isallpass

Determine whether filter is allpass

Syntax

flag = isallpass(b,a)

flag = isallpass(sos)

flag = isallpass(d)

flag = isallpass(___,tol)

Description

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

flag = isallpass(sos) returns 1 if the filter specified by the second-order sections matrix sos is allpass.

flag = isallpass(d) returns 1 if the digital filter d is allpass.

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

Examples

Allpass Filters

Create an allpass filter and verify that the frequency response is allpass.

b = [1/3 1/4 1/5 1];
a = fliplr(b); 
flag = isallpass(b,a)

flag = logical
   1

freqz(b,a)

Create a lattice allpass filter and verify that the filter is allpass.

k = [1/2 1/3 1/4 1/5];
[b,a] = latc2tf(k,"allpass");
flag_isallpass = isallpass(b,a)

flag_isallpass = logical
   1

freqz(b,a)

Input Arguments

b,a — Filter coefficients

vector

Filter 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

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

$$\text{sos}=\left[\begin{array}{cccccc}{b}_{01}& b_{11}& b_{21}& 1& a_{11}& a_{21}\\ b_{02}& b_{12}& b_{22}& 1& a_{12}& a_{22}\\ ⋮& ⋮& ⋮& ⋮& ⋮& ⋮\\ b_{0L}& b_{1L}& b_{2L}& 1& a_{1L}& a_{2L}\end{array}\right]$$

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

$$H(z)={\displaystyle \prod _{k=1}^L{H}_k(z)={\displaystyle \prod _{k=1}^L\frac{b_{0k}+b_{1k}{z}^{-1}+b_{2k}{z}^{-2}}{1+a_{1k}{z}^{-1}+a_{2k}{z}^{-2}}.}}$$

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

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

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

flag — Allpass filter flag

logical

Allpass filter flag, returned as a logical scalar. The function returns 1 when the input is an allpass filter.

Version History

Introduced in R2013a