dsp.AllpassFilter

Single section or cascaded allpass filter

Description

The dsp.AllpassFilter object filters each channel of the input using Allpass filter implementations. To import this object into Simulink^®, use the MATLAB^® System block.

Note

Cell array support for AllpassCoefficients, WDFCoefficients, and LatticeCoefficients has been removed. Use an N-by-1 or N-by-2 numeric array instead. For more information, see Compatibility Considerations.

To filter each channel of the input:

Create the dsp.AllpassFilter 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

Allpass = dsp.AllpassFilter

Allpass = dsp.AllpassFilter(Name,Value)

Description

Allpass = dsp.AllpassFilter returns an allpass filter System object™, Allpass, that filters each channel of the input signal independently using an allpass filter, with the default structure and coefficients.

example

Allpass = dsp.AllpassFilter(Name,Value) returns an allpass filter System object, Allpass, with each property set to the specified value.

Properties

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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.

`Structure` — Internal allpass filter structure
`Minimum multiplier` (default) | `Lattice` | `Wave Digital Filter`

You can specify the internal allpass filter implementation structure as one of | Minimum multiplier | Lattice | Wave Digital Filter. Each structure uses a different set of coefficients, independently stored in the corresponding object property.

`AllpassCoefficients` — Allpass polynomial coefficients
`[-2^(-1/2) 0.5]` (default) | N-by-1 | N-by-2

Specify the real allpass polynomial filter coefficients. Specify this property as either an N-by-1 or N-by-2 matrix of N first-order or second-order allpass sections. The default value defines a stable second-order allpass filter with poles and zeros located at ±π/3 in the Z plane.

Tunable: Yes

Dependencies

This property is applicable only when the Structure property is set to Minimum multiplier.

`WDFCoefficients` — Wave Digital Filter allpass coefficients
[`1/2, -2^(1/2)/3`] (default) | N-by-1 | N-by-2

Specify the real allpass coefficients in the Wave Digital Filter form. Specify this property as either a N-by-1 or N-by-2 matrix of N first-order or second-order allpass sections. All elements must have absolute values less than or equal to 1. This value is a transformed version of the default value of AllpassCoefficients, computed using allpass2wdf(AllpassCoefficients). These coefficients define the same stable second-order allpass filter as when Structure is set to 'Minimum multiplier'.

Tunable: Yes

Dependencies

This property is only applicable when the Structure property is set to Wave Digital Filter.

`LatticeCoefficients` — Lattice allpass coefficients
`[-2^(1/2)/3, 1/2]` (default) | vector

Specify the real or complex allpass coefficients as lattice reflection coefficients. Specify this property as either a row vector (single-section configuration) or a column vector. This value is a transformed and transposed version of the default value of AllpassCoefficients, computed using transpose(tf2latc([1 h.AllpassCoefficients])). These coefficients define the same stable second-order allpass filter as when Structure is set to 'Lattice'.

Tunable: Yes

Dependencies

This property is applicable only if the Structure property is set to Lattice.

`TrailingFirstOrderSection` — Indicate if last section is first order
`false` (default) | `true`

Indicate if last section is first order or second order. When you set TrailingFirstOrderSection to true, the last section is considered to be first-order, and the second element of the last row of the N-by-2 matrix is ignored. When you set TrailingFirstOrderSection to false, the last section is considered to be second-order.

Usage

Syntax

y = Allpass(x)

Description

example

y = Allpass(x) filters the input signal x using an allpass filter to produce the output y. Each column of x is filtered independently as a separate channel over time.

Input Arguments

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`x` — Data input
vector | matrix

Data input, specified as a vector or a matrix. This object also accepts variable-size inputs. Once the object is locked, you can change the size of each input channel, but you cannot change the number of channels.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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`y` — Filtered output
vector | matrix

Filtered output, returned as a vector or a matrix. The size, data type, and complexity of the output signal matches that of the input signal.

Data Types: double | single
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)

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Specific to `dsp.AllpassFilter`

`freqz`	Frequency response of discrete-time filter System object
`fvtool`	Visualize frequency response of DSP filters
`impz`	Impulse response of discrete-time filter System object
`info`	Information about filter System object
`coeffs`	Returns the filter System object coefficients in a structure
`cost`	Estimate cost of implementing filter System object
`grpdelay`	Group delay response of discrete-time filter System object

Common to All System Objects

`step`	Run System object algorithm
`release`	Release resources and allow changes to System object property values and input characteristics
`reset`	Reset internal states of System object

Examples

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Lowpass Filtering using Two Allpass Filters

Open Script

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent step syntax. For example, myObject(x) becomes step(myObject,x).

Construct the Allpass Filters

Fs  = 48000;    % in Hz
FL = 1024;
APF1 = dsp.AllpassFilter('AllpassCoefficients',...
    [-0.710525516540603   0.208818210000029]);
APF2 =  dsp.AllpassFilter('AllpassCoefficients',...
    [-0.940456403667957   0.6;...
    -0.324919696232907   0],...
    'TrailingFirstOrderSection',true);

Construct the Transfer Function Estimator to estimate the transfer function between the random input and the Allpass filtered output

TFE = dsp.TransferFunctionEstimator('FrequencyRange',...
    'onesided','SpectralAverages',2);

Construct the ArrayPlot to plot the magnitude response

AP = dsp.ArrayPlot('PlotType','Line','YLimits', [-80 5],...
    'YLabel','Magnitude (dB)','SampleIncrement', Fs/FL,...
    'XLabel','Frequency (Hz)','Title','Magnitude Response',...
    'ShowLegend', true,'ChannelNames',{'Magnitude Response'});

Filter the Input and show the magnitude response of the estimated transfer function between the input and the filtered output

tic;
while toc < 5
    in  = randn(FL,1);
    out = 0.5.*(APF1(in) + APF2(in));
    A = TFE(in, out);
    AP(db(A));
end

Algorithms

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The transfer function of an allpass filter is given by

$H (z) = \frac{c (n) + c (n - 1) z^{- 1} + ... + z^{- n}}{1 + c (1) z^{- 1} + ... + c (n) z^{- n}}$ .

c is allpass polynomial coefficients vector. The order, n, of the transfer function is the length of vector c.

In the minimum multiplier form and wave digital form, the allpass filter is implemented as a cascade of either second-order (biquad) sections or first-order sections. When the coefficients are specified as an N-by-2 matrix, each row of the matrix specifies the coefficients of a second-order filter. The last element of the last row can be ignored based on the trailing first-order setting. When the coefficients are specified as an N-by-1 matrix, each element in the matrix specifies the coefficient of a first-order filter. The cascade of all the filter sections forms the allpass filter.

In the lattice form, the coefficients are specified as a vector.

These structures are computationally more economical and structurally more stable compared to the generic IIR filters, such as df1, df1t, df2, df2t. For all structures, the allpass filter can be a single-section or a multiple-section (cascaded) filter. The different sections can have different orders, but they are all implemented according to the same structure.

Minimum Multiplier

This structure realizes the allpass filter with the minimum number of required multipliers, equal to the order n. It also uses 2n delay units and 2n adders. The multipliers uses the specified coefficients, which are equal to the polynomial vector c in the allpass transfer function. In this second-order section of the minimum multiplier structure, the coefficients vector, c, is equal to [0.1 -0.7].

Wave Digital Filter

This structure uses n multipliers, but only n delay units, at the expense of requiring 3n adders. To use this structure, specify the coefficients in wave digital filter (WDF) form. Obtain the WDF equivalent of the conventional allpass coefficients using allpass2wdf(allpass_coefficients). To convert WDF coefficients into the equivalent allpass polynomial form, use wdf2allpass(WDF coefficients). In this second-order section of the WDF structure, the coefficients vector w is equal to allpass2wdf([0.1 -0.7]).

Lattice

This lattice structure uses 2n multipliers, n delay units, and 2n adders. To use this structure, specify the coefficients as a vector.

You can obtain the lattice equivalent of the conventional allpass coefficients using transpose(tf2latc(1, [1 allpass_coefficients])). In the following second-order section of the lattice structure, the coefficients vector is computed using transpose(tf2latc(1, [1 0.1 -0.7])). Use these coefficients for a filter that is functionally equivalent to the minimum multiplier structure with coefficients [0.1 -0.7].

Compatibility Considerations

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Cell Array Support for `dsp.AllpassFilter` System object is removed

Errors starting in R2018b

The following properties of dsp.AllpassFilter System object have been removed in R2018b:

LatticeCoefficients
AllpassCoefficients
WDFCoefficients

Use an N-by-1 or N-by-2 numeric array instead.

Update Code

This table shows typical usage of the System object and explains how to update your existing code.

If your code has this form:	Use this code instead:
allpass = dsp.AllpassFilter; allpass.AllpassCoefficients = {0.5 0.7}	allpass = dsp.AllpassFilter; allpass.AllpassCoefficients = [0.5 0.7]
allpass = dsp.AllpassFilter('Structure','Lattice'); allpass.LatticeCoefficients = {-0.4714 0.5000}	allpass = dsp.AllpassFilter('Structure','Lattice'); allpass.LatticeCoefficients = [-0.4714 0.5000]
allpass = dsp.AllpassFilter('Structure','Wave Digital Filter'); allpass.LatticeCoefficients = {0.5000 -0.4714}	allpass = dsp.AllpassFilter('Structure','Wave Digital Filter'); allpass.LatticeCoefficients = [0.5000 -0.4714]

If your code has this form:

Use this code instead:

allpass = dsp.AllpassFilter;
allpass.AllpassCoefficients = {0.5 0.7}

allpass = dsp.AllpassFilter;
allpass.AllpassCoefficients = [0.5 0.7]

allpass = dsp.AllpassFilter('Structure','Lattice');
allpass.LatticeCoefficients = {-0.4714 0.5000}

allpass = dsp.AllpassFilter('Structure','Lattice');
allpass.LatticeCoefficients = [-0.4714 0.5000]

allpass = dsp.AllpassFilter('Structure','Wave Digital Filter');
allpass.LatticeCoefficients = {0.5000 -0.4714}

allpass = dsp.AllpassFilter('Structure','Wave Digital Filter');
allpass.LatticeCoefficients = [0.5000 -0.4714]

References

[1] Regalia, Philip A. and Mitra Sanjit K. and Vaidyanathan, P. P. (1988) “The Digital All-Pass Filter: AVersatile Signal Processing Building Block.” Proceedings of the IEEE, Vol. 76, No. 1, 1988, pp. 19–37

[2] M. Lutovac, D. Tosic, B. Evans, Filter Design for Signal Processing Using MATLAB and Mathematica. Upper Saddle River, NJ: Prentice Hall, 2001.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The System object supports code generation only when the Structure property is set to Minimum multiplier or Lattice.
See System Objects in MATLAB Code Generation (MATLAB Coder).

Documentation

dsp.AllpassFilter

Description

Creation

Syntax

Description

Properties

Structure — Internal allpass filter structure Minimum multiplier (default) | Lattice | Wave Digital Filter

AllpassCoefficients — Allpass polynomial coefficients [-2^(-1/2) 0.5] (default) | N-by-1 | N-by-2

Dependencies

WDFCoefficients — Wave Digital Filter allpass coefficients [1/2, -2^(1/2)/3] (default) | N-by-1 | N-by-2

Dependencies

LatticeCoefficients — Lattice allpass coefficients [-2^(1/2)/3, 1/2] (default) | vector

Dependencies

TrailingFirstOrderSection — Indicate if last section is first order false (default) | true

Usage

Syntax

Description

Input Arguments

x — Data input vector | matrix

Output Arguments

y — Filtered output vector | matrix

Object Functions

Specific to dsp.AllpassFilter

Common to All System Objects

Examples

Lowpass Filtering using Two Allpass Filters

Algorithms

Minimum Multiplier

Wave Digital Filter

Lattice

Compatibility Considerations

Cell Array Support for dsp.AllpassFilter System object is removed

References

Extended Capabilities

C/C++ Code Generation Generate C and C++ code using MATLAB® Coder™.

See Also

Functions

Objects

Topics

DSP System Toolbox Documentation

Support

`Structure` — Internal allpass filter structure
`Minimum multiplier` (default) | `Lattice` | `Wave Digital Filter`

`AllpassCoefficients` — Allpass polynomial coefficients
`[-2^(-1/2) 0.5]` (default) | N-by-1 | N-by-2

`WDFCoefficients` — Wave Digital Filter allpass coefficients
[`1/2, -2^(1/2)/3`] (default) | N-by-1 | N-by-2

`LatticeCoefficients` — Lattice allpass coefficients
`[-2^(1/2)/3, 1/2]` (default) | vector

`TrailingFirstOrderSection` — Indicate if last section is first order
`false` (default) | `true`

`x` — Data input
vector | matrix

`y` — Filtered output
vector | matrix

Specific to `dsp.AllpassFilter`

Cell Array Support for `dsp.AllpassFilter` System object is removed

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.