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

Convert Wave Digital Filter Coefficients to Allpass Polynomial Coefficients

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

w — Transformed Wave Digital Filter allpass coefficients

scalar | vector of real numbers

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

W — Transformed Wave Digital Filter allpass coefficients

scalar cell | vector of cells

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

a — allpass filter coefficients

vector of real numbers

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

Data Types: double | single

A — allpass filter coefficients

vector cell array

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:

$$\begin{array}{l}fororder1\text{:}\\ a_1=w_1\\ fororder2:\\ a_1=w_2(1+w_1)\\ a_2=w_1\\ fororder4:\\ a_2=w_3(1+w_1)\\ a_4=w_1\\ a_1=a_3=0\end{array}$$

References

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

Version History

Introduced in R2014a