Zero-phase response of digital filter
[Hr,w] = zerophase(b,a)
[Hr,w] = zerophase(sos)
[Hr,w] = zerophase(d)
[Hr,w] = zerophase(...,nfft)
[Hr,w] = zerophase(...,nfft,'whole'
)
[Hr,w] = zerophase(...,w)
[Hr,f] = zerophase(...,f,fs)
[Hr,w,phi] = zerophase(...)
zerophase(...)
[Hr,w] = zerophase(b,a)
returns
the zero-phase response Hr
, and the frequency vector w
(in
radians/sample) at which Hr
is computed, given
a filter defined by numerator b
and denominator a
.
For FIR filters where a=1
, you can omit the value a
from
the command. The zero-phase response is evaluated at 512
equally
spaced points on the upper half of the unit circle.
The zero-phase response, H_{r}(ω), is related to the frequency response, H(e^{jω}), by
$$H({e}^{j\omega})={H}_{r}(\omega ){e}^{j\phi (\omega )},$$
where φ(ω) is the continuous phase.
Note The zero-phase response is always real, but it is not the equivalent of the magnitude response. The former can be negative while the latter cannot be negative. |
[Hr,w] = zerophase(sos)
returns the zero-phase
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, zerophase
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)]
.
[Hr,w] = zerophase(d)
returns the zero-phase
response for the digital filter, d
. Use designfilt
to generate d
based
on frequency-response specifications.
[Hr,w] = zerophase(...,nfft)
returns
the zero-phase response Hr
and frequency vector w
(radians/sample),
using nfft
frequency points on the upper half of
the unit circle. For best results, set nfft
to
a value greater than the filter order.
[Hr,w] = zerophase(...,nfft,
returns
the zero-phase response 'whole'
)Hr
and frequency vector w
(radians/sample),
using nfft
frequency points around the whole unit
circle.
[Hr,w] = zerophase(...,w)
returns
the zero-phase response Hr
and frequency vector w
(radians/sample)
at frequencies in vector w
. The vector w
must
have at least two elements.
[Hr,f] = zerophase(...,f,fs)
returns
the zero-phase response Hr
and frequency vector f
(Hz),
using the sampling frequency fs
(in Hz), to determine
the frequency vector f
(in Hz) at which Hr
is
computed. The vector f
must have at least two elements.
[Hr,w,phi] = zerophase(...)
returns
the zero-phase response Hr
, frequency vector w
(rad/sample),
and the continuous phase component, phi
. (Note
that this quantity is not equivalent to the phase response of the
filter when the zero-phase response is negative.)
zerophase(...)
plots the
zero-phase response versus frequency. If you input the filter coefficients
or second order sections matrix, the current figure window is used.
If you input a digitalFilter
,
the step response is displayed in fvtool
.
Note:
If the input to |
designfilt
| digitalFilter
| freqs
| freqz
| fvtool
| grpdelay
| invfreqz
| phasedelay
| phasez