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wdf2allpass

Wave Digital Filter to allpass coefficient transformation

Syntax

a = wdf2allpass(w)
A = wdf2allpass(W)

Description

a = wdf2allpass(w) accepts a vector of transformed real allpass coefficients, w, and returns the conventional allpass polynomial version a. w is used by allpass filter objects such as dsp.AllpassFilter, and dsp.CoupledAllpassFilter, with Structure set to 'Wave Digital Filter'.

A = wdf2allpass(W) accepts the cell array of transformed allpass coefficient vectors W. Each cell of W contains the transformed real coefficients of a section of a cascade allpass filter. The output A is also a cell array, and each cell of A contains the conventional polynomial version of the corresponding cell of W. W is used by allpass filter objects such as dsp.AllpassFilter and dsp.CoupledAllpassFilter, with Structure set to 'Wave Digital Filter'. Every cell of W must contain a real vector of length 1,2, or 4. When the length is 4, the second and fourth components must both be zero. W can be a row or column vector of cells while A is always returned as column.

Examples

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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).

Create a second order allpass filter with wave digital filter coefficients w = [0.5 0]. Convert these coefficients into polynomial form using wdf2allpass. Assign the polynomial coefficients to an allpass filter using the 'Minimum multiplier' structure. Pass a random input to both these filters and compare the outputs.

w = [0.5 0];
allpasswdf = dsp.AllpassFilter('Structure', 'Wave Digital Filter',...
    'WDFCoefficients', w);
a = wdf2allpass(w);
allpass = dsp.AllpassFilter('AllpassCoefficients', a);
in = randn(512, 1);
outputallpasswdf = allpasswdf(in);
outputallpass = allpass(in);
plot(outputallpasswdf-outputallpass);

The difference between the two outputs is very small.

Input Arguments

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Numeric vector of transformed Wave Digital Filter allpass coefficients, specified as a real number. w can have only length equal to 1,2, and 4. When the length is 4, the second and fourth components must both be zero. w can be a row or a column vector.

Example: [0.3,-0.2]

Data Types: double | single

Cascade of allpass filter coefficients in transformed Wave Digital Filter form, specified as a cell vector. Every cell of W must contain a real vector of length 1, 2, or 4. When the length is 4, the second and fourth components must both be zero. W can be a row or a column vector of cells.

Example: {[0.3,-0.2];0.5}

Output Arguments

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Numeric vector of polynomial allpass coefficients, determined as a numeric row vector.

Data Types: double | single

Cascade of allpass filter coefficient, determined as a column of cells, each containing a vector of length 1, 2, or 4.

Example: {0.3 5.0 0.2}

Data Types: double | single

Algorithms

wdf2allpass provides the inverse operation of allpass2wdf, by transforming the transformed cascade of allpass coefficients W into their conventional polynomial representation A. Please refer to the reference page for allpass2wdf for more details about the two representations.

W defines a multisection allpass filter, and wdf2allpass applies separately to each section, with the same transformation used in the single-section case. In this case, the numeric coefficients vector w can have order 1, 2, or 4.

The relations between the vector of section coefficients a and w respectively depend on the order, as follows:

for order 1:a1=w1for order 2:a1=w2(1+w1)a2=w1for order 4:a2=w3(1+w1)a4=w1a1=a3=0

References

[1] M. Lutovac, D. Tosic, B. Evans, Filter Design for Signal Processing using MATLAB and Mathematica. Prentice Hall, 2001.

Introduced in R2014a

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