DADiSP Online Help

Click here to see this page in full context

DADiSP Worksheet Functions > Function Categories > Fourier Transforms and Signal Processing > GRPDELAY

GRPDELAY

Purpose:

Calculates the group delay of a Z-transform.

Syntax:

GRPDELAY(b, a, N, Fs, whole)

A series. The numerator (i.e. zero) coefficients in ascending powers of z^-1.

A series. The denominator (i.e. pole) coefficients in ascending powers of z^-1.

Optional. An integer, the number of output samples, defaults to 2048.

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:

0:	evaluate the transform only over the upper half of the unit circle (default)
1:	evaluate the transform over the entire unit circle

If whole is a string, the transform is evaluated over the entire unit circle.

Alternate Syntax:

GRPDELAY(c, N, Fs, whole)

A series. The system coefficients in cascaded bi-quad form. 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.

Optional. An integer, the number of output samples, defaults to 2048.

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:

0:	evaluate the transform only over the upper half of the unit circle (default)
1:	evaluate the transform over the entire unit circle

If whole is a string, the transform is evaluated over the entire unit circle.

Returns:

A series, the group delay in samples.

Example:

$image\impz01.gif$

W1: grpdelay({1}, {1, -0.5})

returns 512 samples of the group delay in W1.

Example:

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

Remarks:

The group delay is defined as:

$image\grp01.gif$

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:

$image\grp02.gif$

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-transform in direct form:

$image\grp03.gif$

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 bi-quad form. This is the output format of IIR filters designed by DADiSP/Filters and processed by the CASCADE function.

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 Z-transform.

See ZFREQ to calculate the magnitude or phase response of a Z-transform.

GRPDELAY

Purpose:

Syntax:

Alternate Syntax:

Returns:

Example:

Example:

Remarks:

See Also: