# Documentation

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# mfilt.iirdecim

IIR decimator

### Note

`mfilt.iirdecim` will be removed in a future release. Use `dsp.IIRHalfbandDecimator` instead.

## Syntax

```hm = mfilt.iirdecim(c1,c2,...) ```

## Description

`hm = mfilt.iirdecim(c1,c2,...)` constructs an IIR decimator filter given the coefficients specified in the cell arrays `c1`, `c2`, and so on. The resulting IIR decimator is a polyphase IIR filter where each phase is a cascade allpass IIR filter.

Each cell array `ci` contains a set of vectors representing a cascade of allpass sections. Each element in one cell array is one section. For more information about the contents of each cell array, refer to `dfilt.cascadeallpass`. The contents of the cell arrays are the same for both filter constructors and `mfilt.iirdecim` interprets them same way as `mfilt.cascadeallpass`.

The following exception applies to interpreting the contents of a cell array — if one of the cell arrays `ci` contains only one vector, and that vector comprises a series of 0s and one element equal to 1, that cell array represents a `dfilt.delay` section with latency equal to the number of zeros, rather than a `dfilt.cascadeallpass` section. This exception case occurs with quasi-linear phase IIR decimators.

Although the first example shows how to construct an IIR decimators explicitly, one usually constructs an IIR decimators filter as a result of designing an decimators, as shown in the subsequent examples.

## Examples

When the coefficients are known, you can construct the IIR decimator directly using `mfilt.iirdecim`. For example, if the filter's coefficients are [0.6 0.5] for the first phase in the first stage, 0.7 for the second phase in the first stage and 0.8 for the third phase in the first stage; as well as 0.5 for the first phase in the second stage and 0.4 for the second phase in the second stage, construct the filter as shown here.

```Hm = mfilt.iirdecim({[0.6 0.5] 0.7 0.8},{0.5 0.4}) ```

Also refer to the “Quasi-Linear Phase Halfband and Dyadic Halfband Designs” section of the “IIR Polyphase Filter Design” example, iirallpassdemo example.

When the coefficients are not known, use the approach given by the following set of examples. Start by designing an elliptic halfband decimator with a decimation factor of 2. The example specifies the optional sampling frequency argument.

```tw = 100; % Transition width of filter. ast = 80; % Stopband attenuation of filter. fs = 2000; % Sampling frequency of signal to filter. m = 2; % Decimation factor. hm = fdesign.decimator(m,'halfband','tw,ast',tw,ast,fs);```

`hm` contains the specifications for a decimator defined by `tw`, `ast`, `m`, and `fs`.

Use the specification object `hm` to design a `mfilt.iirdecim` filter object.

```d = design(hm,'ellip','filterstructure','iirdecim'); % Note that realizemdl requires Simulink realizemdl(d) % Build model of the filter.```

Designing a linear phase decimator is similar to the previous example. In this case, design a halfband linear phase decimator with decimation factor of 2.

```tw = 100; % Transition width of filter. ast = 60; % Stopband attenuation of filter. fs = 2000; % Sampling frequency of signal to filter. m = 2; % Decimation factor.```

Create a specification object for the decimator.

`hm = fdesign.decimator(m,'halfband','tw,ast',tw,ast,fs);`

Finally, design the filter `d`.

```d = design(hm,'iirlinphase','filterstructure','iirdecim'); % Note that realizemdl requires Simulink realizemdl(d) % Build model of the filter.```

The filter implementation appears in this model, generated by `realizemdl` and Simulink®.

Given the design specifications shown here

the first phase is a delay section with 0s and a 1 for coefficients and the second phase is a linear phase decimator, shown in the next models.

Phase 1 model

Phase 2 model

Overall model

For more information about Multirate Filter Constructors see the “Getting Started with Multirate Filter (MFILT) Objects” example, mfiltgettingstarteddemo.

## See Also

#### Introduced in R2011a

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