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# grpdelay

Group delay response of discrete-time filter System object

## Syntax

``````[gd,w] = grpdelay(sysobj)``````
``````[gd,w] = grpdelay(sysobj,n)``````
``````[gd,w] = grpdelay(sysobj,'Arithmetic',arithType)``````
``grpdelay(sysobj)``

## Description

``````[gd,w] = grpdelay(sysobj)``` returns the group delay `gd` of the filter System object™, `sysobj`, based on the current filter coefficients. The vector `w` contains the frequencies (in radians) at which the group delay is evaluated. The group delay is defined as: $-\frac{d}{dw}\left(angle\left(w\right)\right)$The group delay is evaluated at 8192 points equally spaced around the upper half of the unit circle.```
``````[gd,w] = grpdelay(sysobj,n)``` returns the group delay of the filter System object and the corresponding frequencies at `n` points equally spaced around the upper half of the unit circle.```
``````[gd,w] = grpdelay(sysobj,'Arithmetic',arithType)``` computes the group delay of the filter System object, based on the arithmetic specified in `arithType`, using either of the previous syntaxes.```

example

````grpdelay(sysobj)` plots the group delay of the filter System object in the `fvtool`.For more input options, see `grpdelay`.```

## Examples

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`CICComp = dsp.CICCompensationDecimator;`

`grpdelay` computes the group delay of the filter and displays it using fvtool

`grpdelay(CICComp);`

## Input Arguments

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Number of samples, specified as a positive integer. For an FIR filter where `n` is a power of two, the computation is done faster using FFTs.

Data Types: `single` | `double` | `int8` | `int16` | `int32` | `int64` | `uint8` | `uint16` | `uint32` | `uint64`

Specify the arithmetic used during analysis. When you specify `'double'` or `'single'`, the function performs double- or single-precision analysis. When you specify `'fixed'` , the arithmetic changes depending on the setting of the `CoefficientDataType` property and whether the System object is locked or unlocked.

Details for Fixed-Point Arithmetic

System Object StateCoefficient Data TypeRule
Unlocked`'Same as input'`The function assumes that the coefficient data type is signed, 16 bit, and autoscaled. The function performs fixed-point analysis based on this assumption.
Unlocked`'Custom'`The function performs fixed-point analysis based on the setting of the `CustomCoefficientsDataType` property.
Locked`'Same as input'`When the input data type is `'double'` or `'fixed'`, the function assumes that the coefficient data type is signed, 16-bit, and autoscaled. The function performs fixed-point analysis based on this assumption.
Locked`'Custom'`The function performs fixed-point analysis based on the setting of the `CustomCoefficientsDataType` property.

When you do not specify the arithmetic for non-CIC structures, the function uses double-precision arithmetic if the filter System object is in an unlocked state. If the System object is locked, the function performs analysis based on the locked input data type. CIC structures only support fixed-point arithmetic.

## Output Arguments

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Group delay vector of length `n`. If `n` is not specified, the function uses a default value of `8192`.

Data Types: `double`

Frequency vector of length `n`, in radians/sample. `w` consists of `n` points equally spaced around the upper half of the unit circle (from 0 to π radians/sample). If `n` is not specified, the function uses a default value of `8192`.

Data Types: `double`