Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

allpass2wdf

Allpass to Wave Digital Filter coefficient transformation

Syntax

w = allpass2wdf(a)
W = allpass2wdf(A)

Description

w = allpass2wdf(a) accepts a vector of real allpass polynomial filter coefficients a, and returns the transformed coefficient w. w can be used with allpass filter objects such as dsp.AllpassFilter, and dsp.CoupledAllpassFilter, with Structure set to 'Wave Digital Filter'.

W = allpass2wdf(A) accepts the cell array of allpass polynomial coefficient vectors A. Each cell of A holds the coefficients of a section of a cascade allpass filter. W is also a cell array, and each cell of W contains the transformed version of the coefficients in the corresponding cell of A. W can be used with allpass filter objects such as dsp.AllpassFilter and dsp.CoupledAllpassFilter, with structure set to 'Wave Digital Filter'.

Examples

collapse 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).

Create a second order allpass filter with coefficients a = [0 0.5]. Convert these coefficients into wave digital filter form using allpass2wdf. Assign the transformed coefficients to an allpass filter using the wave digital filter structure. Pass a random input to both these filters and compare the outputs.

a = [0 0.5]; 
allpass = dsp.AllpassFilter('AllpassCoefficients', a);
w = allpass2wdf(a);
allpasswdf = dsp.AllpassFilter('Structure', 'Wave Digital Filter',...
    'WDFCoefficients', w);
in = randn(512, 1);
outputAllpass = allpass(in);
outputAllpasswdf = allpasswdf(in);
plot(outputAllpass-outputAllpasswdf)

The difference between the two outputs is very small.

Input Arguments

collapse all

Numeric vector of allpass filter coefficients, specified as real numbers. a can have length only equal to 1,2, and 4. When the length is 4, the first and third components must both be zero. a can be a row or a column vector.

Example: 0.7

Data Types: double | single

Cascade of allpass filter coefficients, specified as a cell vector. Every cell of A must contain a real vector of length 1,2, or 4. When the length is 4, the first and third components must both be zero. A can be a row or column vector of cells.

Example: {0.7, [0.1, 0.2]}

Data Types: double | single

Output Arguments

collapse all

Numeric vector of transformed coefficients, determined as a real number, to use with single-section allpass filter objects having Structure set to 'Wave Digital Filter'. w is always returned as a numeric row vector.

Example: 0.7

Data Types: double | single

Cascade of transformed allpass filter coefficients, determined as a cell array, to use with multi-section allpass filter objects having Structure set to 'Wave Digital Filter'. W is always returned as a column of cells.

Example: {0.7;[0.2,-0.0833]}

Data Types: double | single

Algorithms

In the more general case, the input coefficients A define a cascade or multisection allpass filter. allpass2wdf applies separately to each section of the same transformation used in the single-section case. In the single-section case, the numeric coefficients vector a contains a standard polynomial representation of an allpass filter of order 1, 2, or 4. For example, in the first order case,

a=[a1]

represents the first order transfer function:

H1(z)=z1+a11+a1z1

and in the second order case,

a=[a1,a2]

represents the second order transfer function:

H2(z)=z2+a1z1+a21+a1z1+a2z2

.

The allpass transfer functions H1 and H2 can also have the following alternative representations, using decoupled coefficients in vector w1 or w2 respectively.

H~1(z)=z1+w11+w1z1

H~2(z)=z2+w2(1+w1)z1+w11+w2(1+w1)z1+w1z2

For allpass coefficients, w is often used to derive adaptor multipliers for Wave Digital Filter structures, and it is required by a number of allpass based filters in DSP System Toolbox™ when Structure is set to 'Wave Digital Filter' (e.g. dsp.AllpassFilter, and dsp.CoupledAllpassFilter).

For a given vector of section coefficients a, allpass2wdf computes the corresponding vector w such that

when i = 1, 2 or 4H~i(z)=Hi(z)

This results in using the following formulas:

for order 1:w1=a1for order 2:w1=a2w2=a11+a2for order 4:w1=a4w3=a21+a4w2=w4=0

References

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

Introduced in R2014a

Was this topic helpful?