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Determine whether filter is stable


flag = isstable(b,a)
flag = isstable(sos)
flag = isstable(d)


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.


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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


Figure contains an axes object. The axes object contains 4 objects of type line, text.

Redesign the filter using designfilt and check it for stability.

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


Figure Filter Visualization Tool - Pole-Zero Plot contains an axes object and other objects of type uitoolbar, uimenu. The axes object with title Pole-Zero Plot contains 4 objects of type line, text.

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