Determine whether filter is stable


flag = isstable(b,a)
flag = isstable(sos)
flag = isstable(d)
flag = isstable(hs)
flag = isstable(hs,'Arithmetic',arithtype)


flag = isstable(b,a) returns a logical output, flag, equal to true if the filter specified by numerator coefficients, b, and denominator coefficients, a, is a stable filter. If the poles lie on or outside the circle, isstable returns false. If the poles are inside the circle, isstable returns true.

flag = isstable(sos) returns true if the filter specified by second order sections matrix, sos, is stable. 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 = isstable(d) returns true if the digital filter, d, is stable. Use designfilt to generate d based on frequency-response specifications.

flag = isstable(hs) returns true if the filter System object™ hs is stable. You must have the DSP System Toolbox™ software to use this syntax.

flag = isstable(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

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.


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Design a sixth-order Butterworth highpass IIR filter using second order sections. Specify a normalized 3-dB frequency of 0.7. Determine if the filter is stable.

[z,p,k] = butter(6,0.7,'high');
SOS = zp2sos(z,p,k);    
flag = isstable(SOS)        
flag = logical


Redesign the filter using designfilt and check it for stability.

d = designfilt('highpassiir','DesignMethod','butter','FilterOrder',6, ...
dflg = isstable(d)
dflg = logical


Create a filter and determine its stability at double and single precision.

b = [1 -0.5];
a = [1 -0.999999999];
act_flag1 = isstable(b,a)
act_flag1 = logical

act_flag2 = isstable(single(b),single(a))
act_flag2 = logical

Introduced in R2013a