# isstable

Verify that discrete-time filter System object is stable

## Description

example

flag = isstable(sysobj) returns true if filter System object™ is stable. The function returns false if filter System object is not stable.

flag = isstable(sysobj,Arithmetic=arithType) analyzes the filter System object based on the arithmetic specified in the arithType input.

For more input options, see isstable 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.SOSFilter with properties:

Structure: 'Direct form II'
CoefficientSource: 'Property'
Numerator: [5x3 double]
Denominator: [5x3 double]
HasScaleValues: true
ScaleValues: [0.3318 0.2750 0.1876 0.0904 0.0225 0.9441]

Use get to 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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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 is stable, returned as a logical:

• 1 –– Filter is stable.

• 0 –– Filter is not stable.

Data Types: logical

## Version History

Introduced in R2013a

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