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isstable

Determine whether filter is stable

Description

flag = isstable(b,a) returns a logical output equal to 1 if the specified filter is stable. Specify a filter with numerator coefficients b and denominator coefficients a.

example

flag = isstable(B,A,"ctf") returns 1 if the filter specified as Cascaded Transfer Functions (CTF) with numerator coefficients B and denominator coefficients A is stable. (since R2024b)

example

flag = isstable({B,A,g},"ctf") returns 1 if the filter specified in CTF format is stable. Specify the filter with numerator coefficients B, denominator coefficients A, and scaling values g across filter sections. (since R2024b)

example

flag = isstable(d) returns 1 if the digital filter d is stable. Use designfilt to generate d based on frequency-response specifications.

flag = isstable(sos) returns 1 if the filter specified by second order sections matrix sos is stable.

example

Examples

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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
   1

zplane(z,p)

Figure contains an axes object. The axes object with title Pole-Zero Plot, xlabel Real Part, ylabel Imaginary Part contains 4 objects of type line, text. One or more of the lines displays its values using only markers

Redesign the filter using designfilt and check it for stability.

d = designfilt("highpassiir",DesignMethod="butter",FilterOrder=6, ...
               HalfPowerFrequency=0.7);
dflg = isstable(d)
dflg = logical
   1

zplane(d)

Figure contains an axes object. The axes object with title Pole-Zero Plot, xlabel Real Part, ylabel Imaginary Part contains 4 objects of type line, text. One or more of the lines displays its values using only markers

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
   1

act_flag2 = isstable(single(b),single(a))
act_flag2 = logical
   0

Since R2024b

Design a 40th-order lowpass Chebyshev type II digital filter with a stopband edge frequency of 0.4 and stopband attenuation of 50 dB. Verify that the filter is stable using the filter coefficients in the CTF format.

[B,A] = cheby2(40,50,0.4,"ctf");

flag = isstable(B,A,"ctf")
flag = logical
   1

Design a 30th-order bandpass elliptic digital filter with passband edge frequencies of 0.3 and 0.7, passband ripple of 0.1 dB, and stopband attenuation of 50 dB. Verify that the filter is stable using the filter coefficients and gain in the CTF format.

[B,A,g] = ellip(30,0.1,50,[0.3 0.7],"ctf");
flag = isstable({B,A,g},"ctf")
flag = logical
   1

Input Arguments

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Transfer function coefficients, specified as vectors.

Data Types: single | double

Since R2024b

Cascaded transfer function (CTF) coefficients, specified as scalars, vectors, or matrices. B and A list the numerator and denominator coefficients of the cascaded transfer function, respectively.

B must be of size L-by-(m + 1) and A must be of size L-by-(n + 1), where:

  • L represents the number of filter sections.

  • m represents the order of the filter numerators.

  • n represents the order of the filter denominators.

For more information about the cascaded transfer function format and coefficient matrices, see Specify Digital Filters in CTF Format.

Note

If any element of A(:,1) is not equal to 1, then isstable normalizes the filter coefficients by A(:,1). In this case, A(:,1) must be nonzero.

Data Types: double | single
Complex Number Support: Yes

Since R2024b

Scale values, specified as a real-valued scalar or as a real-valued vector with L + 1 elements, where L is the number of CTF sections. The scale values represent the distribution of the filter gain across sections of the cascaded filter representation.

The isstable function applies a gain to the filter sections using the scaleFilterSections function depending on how you specify g:

  • Scalar — The function distributes the gain uniformly across all filter sections.

  • Vector — The function applies the first L gain values to the corresponding filter sections and distributes the last gain value uniformly across all filter sections.

Data Types: double | single

Digital filter, specified as a digitalFilter object.

Second order sections, specified as 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 matrix corresponds to [bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)].

Data Types: double

Output Arguments

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Logical output, returned as 1 or 0. If the poles lie on or outside the circle, the function returns 0. If the poles are inside the circle, the function returns 1.

Data Types: logical

More About

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Tips

  • You can obtain filters in CTF format, including the scaling gain. Use the outputs of digital IIR filter design functions, such as butter, cheby1, cheby2, and ellip. Specify the "ctf" filter-type argument in these functions and specify to return B, A, and g to get the scale values. (since R2024b)

References

[1] Lyons, Richard G. Understanding Digital Signal Processing. Upper Saddle River, NJ: Prentice Hall, 2004.

Extended Capabilities

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Version History

Introduced in R2013a

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