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isminphase

Verify that discrete-time filter System object is minimum phase

Description

example

flag = isminphase(sysobj) returns true if the filter System object™ has minimum phase.

flag = isminphase(sysobj,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(___,'Arithmetic',arithType) analyzes the filter System object based on the arithmetic specified in the arithType input using either of the previous syntaxes.

For more input options, see isminphase in Signal Processing Toolbox™.

Examples

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Design a Chebyshev Type I IIR filter and determine if the filter has minimum phase and is stable.

Using the fdesign.lowpass and design functions, design a Chebyshev Type I IIR filter with a passband ripple of 0.5 dB and a 3 dB cutoff frequency at 9600 Hz.

Fs = 48000; % Sampling frequency of input signal
d  = fdesign.lowpass('N,F3dB,Ap', 10, 9600, .5, Fs);
filt = design(d,'cheby1','Systemobject',true)
filt = 
  dsp.BiquadFilter with properties:

                   Structure: 'Direct form II'
             SOSMatrixSource: 'Property'
                   SOSMatrix: [5x6 double]
                 ScaleValues: [6x1 double]
           InitialConditions: 0
    OptimizeUnityScaleValues: true

  Show all properties

Using the isminphase function, determine if the filter has minimum phase.

isminphase(filt)
ans = logical
   1

Verify the location of poles and zeros of the filter transfer function on the z-plane. By definition, the poles and zeros of the minimum phase filter must be on or inside the unit circle.

zplane(filt)

All minimum phase filters are stable. To verify if the designed filter is stable, use the isstable function.

isstable(filt)
ans = logical
   1

Input Arguments

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Tolerance value to determine when two numbers are close enough to be considered equal, specified as a positive scalar. If not specified, tol defaults to eps^(2/3).

Arithmetic used in the filter analysis, specified as 'double', 'single', or 'Fixed'. When the arithmetic input is not specified and the filter System object is unlocked, the analysis tool assumes a double-precision filter. When the arithmetic input is not specified and the System object is locked, the function performs the analysis based on the data type of the locked input.

The 'Fixed' value applies to filter System objects with fixed-point properties only.

When the 'Arithmetic' input argument is specified as 'Fixed' and the filter object has the data type of the coefficients set to 'Same word length as input', the arithmetic analysis depends on whether the System object is unlocked or locked.

  • unlocked –– The analysis object function cannot determine the coefficients data type. The function assumes that the coefficients data type is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.

  • locked –– When the input data type is 'double' or 'single', the analysis object function cannot determine the coefficients data type. The function assumes that the data type of the coefficients is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.

To check if the System object is locked or unlocked, use the isLocked function.

When the arithmetic input is specified as 'Fixed' and the filter object has the data type of the coefficients set to a custom numeric type, the object function performs fixed-point analysis based on the custom numeric data type.

Output Arguments

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Flag to determine if the filter has minimum phase, returned as a logical:

  • 1 –– Filter has minimum phase.

  • 0 –– Filter has non minimum phase.

Data Types: logical

More About

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Minimum Phase Filters

A causal and stable discrete-time system is said to be strictly minimum-phase when all its zeros are inside the unit circle. A causal and stable LTI system is a minimum-phase system if its inverse is causal and stable as well.

Such a system is called a minimum-phase system because it has the minimum group delay (grpdelay) of the set of systems that have the same magnitude response.

Introduced in R2013a