Average filter delay (group delay)
[gd,w] = grpdelay(b,a)
[gd,w] = grpdelay(b,a,n)
[gd,w] = grpdelay(sos,n)
[gd,w] = grpdelay(d,n)
[gd,f] = grpdelay(...,n,fs)
[gd,w] = grpdelay(...,n,'whole
')
[gd,f] =
grpdelay(...,n,'whole
',fs)
gd = grpdelay(...,w)
gd =
grpdelay(...,f,fs)
grpdelay(...)
[gd,w] = grpdelay(b,a)
returns
the group delay response, gd
, of the discrete-time
filter specified by the input vectors, b
and a
.
The input vectors are the coefficients for the numerator, b
,
and denominator, a
, polynomials in z^{-1}.
The Z-transform of the discrete-time filter is
$$H(z)=\frac{B(z)}{A(z)}=\frac{{\displaystyle \sum _{l=0}^{N-1}b}(l+1){z}^{-l}}{{\displaystyle \sum _{l=0}^{M-1}a}(l+1){z}^{-l}},$$
The filter's group delay response is evaluated at 512
equally spaced points in the interval [0,π)
on the unit circle. The evaluation points on the unit circle are returned
in w
.
[gd,w] = grpdelay(b,a,n)
returns
the group delay response of the discrete-time filter evaluated at n
equally
spaced points on the unit circle in the interval [0,π). n
is
a positive integer. For best results, set n
to
a value greater than the filter order.
[gd,w] = grpdelay(sos,n)
returns the group
delay response for the second-order sections matrix, sos
. 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, grpdelay
considers the input to be the
numerator vector, b
. 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)]
.
[gd,w] = grpdelay(d,n)
returns the group
delay response for the digital filter, d
. Use designfilt
to generate d
based
on frequency-response specifications.
[gd,f] = grpdelay(...,n,fs)
specifies
a positive sampling frequency fs
in hertz. It returns
a length-n
vector, f
, containing
the frequency points in hertz at which the group delay response is
evaluated. f
contains n
points
between 0 and fs/2
.
[gd,w] = grpdelay(...,n,'
and whole
')[gd,f]
use =
grpdelay(...,n,'whole
',fs)n
points
around the whole unit circle (from 0 to 2π,
or from 0 to fs
).
gd = grpdelay(...,w)
and gd
return
the group delay response evaluated at the angular frequencies in =
grpdelay(...,f,fs)w
(in
radians/sample) or in f
(in cycles/unit time),
respectively, where fs
is the sampling frequency. w
and f
are
vectors with at least two elements.
grpdelay(...)
with no output
arguments plots the group delay response versus frequency.
grpdelay
works for both real and complex
filters.
Note:
If the input to |
grpdelay
multiplies the filter coefficients
by a unit ramp. After Fourier transformation, this process corresponds
to differentiation.
cceps
| designfilt
| digitalFilter
| fft
| freqz
| fvtool
| hilbert
| icceps
| phasedelay
| rceps