# Documentation

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# dfilt.allpass

Allpass filter

## Syntax

`hd = dfilt.allpass(c)`

## Description

`hd = dfilt.allpass(c)` constructs an allpass filter with the minimum number of multipliers from the elements in vector `c`. To be valid, `c` must contain one, two, three, or four real elements. The number of elements in `c` determines the order of the filter. For example, `c` with two elements creates a second-order filter and `c` with four elements creates a fourth-order filter.

The transfer function for the allpass filter is defined by

`$H\left(z\right)=\frac{c\left(n\right)+c\left(n-1\right){z}^{-1}+\dots +{z}^{-n}}{1+c\left(1\right){z}^{-1}+\dots +c\left(n\right){z}^{-n}}$`

given the coefficients in `c`.

To construct a cascade of allpass filter objects, use `dfilt.cascadeallpass`. For more information about creating cascades of allpass filters, refer to `dfilt.cascadeallpass`.

## Properties

The following table provides a list of all the properties associated with an allpass `dfilt` object.

Property Name

Brief Description

`AllpassCoefficients`

Contains the coefficients for the allpass filter object

`FilterStructure`

Describes the signal flow for the filter object, including all of the active elements that perform operations during filtering — gains, delays, sums, products, and input/output.

`PersistentMemory`

Specifies whether to reset the filter states and memory before each filtering operation. Lets you decide whether your filter retains states from previous filtering runs. `False` is the default setting.

`States`

This property contains the filter states before, during, and after filter operations. States act as filter memory between filtering runs or sessions. They also provide linkage between the sections of a multisection filter, such as a cascade filter. For details, refer to `filtstates` in Signal Processing Toolbox™ documentation or in the Help system.

## Examples

This example constructs and displays the information about a second-order allpass filter that uses the minimum number of multipliers.

```c = [1.5, 0.7]; % Create a second-order dfilt object. hd = dfilt.allpass(c);```