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# isminphase

Determine whether filter is minimum phase

## Syntax

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

## Description

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 i-th row of the sos matrix corresponds to [bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)].

flag = isminphase(h) determines if the dfilt filter object h is minimum phase. If you have the DSP System Toolbox™ software, isminphase works with adapfilt and mfilt objects.

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).

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(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.

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.

## Examples

Design a lowpass Butterworth IIR filter using second order sections and check if the filter is minimum phase.

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

For a filter defined with a set of single precision numerator and denominator coefficients, check if the filter is minimum phase for different tolerances.

```    b = single([1 1.00001]);
a = single([1 .45]);
min_flag1 = isminphase(b,a)
min_flag2 = isminphase(b,a,1e-3)   ```