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.

example

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

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Allpass Filters

Open Live Script

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)

$Figure contains 2 axes objects. Axes object 1 with title Phase, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Phase (degrees) contains an object of type line. Axes object 2 with title Magnitude, xlabel Normalized Frequency (\times\pi rad/sample), ylabel Magnitude (dB) contains an object of type line.$

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

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`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

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

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

`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