Documentation

dsp.AllpassFilter System object

Package: dsp

Single section or cascaded allpass filter

    Note:   MATLAB® code with LatticeCoefficients, AllpassCoefficients, and WDFCoefficients properties set to cell arrays will error in a future release. Set these properties to array values instead.

Description

The AllpassFilter object filters each channel of the input using Allpass filter implementations. This System object™ supports code generation. To import this object into Simulink®, use the MATLAB System block.

To filter each channel of the input:

  1. Define and set up your Allpass filter. See Construction.

  2. Call step to filter each channel of the input according to the properties of dsp.AllpassFilter. The behavior of step is specific to each object in the toolbox.

Construction

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.

Allpass = dsp.AllpassFilter('PropertyName',PropertyValue, ...) returns an Allpass filter System object, Allpass, with each property set to the specified value.

Properties

Structure

Internal allpass filter structure

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

AllpassCoefficients

Allpass polynomial coefficients

Specify the real allpass polynomial filter coefficients. This property is applicable only when the Structure property is set to Minimum multiplier. 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 of this property is [-2^(-1/2) 0.5]. The default value defines a stable second-order allpass filter with poles and zeros located at ±π/3 in the Z plane. This property is tunable.

WDFCoefficients

Wave Digital Filter allpass coefficients

Specify the real allpass coefficients in the Wave Digital Filter form. This property is only applicable when the Structure property is set to Wave Digital Filter. 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. The default value for this property is [1/2, -2^(1/2)/3]. 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 'Wave Digital Filter'. This property is tunable.

LatticeCoefficients

Lattice allpass coefficients

Specify the real or complex allpass coefficients as lattice reflection coefficients. This property is applicable only if the Structure property is set to Lattice. Specify this property as either a row vector (single-section configuration) or a column vector. The default is [-2^(1/2)/3, 1/2]. 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'. This property is tunable.

TrailingFirstOrderSection

Indicate if last section is first order

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. The default is false.

Methods

cloneCreate System object with same property values
isLockedLocked status for input attributes and nontunable properties
releaseAllow property value and input characteristics changes
resetReset internal states of a System object
stepProcess inputs using allpass filter

For additional methods, see Analysis Methods for Filter System Objects.

For a complete list of analysis methods supported for the dsp.AllpassFilter object, enter dsp.AllpassFilter.helpFilterAnalysis at the MATLAB command prompt.

Examples

expand all

Lowpass Filtering using Two Allpass Filters

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.*(step(APF1,in) + step(APF2,in));
    A = step(TFE, in, out);
    step(AP,db(A));
end

Algorithms

The transfer function of an allpass filter is defined by:

H(z)=c(n)+c(n1)z1+...+zn1+c(1)z1+...+c(n)zn

given the nontrivial polynomial coefficients in c. The order n of the transfer function is given by the length of the vector c.

dsp.AllpassFilter realizes an allpass filter using three different implementation structures: Minimum multiplier, Wave Digital Filter, and Lattice. These structures differ from generic IIR filters such as df1, df1t, df2, df2t, in that they are computationally more economical and structurally more stable [1]. For all structures, a single instance of dsp.AllpassFilter can handle either a single-section or a multiple-section (cascaded) allpass 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 coefficients used by the multipliers are the same as AllpassCoefficients, which are equal to the polynomial vector c in the allpass transfer function. The following code shows an example of a second-order section as a Simulink diagram using basic building blocks. You need a Simulink license to generate the actual diagram using realizemdl.

hap = dsp.AllpassFilter('AllpassCoefficients', [0.1, -0.7]);
realizemdl(hap)

Wave Digital Filter

This structure uses n multipliers, but only n delay units at the expense of requiring 3n adders. To use this structure, you must specify the coefficients as WDFCoefficients in Wave Digital Filter (WDF) form. Obtain the WDF equivalent of the conventional allpass coefficients such as those in vector c in the preceding equation, by using the static method dsp.AllpassFilter.poly2wdf. You can also use a similar method, dsp.AllpassFilter.wdf2poly to convert given WDF-form coefficients into their equivalent allpass polynomial form. The following code shows an example of a second-order section as a Simulink diagram using basic operation blocks. You need a Simulink license to generate the actual diagram using realizemdl. Use these coefficients for a functionally equivalent filter to the previous Minimum multiplier example.

c = [0.1, -0.7];
w = dsp.AllpassFilter.poly2wdf(c);
hap = dsp.AllpassFilter('Structure', 'Wave Digital Filter', 'WDFCoefficients', w);
realizemdl(hap)

The multipliers used in the filter implementation are a transformation of the WDF coefficients previously provided. The implementation structure around each multiplier depends on the actual value of the multiplier and can vary for different filtering stages among five different options. For example notice how in the preceding diagram, the first and the second stages are realized with two different inner structures. For more details refer to [2].

Lattice

This lattice structure uses 2n multipliers, n delay units, and 2n adders. To use this structure, you must specify the coefficients as LatticeCoefficients in Lattice form. Obtain these from the conventional polynomial form of the allpass coefficients by using an appropriate conversion function, such as tf2latc. The following code shows an example of a second-order section as a Simulink diagram using basic operation blocks. You need a Simulink license to generate the actual diagram using realizemdl. Use these coefficients for a functionally equivalent filter to the Minimum multiplier structure.

c = [0.1 -0.7];
k = tf2latc([1 c]);
hap = dsp.AllpassFilter('Structure', 'Lattice', 'LatticeCoefficients', k);
realizemdl(hap)

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. Prentice Hall, 2001

Introduced in R2013a

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