Calculates the group delay of a
GRPDELAY(b, a, N, Fs, whole)
b |
- |
A series. The numerator (i.e. zero) coefficients
in ascending powers of | ||||
a |
- |
A series. The denominator (i.e. pole) coefficients
in ascending powers of | ||||
N |
- |
Optional. An integer, the number of output samples, defaults to 2048. | ||||
Fs |
- |
Optional. A real, the sample rate of data. If the rates of the numerator and denominator coefficients are equal, the rate defaults to the coefficient rate, else the rate defaults to 1.0. | ||||
whole |
- |
Optional. An integer or string, the evaluation contour. Valid inputs are:
If whole is a string, the transform is evaluated over the entire unit circle. |
GRPDELAY(c, N, Fs, whole)
c |
- |
A series. The system coefficients in cascaded
| ||||
N |
- |
Optional. An integer, the number of output samples, defaults to 2048. | ||||
Fs |
- |
Optional. A real, the sample rate of data. Defaults to the rate of the coefficients. | ||||
whole |
- |
Optional. An integer or string, the evaluation contour. Valid inputs are:
If whole is a string, the transform is evaluated over the entire unit circle. |
A series, the group delay in samples.
W1: grpdelay({1}, {1, -0.5})
returns 512 samples of the group delay in W1.
W1: butterworth(1, 100.0, 10.0)
W2: grpdelay(w1, 1024)
creates a 10 Hz low pass BUTTERWORTH filter. W2 calculates and displays 1024 samples of the group delay response of the filter
The group delay is defined as:
Where phase(f) is the unwrapped phase response of the filter. To avoid difficulties in determining the unwrapped phase, the derivative is calculated by the following equivalent FFT expression:
where t is the time index series and h(t) is the impulse response of the filter.
GRPDELAY uses the above method evaluate N uniformly spaced
samples of the group delay over the unit circle of a
z^{ } |
=^{ } |
e^{ jω} complex frequency |
N |
= |
number of numerator terms |
M |
= |
number of denominator terms |
For grpdelay(c,
N, Fs, whole), the input c is assumed
to be a single column of coefficients in cascaded
or equivalently:
where G is the system gain, b_{k} and a_{k} are the filter coefficients for the k^{th} stage.
If c contains 2 columns, the coefficients are assumed to be in direct form, where the first column is b and the second column is a.
The amplitude of the group delay is in samples.
See IMPZ to display the impulse response of a
See ZFREQ to calculate the magnitude or phase
response of a