isminphase

Determine whether filter is minimum phase

Syntax

flag = isminphase(b,a)

flag = isminphase(sos)

flag = isminphase(d)

flag = isminphase(___,tol)

Description

flag = isminphase(b,a) returns a logical output equal to 1 if the filter specified by numerator coefficients b and denominator coefficients a is minimum phase.

flag = isminphase(sos) returns 1 if the filter specified by second order sections matrix sos is minimum phase.

flag = isminphase(d) returns 1 if the digital filter d is 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.

Examples

Minimum Phase Filters

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 is minimum phase.

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

min_flag = logical
   1

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, ...
               HalfPowerFrequency=0.25);
d_flag = isminphase(d)

d_flag = logical
   1

zplane(d)

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

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

min_flag1 = logical
   0

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

min_flag2 = logical
   1

Input Arguments

b, a — Filter coefficients

vector

Filter coefficients, specified as vectors.

Data Types: single | double

sos — Second order sections

k-by-6 matrix

Second order sections, specified as 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)].

Data Types: double

d — Digital filter

digitalFilter object

Digital filter, specified as a digitalFilter object.

tol — Tolerance

eps^(2/3) (default) | positive scalar

Tolerance, specified as a positive scalar. The tolerance value determines when two numbers are close enough to be considered equal.

Data Types: double

Output Arguments

flag — Logical output

1 (true) | 0 (false)

Logical output, returned as 1 or 0. The function returns 1 when the input is a minimum phase filter.

Version History

Introduced in R2013a