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# isminphase() - Signal Processing

```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).flag = isminphase(hs,...) determines
whether the filter System object™ hs is minimum
phase, returning 1 if true and 0 if
false. You must have the DSP System Toolbox™ software to use this
syntax.isminphase(hs,'Arithmetic',arithtype) analyzes
the filter System object hs based on the specified arithtype. arithtype can
be 'double', 'single', or 'fixed'.
When you specify 'double' or 'single',
the function performs double- or single-precision analysis. When you
specify 'fixed' , the arithmetic changes depending
on the setting of the CoefficientDataType property
and whether the System object is locked or unlocked. You must
have the DSP System Toolbox software to use this syntax. Details for Fixed-Point Arithmetic

System Object StateCoefficient Data TypeRule
Unlocked'Same as input'The function assumes that the coefficient data type is signed,
16 bit, and autoscaled. The function performs fixed-point analysis
based on this assumption.
Unlocked'Custom'The function performs fixed-point analysis based on the setting
of the CustomCoefficientsDataType property.
Locked'Same as input'When the input data type is 'double' or 'fixed',
the function assumes that the coefficient data type is signed, 16-bit,
and autoscaled. The function performs fixed-point analysis based on
this assumption.
Locked'Custom'The function performs fixed-point analysis based on the setting
of the CustomCoefficientsDataType property.

When you do not specify the arithmetic for non-CIC structures,
the function uses double-precision arithmetic if the filter System object is
in an unlocked state. If the System object is locked, the function
performs analysis based on the locked input data type. CIC structures
only support fixed-point arithmetic.flag = isminphase(h) determines
if the dfilt filter object h is
minimum phase.```

### Syntax

`flag = isminphase(b,a)flag = isminphase(sos)flag = isminphase(d)flag = isminphase(...,tol)flag = isminphase(hs,...)isminphase(hs,'Arithmetic',arithtype)flag = isminphase(h)`

### Example

```Minimum Phase FiltersOpen This Example
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 =

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)
zplane(d)

d_flag =

1

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_flag2 = isminphase(b,a,1e-3)

min_flag1 =

0

min_flag2 =

1```