# Documentation

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# islinphase

Determine whether filter has linear phase

## Syntax

flag = islinphase(b,a)flag = islinphase(sos)flag = islinphase(d)flag = islinphase(...,tol)flag = islinphase(h)

## Description

flag = islinphase(b,a) returns a logical output, flag, equal to true if the filter coefficients in b and a define a linear phase filter. flag is equal to false if the filter does not have linear phase.

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

flag = islinphase(...,tol) uses the tolerance, tol, to determine when two numbers are close enough to be considered equal. If not specified, tol, defaults to eps^(2/3).

flag = islinphase(h) determines if the dfilt filter object h has linear phase.

## Examples

collapse all

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('Frequency \omega/\pi') ylabel('Phase')

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); sosc = zp2sos(zc,pc,kc); [zd,pd,kd] = cheby2(ord,atten,Wcut); sosd = 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.

fv = fvtool(sosb,sosc,sosd,sose,'Analysis','phase'); legend(fv,'Butterworth','Chebyshev I','Chebyshev II','Elliptic')

phs = [islinphase(sosb) islinphase(sosc) ... islinphase(sosd) islinphase(sose)]
phs = 1×4 logical array 0 0 0 0