[phi,w] = phasez(b,a,n)
returns the n-point phase response vector phi
and the corresponding angular frequency vector w for the digital
filter with the transfer function coefficients stored in b and
a.

[phi,w] = phasez(sos,n)
returns the n-point phase response corresponding to the second-order
sections matrix sos.

[phi,w] = phasez(d,n)
returns the n-point phase response for the digital filter
d.

[phi,w]
= phasez(___,n,'whole')
returns the phase response at n sample points around the entire unit
circle. This syntax can include any combination of input arguments from the previous
syntaxes.

[phi,f]
= phasez(___,n,fs)
returns the frequency vector.

phi = phasez(___,f,fs)
returns the phase response vector phi evaluated at the physical frequencies supplied in
f. This syntax can include any combination of input arguments from
the previous syntaxes.

phi = phasez(___,w)
returns the unwrapped phase response in radians at frequencies specified in
w.

Use designfilt to design an FIR filter of order 54, normalized cutoff frequency $$0.3\pi $$ rad/s, passband ripple 0.7 dB, and stopband attenuation 42 dB. Use the method of constrained least squares. Display the phase response of the filter.

Nf = 54;
Fc = 0.3;
Ap = 0.7;
As = 42;
d = designfilt('lowpassfir','CutoffFrequency',Fc,'FilterOrder',Nf, ...'PassbandRipple',Ap,'StopbandAttenuation',As, ...'DesignMethod','cls');
phasez(d)

Design the same filter using fircls1. Keep in mind that fircls1 uses linear units to measure the ripple and attenuation.

pAp = 10^(Ap/40);
Apl = (pAp-1)/(pAp+1);
pAs = 10^(As/20);
Asl = 1/pAs;
b = fircls1(Nf,Fc,Apl,Asl);
phasez(b)

Design a lowpass equiripple filter with normalized passband frequency $$0.45\pi $$ rad/s, normalized stopband frequency $$0.55\pi $$ rad/s, passband ripple 1 dB, and stopband attenuation 60 dB. Display the phase response of the filter.

d = designfilt('lowpassfir', ...'PassbandFrequency',0.45,'StopbandFrequency',0.55, ...'PassbandRipple',1,'StopbandAttenuation',60, ...'DesignMethod','equiripple');
phasez(d)

Design an elliptic lowpass IIR filter with normalized passband frequency $$0.4\pi $$ rad/s, normalized stopband frequency $$0.5\pi $$ rad/s, passband ripple 1 dB, and stopband attenuation 60 dB. Display the phase response of the filter.

d = designfilt('lowpassiir', ...'PassbandFrequency',0.4,'StopbandFrequency',0.5, ...'PassbandRipple',1,'StopbandAttenuation',60, ...'DesignMethod','ellip');
phasez(d)

Example: b = [1 3 3 1]/6 and a = [3 0 1 0]/3
specify a third-order Butterworth filter with normalized 3 dB frequency 0.5π
rad/sample.

Data Types: double | single Complex Number Support: Yes

n — Number of evaluation points 512 (default) | positive integer scalar

Number of evaluation points, specified as a positive integer
scalar no less than 2. When n is absent, it defaults
to 512. For best results, set n to a value greater
than the filter order.

Data Types: double

sos — Second-order section coefficients matrix

Second-order section coefficients, specified as a matrix. sos is a
K-by-6 matrix, where the number of sections,
K, must be greater than or equal to 2. If the number of sections is
less than 2, the function treats the input as a numerator vector. Each row of
sos corresponds to the coefficients of a second-order (biquad)
filter. The ith row of sos corresponds to
[bi(1) bi(2) bi(3) ai(1) ai(2) ai(3)].

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

Data Types: double | single Complex Number Support: Yes

d — Digital filter digitalFilter object

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

Example: d =
designfilt('lowpassiir','FilterOrder',3,'HalfPowerFrequency',0.5)
specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π
rad/sample.

fs — Sample rate positive scalar

Sample rate, specified as a positive scalar. When the unit of time is seconds,
fs is expressed in hertz.

Data Types: double

w — Angular frequencies vector

Angular frequencies, specified as a vector and expressed in rad/sample. w
must have at least two elements, because otherwise the function interprets it as
n. w = π corresponds to the Nyquist frequency.

f — Frequencies vector

Frequencies, specified as a vector. f must have at least two elements,
because otherwise the function interprets it as n. When the unit of
time is seconds, f is expressed in hertz.

Phase response, returned as a vector. If you specify n, then
phi has length n. If you do not specify
n, or specify n as an empty vector, then
phi has length 512.

If the input to phasez is single precision, the function
computes the phase response using single-precision arithmetic. The output
phi is single precision.

w — Angular frequencies vector

Angular frequencies, returned as a vector. w has values ranging
from 0 to π. If you specify 'whole' in your input,
the values in w range from 0 to 2π. If you
specify n, w has length
n. If you do not specify n, or specify
n as the empty vector, w has length
512.

f — Frequencies vector

Frequencies, returned as a vector expressed in hertz. f has
values ranging from 0 to fs/2 Hz. If you specify
'whole' in your input, the values in f range
from 0 to fs Hz. If you specify n,
f has length n. If you do not specify
n, or specify n as an empty vector,
f has length 512.

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