designfilt('lowpassiir','DesignMethod','butter','FilterOrder',6, ...
d_flag = isminphase(d)
d_flag = logical


Given a filter defined with a set of single-precision numerator and denominator coefficients, check if it has minimum phase for different tolerance values.

b = single([1 1.00001]);  
a = single([1 0.45]);               
min_flag1 = isminphase(b,a)        
min_flag1 = logical

min_flag2 = isminphase(b,a,1e-3)
min_flag2 = logical

Introduced in R2013a