# dsp.IIRHalfbandInterpolator

Interpolate by a factor of two using polyphase IIR

## Description

The `dsp.IIRHalfbandInterpolator`

System object™ performs efficient polyphase interpolation of the input signal by a factor of
two. To design the halfband filter, you can specify the object to use an elliptic design or a
quasi-linear phase design. The object uses these design methods to compute the filter
coefficients. To filter the inputs, the object uses a polyphase structure. The allpass filters
in the polyphase structure are in a minimum multiplier form.

Elliptic design introduces nonlinear phase and creates the filter using fewer coefficients than quasi linear design. Quasi-linear phase design overcomes phase nonlinearity at the cost of additional coefficients.

Alternatively, instead of designing the halfband filter using a design method, you can specify the filter coefficients directly. When you choose this option, the allpass filters in the two branches of the polyphase implementation can be in a minimum multiplier form or in a wave digital form.

You can also use `dsp.IIRHalfbandInterpolator`

object to implement the
synthesis portion of a two-band filter bank to synthesize a signal from lowpass and highpass
subbands.

To upsample and interpolate your data:

Create the

`dsp.IIRHalfbandInterpolator`

object and set its properties.Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

## Creation

### Syntax

### Description

`iirhalfbandinterp = dsp.IIRHalfbandInterpolator`

returns an IIR
halfband interpolation filter, `iirhalfbandinterp`

, with the default
settings. Under the default settings, the System object upsamples and interpolates the input data using a halfband frequency of
`22050`

Hz, a transition width of `4100`

Hz, and a
stopband attenuation of `80`

dB.

returns an IIR halfband interpolator, with additional properties specified by one or more
`iirhalfbandinterp`

= dsp.IIRHalfbandInterpolator(`Name=Value`

)`Name-Value`

pair arguments.

**Example: **```
iirhalfbandinterp = dsp.IIRHalfbandInterpolator(Specification="Filter
order and stopband attenuation")
```

creates an IIR halfband interpolator object
with filter order set to `9`

and stopband attenuation set to
`80`

dB.

## Properties

Unless otherwise indicated, properties are *nontunable*, which means you cannot change their
values after calling the object. Objects lock when you call them, and the
`release`

function unlocks them.

If a property is *tunable*, you can change its value at
any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

`Specification`

— Filter design parameters

```
"Transition width and stopband
attenuation"
```

(default) | `"Filter order and stopband attenuation"`

| `"Filter order and transition width"`

| `"Coefficients"`

Filter design parameters, specified as a character vector. When you set
`Specification`

to one of the filter design options, you can
specify the filter design parameters using the corresponding
`FilterOrder`

, `StopbandAttenuation`

, and
`TransitionWidth`

properties. Also, you can specify the design
method using `DesignMethod`

. When you set
`Specification`

to `"Coefficients"`

, you can
specify the coefficients directly.

`FilterOrder`

— Order of the IIR halfband filter

9 (default) | positive scalar integer

Order of the IIR halfband filter, specified as a positive scalar integer. If you set
`DesignMethod`

to `"Elliptic"`

, then
`FilterOrder`

must be an odd integer greater than one. If you set
`DesignMethod`

to `"Quasi-linear phase"`

, then
`FilterOrder`

must be a multiple of four.

#### Dependencies

To enable this property, set `Specification`

to
`"Filter order and stopband attenuation"`

or ```
"Filter order
and transition width"
```

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`StopbandAttenuation`

— Minimum attenuation needed in stopband

80 (default) | positive real scalar

Minimum attenuation needed in the stopband of the IIR halfband filter, specified as a positive real scalar. Units are in dB.

#### Dependencies

To enable this property, set `Specification`

to
`"Filter order and stopband attenuation"`

or ```
"Transition
width and stopband attenuation"
```

.

**Data Types: **`single`

| `double`

`TransitionWidth`

— Transition width

4100 (default) | positive real scalar

Transition width of the IIR halfband filter, specified as a positive real scalar
or in normalized frequency units* (since R2023b)*.

If you set the
`NormalizedFrequency`

property to:

`false`

–– The value of the transition width is in Hz and must be less than half the output sample rate (2 ×`SampleRate`

property) value.`true`

–– The value of the transition width is in normalized frequency units. The value must be a positive scalar less than`1.0`

.When you set the

`NormalizedFrequency`

property to`true`

while creating the object and you do not set the transition width, the default transition width is automatically set to normalized frequency units using the default sample rate at which the filter operates (2 × 44100) Hz. The filter in the halfband interpolator effectively runs at twice the sample rate of the input signal.When you set the

`NormalizedFrequency`

property to`true`

after you create the object, the transition width must be specified in normalized units before you run the object algorithm. To specify the normalized frequency value, set`NormalizedFrequency`

to`true`

and manually convert the frequency value in Hz to the normalized value using the input sample rate in Hz. For example, if the input sample rate is 22050 Hz, the corresponding transition width value in normalized units is*TW*/(2×_{Hz}*Fs*/2).iirhalfbandinterp = dsp.IIRHalfbandInterpolator; iirhalfbandinterp.NormalizedFrequency = true; iirhalfbandinterp.TransitionWidth = 4100/((2x22050)/2)

* (since R2023b)*

#### Dependencies

To enable this property, set `Specification`

to
`"Transition width and stopband attenuation"`

or ```
"Filter
order and transition width"
```

.

**Data Types: **`single`

| `double`

`DesignMethod`

— Design method

`"Elliptic"`

(default) | `"Quasi-linear phase"`

Design method for the IIR halfband filter, specified as
`"Elliptic"`

or `"Quasi-linear phase"`

. When you set
this property to `"Quasi-linear phase"`

, the first branch of the
polyphase structure is a pure delay, which results in an approximately linear phase
response.

#### Dependencies

To enable this property, set `Specification`

to any accepted
value except `"Coefficients"`

.

`NormalizedFrequency`

— Flag to set frequencies in normalized units

`false`

(default) | `true`

*Since R2023b*

Flag to set frequencies in normalized units, specified as one of these values:

`true`

–– The transition width must be in the normalized frequency units and less than`1.0`

.When you set the

`NormalizedFrequency`

property to`true`

while creating the object and you do not set the transition width, the default transition width is automatically set to normalized frequency units using the default sample rate at which the filter operates (2 × 44100) Hz. The filter in the halfband interpolator effectively runs at twice the sample rate of the input signal.When you set the

`NormalizedFrequency`

property to`true`

after you create the object, the transition width must be specified in normalized units before you run the object algorithm. To specify the normalized frequency value, set`NormalizedFrequency`

to`true`

and manually convert the frequency value in Hz to the normalized value using the input sample rate in Hz. For example, if the input sample rate is 22050 Hz, the corresponding transition width value in normalized units is*TW*/(2×_{Hz}*Fs*/2).iirhalfbandinterp = dsp.IIRHalfbandInterpolator; iirhalfbandinterp.NormalizedFrequency = true; iirhalfbandinterp.TransitionWidth = 4100/((2x22050)/2)

`false`

–– The transition width is in Hz. You can specify the input sample rate through the`SampleRate`

property.

#### Dependency

To enable this property, set `Specification`

to any accepted
value except `"Coefficients"`

.

**Data Types: **`logical`

`SampleRate`

— Input sample rate

44100 (default) | positive real scalar

Input sample rate, specified as a positive real scalar. Units are in Hz.

#### Dependency

To enable this property, set:

`Specification`

to any accepted value except`"Coefficients"`

.`NormalizedFrequency`

to`false`

.*(since R2023b)*

**Data Types: **`single`

| `double`

`FilterBankInputPort`

— Option to use object as synthesis filter bank

`false`

(default) | `true`

Option to use object as synthesis filter bank, specified as a logical value. If this
property is `false`

, `dsp.IIRHalfbandInterpolator`

acts as an interpolator. If this property is
`true`

, then `dsp.IIRHalfbandInterpolator`

acts as a synthesis filter bank and the
algorithm accepts two inputs: the lowpass and highpass subbands.

#### Dependencies

To enable this property, set `Specification`

to any accepted
value except `"Coefficients"`

.

`Structure`

— Filter structure used in coefficient mode

`"Minimum multiplier"`

(default) | `"Wave Digital Filter"`

Internal allpass filter implementation structure, specified as ```
"Minimum
multiplier"
```

or `"Wave Digital Filter"`

. Each structure uses
a different coefficients set, independently stored in the corresponding object
property.

This property is not tunable.

#### Dependencies

To enable this property, set `Specification`

to
`"Coefficients"`

.

`AllpassCoefficients1`

— Allpass polynomial filter coefficients of first branch

`[0.1284563; 0.7906755]`

(default) | `[0.1284563 0.1534; 0.7906755 0.6745]`

Allpass polynomial filter coefficients of the first branch, specified as an
*N*-by-`1`

or
*N*-by-`2`

matrix. *N* is the
number of first-order or second-order allpass sections.

**Tunable: **Yes

#### Dependencies

To enable this property, set `Specification`

to
`"Coefficients"`

and `Structure`

to
`"Minimum multiplier"`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`AllpassCoefficients2`

— Allpass polynomial filter coefficients of second branch

`[0.4295667]`

(default) | `[0.7906755 0.1534]`

Allpass polynomial filter coefficients of the second branch, specified as an
*N*-by-`1`

or
*N*-by-`2`

matrix. *N* is the
number of first-order or second-order allpass sections.

**Tunable: **Yes

#### Dependencies

To enable this property, set `Specification`

to
`"Coefficients"`

and `Structure`

to
`"Minimum multiplier"`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`WDFCoefficients1`

— Allpass filter coefficients of first branch in Wave Digital Filter form

`[0.1284563; 0.7906755]`

(default) | `[0.1284563 0.1534; 0.7906755 0.6745]`

Allpass filter coefficients of the first branch in Wave Digital Filter form,
specified as an *N*-by-`1`

or
*N*-by-`2`

matrix. *N* is the
number of first-order or second-order allpass sections. All elements must have an
absolute value less than or equal to `1`

.

This property is not tunable.

#### Dependencies

To enable this property, set `Specification`

to
`"Coefficients"`

and `Structure`

to
`"Wave Digital Filter"`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`WDFCoefficients2`

— Allpass filter coefficients of second branch in Wave Digital Filter form

`[0.4295667]`

(default) | `[0.7906755 0.1534]`

Allpass filter coefficients of the second branch in Wave Digital Filter form,
specified as an *N*-by-`1`

or
*N*-by-`2`

matrix. *N* is the
number of first-order or second-order allpass sections. All elements must have an
absolute value less than or equal to `1`

.

This property is not tunable.

#### Dependencies

To enable this property, set `Specification`

to
`"Coefficients"`

and `Structure`

to
`"Wave Digital Filter"`

.

**Data Types: **`single`

| `double`

| `int8`

| `int16`

| `int32`

| `int64`

| `uint8`

| `uint16`

| `uint32`

| `uint64`

`HasPureDelayBranch`

— Make the first branch a pure delay

`false`

(default) | `true`

Flag to make the first allpass branch a delay, specified as a logical scalar. When
this property is true, the first branch is treated as a pure delay and the properties
`AllpassCoefficients1`

and `WDFCoefficients1`

do
not apply.

This property is not tunable.

#### Dependencies

To enable this property, set `Specification`

to
`"Coefficients"`

.

`Delay`

— Length of the delay

`1`

(default) | finite positive scalar

Length of the first branch delay, specified as a finite positive scalar. The value of this property specifies the number of samples by which you can delay the input to the first branch.

This property is not tunable.

#### Dependencies

To enable this property, set `Specification`

to
`"Coefficients"`

and `HasPureDelayBranch`

to
1.

**Data Types: **`single`

| `double`

`HasTrailingFirstOrderSection`

— Make the last section of the second branch as first order

`false`

(default) | `true`

Option to treat the last section of the second branch as first order, specified as a
logical scalar. When this property is 1 and the coefficients of the second branch are in
an *N*-by-2 matrix, the object ignores the second element of the last
row of the matrix. The last section of the second branch then becomes a first-order
section. When this property is set to `0`

, the last section of the
second branch is a second-order section. When the coefficients of the second branch are
in an *N*-by-1 matrix, this property is ignored.

This property is not tunable.

#### Dependencies

To enable this property, set `Specification`

to
`"Coefficients"`

.

## Usage

### Description

implements a halfband synthesis filter bank for the inputs `y`

= iirhalfbandinterp(`x1`

,`x2`

)`x1`

and
`x2`

. `x1`

is the lowpass output of a halfband
analysis filter bank and `x2`

is the highpass output of a halfband
analysis filter bank. `dsp.IIRHalfbandInterpolator`

implements a synthesis
filter bank only when the `FilterBankInputPort`

property is
`true`

.

### Input Arguments

`x1`

— Data input

column vector | matrix

Data input to the IIR halfband interpolator, specified as a column vector or a matrix. This signal is the lowpass output of a halfband analysis filter bank. If the input signal is a matrix, each column of the matrix is treated as an independent channel.

**Data Types: **`single`

| `double`

**Complex Number Support: **Yes

`x2`

— Second data input

column vector | matrix

Second data input to the synthesis filter bank, specified as a column vector or a matrix. This signal is the highpass output of a halfband analysis filter bank. If the input signal is a matrix, each column of the matrix is treated as an independent channel.

The size, data type, and complexity of both the inputs must be the same.

**Data Types: **`single`

| `double`

**Complex Number Support: **Yes

### Output Arguments

`y`

— Output of interpolator

column vector | matrix

Output of the interpolator, returned as a column vector or a matrix. The number of rows in the interpolator output is twice the number of rows in the input signal.

**Data Types: **`single`

| `double`

**Complex Number Support: **Yes

## Object Functions

To use an object function, specify the
System object as the first input argument. For
example, to release system resources of a System object named `obj`

, use
this syntax:

release(obj)

### Specific to `dsp.IIRHalfbandInterpolator`

`freqz` | Frequency response of discrete-time filter System object |

`freqzmr` | Compute DTFT approximation of impulse response of multirate or single-rate filter |

`filterAnalyzer` | Analyze filters with Filter Analyzer app |

`info` | Information about filter System object |

`cost` | Estimate cost of implementing filter System object |

`polyphase` | Polyphase decomposition of multirate filter |

`outputDelay` | Determine output delay of single-rate or multirate filter |

## Examples

### Frequency response of Quasi-linear Phase IIR Halfband Interpolator

Create a minimum order lowpass IIR halfband interpolation filter. The filter has a transition width of 0.0930 in normalized frequency units, and a stopband attenuation of 80 dB.

IIRHalfbandInterp = dsp.IIRHalfbandInterpolator(... NormalizedFrequency=true,... DesignMethod="Quasi-linear phase");

Obtain filter coefficients

c = coeffs(IIRHalfbandInterp);

Plot the Magnitude and Phase response

freqz(IIRHalfbandInterp)

### Design and Implement IIR Halfband Interpolator

Design an elliptic IIR halfband interpolator object of order 31 and a transition width of 0.1 using the `designHalfbandIIR`

function. Set the `Verbose`

argument to `true`

.

hbIIR = designHalfbandIIR(FilterOrder=31,TransitionWidth=0.1,DesignMethod="ellip",... Structure='interp',SystemObject=true,Verbose=true)

designHalfbandIIR(FilterOrder=31, TransitionWidth=0.1, DesignMethod="ellip", Structure="interp", Datatype="double", SystemObject=true, Passband="lowpass")

hbIIR = dsp.IIRHalfbandInterpolator with properties: Specification: 'Coefficients' FilterBankInputPort: false Structure: 'Minimum multiplier' HasPureDelayBranch: false AllpassCoefficients1: [8x1 double] AllpassCoefficients2: [7x1 double] HasTrailingFirstOrderSection: false

Create a `dsp.DynamicFilterVisualizer`

object and visualize the magnitude response of the filter.

dfv = dsp.DynamicFilterVisualizer(NormalizedFrequency=true); dfv(hbIIR);

The input is a cosine wave.

Fs = 1; Fc = 0.08; input = cos(2*pi*Fc*(0:39)'/Fs);

Interpolate the cosine signal using the IIR halfband interpolator.

output = hbIIR(input);

Plot the original and interpolated signals. In order to plot the two signals in the same plot, you must account for the output delay introduced by the IIR halfband interpolator and the scaling introduced by the filter. Use the `outputDelay`

function to compute the `delay`

introduced by the interpolator. Shift the output by this delay value.

Visualize the input and the resampled signals. The input and output values coincide every other sample, due to the interpolation factor of 2.

[delay,FsOut] = outputDelay(hbIIR,FsIn=Fs,Fc=Fc)

delay = 3.5090

FsOut = 2

nInput = (0:length(input)-1); tOutput = (0:length(output)-1)/FsOut-delay; stem(tOutput,output,'filled',MarkerSize=4); hold on; stem(nInput,input); hold off; xlim([-5,20]) legend('Interpolated by 2','Input signal','Location','best');

### Extract Low Frequency Subband from Speech

Use a halfband analysis filter bank and interpolation filter to extract the low frequency subband from a speech signal.

**Note:** The `audioDeviceWriter`

System object™ is not supported in MATLAB Online.

Set up the audio file reader, the analysis filter bank, the audio device writer, and the interpolation filter. The sampling rate of the audio data is 22050 Hz. The halfband filter has an order of 21 and a transition width of 2 kHz.

afr = dsp.AudioFileReader('speech_dft.mp3',SamplesPerFrame=1024); filterspec = "Filter order and transition width"; Order = 21; TW = 2000; IIRHalfbandDecim = dsp.IIRHalfbandDecimator(... Specification=filterspec,FilterOrder=Order,... TransitionWidth=TW,SampleRate=afr.SampleRate); IIRHalfbandInterp = dsp.IIRHalfbandInterpolator(... Specification=filterspec,FilterOrder=Order,... TransitionWidth=TW,SampleRate=afr.SampleRate/2); ap = audioDeviceWriter(SampleRate=afr.SampleRate);

View the magnitude response of the halfband filter.

filterAnalyzer(IIRHalfbandDecim)

Read the speech signal from the audio file in frames of 1024 samples. Filter the speech signal into lowpass and highpass subbands with a halfband frequency of 5512.5 Hz. Reconstruct a lowpass approximation of the speech signal by interpolating the lowpass subband. Play the filtered output.

while ~isDone(afr) audioframe = afr(); xlo = IIRHalfbandDecim(audioframe); ylow = IIRHalfbandInterp(xlo); ap(ylow); end

Wait until the audio file ends, and then close the input file and release the audio output resource.

release(afr); release(ap);

### Two-Channel Filter Bank

Use a halfband decimator and interpolator to implement a two-channel filter bank. This example uses an audio file input and shows that the power spectrum of the filter bank output does not differ significantly from the input.

**Note**: The `audioDeviceWriter`

System object™ is not supported in MATLAB Online.

Set up the audio file reader and audio device writer. Construct the IIR halfband decimator and interpolator. Finally, set up the spectrum analyzer to display the power spectra of the filter-bank input and output.

AF = dsp.AudioFileReader('speech_dft.mp3',SamplesPerFrame=1024); AP = audioDeviceWriter(SampleRate=AF.SampleRate); filterspec = "Filter order and transition width"; Order = 51; TW = 2000; IIRHalfbandDecim = dsp.IIRHalfbandDecimator(... Specification=filterspec,FilterOrder=Order,... TransitionWidth=TW,SampleRate=AF.SampleRate); IIRHalfbandInterp = dsp.IIRHalfbandInterpolator(... Specification=filterspec,FilterOrder=Order,... TransitionWidth=TW,SampleRate=AF.SampleRate/2,... FilterBankInputPort=true); SpecAna = spectrumAnalyzer(SampleRate=AF.SampleRate,... PlotAsTwoSidedSpectrum=false,... ShowLegend=true,... ChannelNames={'Input signal','Filtered output signal'});

Read the audio 1024 samples at a time. Filter the input to obtain the lowpass and highpass subband signals decimated by a factor of two. This is the analysis filter bank. Use the halfband interpolator as the synthesis filter bank. Display the running power spectrum of the audio input and the output of the synthesis filter bank. Play the output.

while ~isDone(AF) audioInput = AF(); [xlo,xhigh] = IIRHalfbandDecim(audioInput); audioOutput = IIRHalfbandInterp(xlo,xhigh); spectrumInput = [audioInput audioOutput]; SpecAna(spectrumInput); AP(audioOutput); end release(AF); release(AP); release(SpecAna);

### Upsample and Interpolate Multichannel Input with IIR Halfband Interpolator

Create a halfband interpolation filter. The filter order is 51 with a transition width of 0.0930 in normalized frequency units.

filterspec = "Filter order and transition width"; Order = 51; TW = 0.0930; iirhalfbandinterp = dsp.IIRHalfbandInterpolator(... NormalizedFrequency=true,... Specification=filterspec,... FilterOrder=Order,... TransitionWidth=TW);

Use the filter to upsample and interpolate a multichannel input.

x = randn(1024,4); y = iirhalfbandinterp(x);

## Algorithms

### Polyphase Implementation with Halfband Filters

When you filter your signal, the IIR halfband interpolator uses an efficient polyphase implementation for halfband filters. You can use a polyphase implementation to move the upsampling operation after filtering. This change enables you to filter at a lower sampling rate.

IIR halfband filters are generally modeled using two parallel allpass filter branches.

$$H(z)=0.5*[{A}_{1}({z}^{2})+{z}^{-1}{A}_{2}({z}^{2})]$$

**Elliptic Design**

The allpass filters for elliptic IIR halfband filter are given as

$${A}_{1}(z)={\displaystyle \prod _{k=1}^{{K}_{1}}\frac{{a}_{k}^{(1)}+{z}^{-1}}{1+{a}_{k}^{(1)}{z}^{-1}}}$$

$${A}_{2}(z)={\displaystyle \prod _{k=1}^{{K}_{2}}\frac{{a}_{k}^{(2)}+{z}^{-1}}{1+{a}_{k}^{(2)}{z}^{-1}}}$$

**Quasi-Linear Phase Design**

A near-linear phase response for IIR halfband filters is achieved by making one of the branches a pure delay. In this design, the cost of the filter increases.

The allpass filters for quasi-linear phase IIR halfband filter are

$${A}_{1}(z)={z}^{-k}$$

where, *k* is the length of the delay.

$${A}_{2}(z)={\displaystyle \prod _{K=1}^{{K}_{2}^{(1)}}\frac{{a}_{k}+{z}^{-1}}{1+{a}_{k}{z}^{-1}}}{\displaystyle \prod _{K=1}^{{K}_{2}^{(2)}}\frac{{c}_{k}+{b}_{k}{z}^{-1}+{z}^{-2}}{1+{b}_{k}{z}^{-1}+{c}_{k}{z}^{-2}}}$$

where *N* is the order of the IIR halfband filter.

You can represent the upsampling-by-2 operation followed by the filtering operation using this figure.

Using the multirate noble identity for upsampling, you can move the upsampling operation after filtering. This enables you to filter at a lower rate.

To efficiently implement the halfband interpolator, this algorithm replaces the upsampling operator, delay block, and adder with a commutator switch. The commutator switch starts on the first branch and takes input samples from the two branches alternately, one sample at a time. This doubles the sampling rate of the input signal. This is shown in the following figure.

**Synthesis Filter Bank**

Transfer function of the complementary highpass filter branch of the synthesis filter bank is given by

$$G(z)=0.5*[{A}_{1}({z}^{2})-{z}^{-1}{A}_{2}({z}^{2})]$$

You can represent the synthesis filter bank as in this diagram.

The IIR halfband interpolator implements the synthesis portion of a two-band filter bank to synthesize a signal from lowpass and highpass subbands.

For more information on filter banks, see Overview of Filter Banks.

To summarize, the IIR halfband interpolator:

Filters the input before upsampling

Acts as a synthesis filter bank

Has a nonlinear phase response and uses few coefficients with the elliptic design method

Has near-linear phase response at the cost of additional coefficients with the quasi-linear phase design method, where one of the branches is a pure delay

## References

[1] Lang, M. *Allpass Filter Design and Applications.* IEEE
Transactions on Signal Processing. Vol. 46, No. 9, Sept 1998, pp. 2505–2514.

[2] Harris, F.J. *Multirate Signal Processing for Communication
Systems*. Prentice Hall. 2004, pp. 208–209.

[3] Regalia, Phillip A., Sanjit K. Mitra, and P. P. Vaidyanathan. "The Digital All-Pass
Filter: A Versatile Signal Processing Building Block." *Proceedings of the
IEEE.* Vol. 76, Number 1, 1988, pp. 19-37.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

This object supports code generation for ARM^{®}
Cortex^{®}-M and ARM
Cortex-A processors.

## Version History

**Introduced in R2015b**

### R2023b: Support for normalized frequencies

When you set the `NormalizedFrequency`

property to
`true`

, you must specify the transition width in normalized frequency
units (0 to 1).

When you set the `NormalizedFrequency`

property to
`true`

while creating the object and you do not set the transition width,
the default transition width is automatically set to normalized frequency units using the
default sample rate at which the filter operates (2 × 44100) Hz. The filter in the halfband
interpolator effectively runs at twice the sample rate of the input signal.

iirhalfbandinterp = dsp.IIRHalfbandInterpolator(NormalizedFrequency=true)

iirhalfbandinterp = dsp.IIRHalfbandInterpolator with properties: Specification: 'Transition width and stopband attenuation' TransitionWidth: 0.1859 StopbandAttenuation: 80 DesignMethod: 'Elliptic' FilterBankInputPort: false NormalizedFrequency: true

When you set the `NormalizedFrequency`

property to
`true`

after you create the object, the transition width must be
specified in normalized units before you run the object
algorithm.

iirhalfbandinterp = dsp.IIRHalfbandInterpolator

iirhalfbandinterp = dsp.IIRHalfbandInterpolator with properties: Specification: 'Transition width and stopband attenuation' TransitionWidth: 4100 StopbandAttenuation: 80 DesignMethod: 'Elliptic' FilterBankInputPort: false NormalizedFrequency: false SampleRate: 22050

`NormalizedFrequency`

to `true`

and manually convert
the frequency values in Hz to normalized values using the input sample rate in Hz. For
example, if the input sample rate is 22050 Hz, the corresponding values in normalized units
are computed using these equations.iirhalfbandinterp.NormalizedFrequency = true; iirhalfbandinterp.TransitionWidth = 4100/((2x22050)/2)

iirhalfbandinterp = dsp.IIRHalfbandInterpolator with properties: Specification: 'Transition width and stopband attenuation' TransitionWidth: 0.1859 StopbandAttenuation: 80 DesignMethod: 'Elliptic' FilterBankInputPort: false NormalizedFrequency: true

## See Also

### Functions

`freqz`

|`freqzmr`

|`filterAnalyzer`

|`info`

|`cost`

|`polyphase`

|`outputDelay`

|`designHalfbandIIR`

### Objects

### Blocks

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