# Documentation

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# dfilt.wdfallpass

Wave digital allpass filter

## Syntax

`hd = dfilt.wdfallpass(c)`

## Description

`hd = dfilt.wdfallpass(c)` constructs an allpass wave digital filter structure given the allpass coefficients in vector `c`.

Vector `c` must have, one, two, or four elements (filter coefficients). Filters with three coefficients are not supported. When you use `c` with four coefficients, the first and third coefficients must be 0.

Given the coefficients in `c`, the transfer function for the wave digital allpass filter is defined by

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

Internally, the allpass coefficients are converted to wave digital filters for filtering. Note that `dfilt.wdfallpass` allows only stable filters. Also note that the leading coefficient in the denominator, a 1, does not need to be included in vector `c`.

Use the constructor `dfilt.cascadewdfallpass` to cascade `wdfallpass` filters.

To compare these filters to other similar filters, `dfilt.wdfallpass` and `dfilt.cascadewdfallpass` filters have the same number of multipliers as the non-wave digital filters `dfilt.allpass` and `dfilt.cascadeallpass`. However, the wave digital filters use fewer states and they may require more adders in the filter structure.

Wave digital filters are usually used to create other filters. This toolbox uses them to implement halfband filters, which the first example in Examples demonstrates. They are most often building blocks for filters.

## Properties

In the next table, the row entries are the filter properties and a brief description of each property.

Property Name

Brief Description

`AllpassCoefficients`

Contains the coefficients for the allpass wave digital 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.

## Filter Structure

When you change the order of the wave digital filters in the cascade, the filter structure changes as well.

As shown in this example, `realizemdl` lets you see the filter structure used for your filter, if you have Simulink® installed.

```section11=0.8; section12=[1.5,0.7]; section13=[1.8,0.9]; hd1=dfilt.cascadewdfallpass(section11,section12,section13); section21=[0.8,0.4]; section22=[0,1.5,0,0.7]; section23=[0,1.8,0,0.9]; hd2=dfilt.cascadewdfallpass(section21,section22,section23); % If you have Simulink realizemdl(hd2)```

`hd1` has this filter structure with three sections.

The filter structure for `hd2` is somewhat different, with the different orders and interconnections between the three sections.

## Examples

Construct a second-order wave digital allpass filter with two coefficients. Note that to use `realizemdl`, you must have Simulink.

```c = [1.5,0.7]; hd = dfilt.wdfallpass(c);```

With Simulink installed, `realizemdl` returns this structure for `hd`.