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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.

    Note:   Starting in R2016b, instead of using the step method to perform the operation defined by the System object, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

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 'Minimum multiplier'. 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

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

The transfer function of an allpass filter is given by

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

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].

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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