islinphase

R2026b

Determine whether filter has linear phase

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Syntax

flag = islinphase(b,a)

flag = islinphase(B,A,"ctf")

flag = islinphase({B,A,g},"ctf")

flag = islinphase(d)

flag = islinphase(sos)

flag = islinphase(___,tol)

Description

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

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

example

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

example

flag = islinphase(d) returns 1 if the digital filter d is linear phase.

example

flag = islinphase(sos) returns 1 if the filter specified by the second-order sections matrix sos is linear phase.

example

flag = islinphase(___,tol) specifies a tolerance tol to determine when two numbers are close enough to be considered equal.

Examples

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Linear and Nonlinear Phase Filters

Open Live Script

Use the window method to design a tenth-order lowpass FIR filter with normalized cutoff frequency 0.55. Verify that the filter has linear phase.

d = designfilt("lowpassfir",DesignMethod="window", ...
    FilterOrder=10,CutoffFrequency=0.55);
flag = islinphase(d)

flag = logical
   1

[phs,w] = phasez(d);

plot(w/pi,phs)
xlabel("Normalized Frequency (\times\pi rad/sample)")
ylabel("Phase (radians)")

Figure contains an axes object. The axes object with xlabel Normalized Frequency ( times pi rad/sample), ylabel Phase (radians) contains an object of type line.

IIR filters in general do not have linear phase. Verify the statement by constructing eighth-order Butterworth, Chebyshev, and elliptic filters with similar specifications.

ord = 8;
Wcut = 0.35;
atten = 20;
rippl = 1;

[zb,pb,kb] = butter(ord,Wcut);
sosB = zp2sos(zb,pb,kb);

[zc,pc,kc] = cheby1(ord,rippl,Wcut);
sosC1 = zp2sos(zc,pc,kc);

[zd,pd,kd] = cheby2(ord,atten,Wcut);
sosC2 = zp2sos(zd,pd,kd);

[ze,pe,ke] = ellip(ord,rippl,atten,Wcut);
sosE = zp2sos(ze,pe,ke);

Plot the phase responses of the filters. Determine whether they have linear phase.

phasez(sosB)
hold on
phasez(sosC1)
phasez(sosC2)
phasez(sosE)
hold off
ylim([-14 2])
legend("Butterworth","Chebyshev I", ...
    "Chebyshev II","Elliptic",Location="best")

Figure contains an axes object. The axes object with title Phase Response, xlabel Normalized Frequency ( times pi rad/sample), ylabel Phase (radians) contains 4 objects of type line. These objects represent Butterworth, Chebyshev I, Chebyshev II, Elliptic.

phs = [islinphase(sosB) islinphase(sosC1) ...
       islinphase(sosC2) islinphase(sosE)]

phs = 1×4 logical array

   0   0   0   0

Verify Linear Phase from Cascaded Transfer Functions

Since R2024b

Open Live Script

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 has linear phase using the filter coefficients in the CTF format.

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

flag = islinphase(B,A,"ctf")

flag = logical
   0

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 has linear phase using the filter coefficients and gain in the CTF format.

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

flag = logical
   0

Input Arguments

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`b,a` — Transfer function coefficients
vector

Transfer function coefficients, specified as a vector. The values of b and a represent the numerator and denominator polynomial coefficients, respectively.

Example: [b,a] = cheby2(5,30,0.7) creates a digital 5th-order Butterworth lowpass filter with coefficients b and a, having a normalized 3 dB frequency of 0.7π rad/sample and 30 dB attenuation at stopband.

Data Types: single | double
Complex Number Support: Yes

`B,A` — Cascaded transfer function (CTF) coefficients
scalars | vectors | matrices

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 islinphase normalizes the filter coefficients by A(:,1). In this case, A(:,1) must be nonzero.

Example: B = [2 4 2;3 3 0] and A = [6 0 2;6 0 0] specify a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Data Types: double | single
Complex Number Support: Yes

`g` — Scale values
scalar | vector

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.

Depending on how you specify g, islinphase applies a gain to the filter sections using the scaleFilterSections function:

Scalar — islinphase distributes the gain uniformly across all filter sections.
Vector — islinphase 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

`d` — Digital filter
`digitalFilter` object

Digital filter, specified as a digitalFilter object. Use designfilt to generate d based on frequency-response specifications.

Example: designfilt("lowpassfir",FilterOrder=10,CutoffFrequency=0.55) generates a digitalFilter object for a 10th order FIR lowpass filter with a normalized 3 dB frequency of 0.55π rad/sample.

Data Types: digitalFilter

`sos` — Second-order section representation
L-by-6 matrix

Second-order section representation, specified as an L-by-6 matrix, where L is the number of second-order sections. The matrix

$sos = [\begin{matrix} b_{01} & b_{11} & b_{21} & 1 & a_{11} & a_{21} \\ b_{02} & b_{12} & b_{22} & 1 & a_{12} & a_{22} \\ ⋮ & ⋮ & ⋮ & ⋮ & ⋮ & ⋮ \\ b_{0 L} & b_{1 L} & b_{2 L} & 1 & a_{1 L} & a_{2 L} \end{matrix}]$

represents the second-order sections of H(z):

$H (z) = \prod_{k = 1}^{L} H_{k} (z) = \prod_{k = 1}^{L} \frac{b_{0 k} + b_{1 k} z^{- 1} + b_{2 k} z^{- 2}}{1 + a_{1 k} z^{- 1} + a_{2 k} z^{- 2}} .$

Example: [z,p,k] = butter(3,1/32); sos = zp2sos(z,p,k) specifies a third-order Butterworth filter with a normalized 3 dB frequency of π/32 rad/sample.

Data Types: single | double
Complex Number Support: Yes

`tol` — Tolerance
`eps^(2/3)` (default) | positive scalar

Tolerance to distinguish between close numbers, specified as a positive scalar. The tolerance value determines when two numbers are close enough to be considered equal.

Data Types: single | double

Output Arguments

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`flag` — Linear phase flag
logical

Linear phase flag, returned as a logical scalar. The function returns 1 when the input is a minimum phase filter.

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)

Extended Capabilities

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Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.

The islinphase function supports thread-based environments with these usage notes and limitations:

Inputs containing digitalFilter objects are not supported.

For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2013a

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R2026b: Use thread-based environments

You can use islinphase in thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

R2024b: Analyze filters using cascaded transfer functions

The islinphase function supports inputs in the cascaded transfer function (CTF) format.

islinphase

Syntax

Description

Examples

Linear and Nonlinear Phase Filters

Verify Linear Phase from Cascaded Transfer Functions

Input Arguments

b,a — Transfer function coefficients vector

B,A — Cascaded transfer function (CTF) coefficients scalars | vectors | matrices

g — Scale values scalar | vector

d — Digital filter digitalFilter object

sos — Second-order section representation L-by-6 matrix

tol — Tolerance eps^(2/3) (default) | positive scalar

Output Arguments

flag — Linear phase flag logical

Tips

Extended Capabilities

Thread-Based Environment Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

Version History

R2026b: Use thread-based environments

R2024b: Analyze filters using cascaded transfer functions

See Also

`b,a` — Transfer function coefficients
vector

`B,A` — Cascaded transfer function (CTF) coefficients
scalars | vectors | matrices

`g` — Scale values
scalar | vector

`d` — Digital filter
`digitalFilter` object

`sos` — Second-order section representation
L-by-6 matrix

`tol` — Tolerance
`eps^(2/3)` (default) | positive scalar

`flag` — Linear phase flag
logical

Thread-Based Environment
Run code in the background using MATLAB® `backgroundPool` or accelerate code with Parallel Computing Toolbox™ `ThreadPool`.