allpass2wdf | Engee Documentation

Syntax

Function call

w = allpass2wdf(a) — takes a vector of real coefficients a a universal polynomial filter and returns the converted coefficients w.

W = allpass2wdf(A) — accepts an array of coefficient vector cells A a universal polynomial filter. Each cell A It contains the coefficients of the cascade universal filter section. Argument W it is also an array of cells, and each cell W contains the converted version of the coefficients of the corresponding cell A.

Arguments

Input arguments

# a — coefficients of the universal filter

+ vector of real numbers

Details

Coefficients of the universal filter, specified as a vector of real numbers. Vector a it can have a length equal to only 1, 2 and 4. If the length is 4, then the first and third components must be equal to zero. Vector a it can be a row vector or a column vector.

Data types

Float32, Float64

# A — coefficients of the universal filter

+ vector of cells

Details

A cascade of universal filter coefficients defined as a vector of cells. Each cell A must contain a vector of length 1, 2 and 4. If the length is 4, then the first and third components must be equal to zero. Vector of cells A it can be a row vector or a column vector.

Data types

Float32, Float64

Output arguments

# w — converted coefficients a
vector of real numbers

Details

Converted coefficients for a single-section filter, returned as a vector of real numbers. Argument w it is always returned as a string vector.

Data types

Float32, Float64

# W — converted coefficients A
vector of cells

Details

A cascade of transformed coefficients for a multi-section filter, returned as a vector of cells. Argument W it is always returned as a column vector of cells.

Data types

Float32, Float64

Algorithms

More generally, the input coefficients are A A cascade or multi-section universal filter is defined. Function allpass2wdf applies separately to each section of the same transformation as in the case of a single-section filter. In the case of a single-section filter, the vector of numerical coefficients is a It contains a standard polynomial representation of a universal pass filter of the first, second, or fourth order. For example, in the case of the first order:

defines a first-order transfer function:

and in the case of the first order:

defines a second-order transfer function:

Universal transfer functions and they may also have the following alternative representations using separated coefficients in vectors or accordingly:

For universal coefficients, It is often used to obtain the adapter multipliers for digital wave filter structures, and it is required for a number of universal filters.

For a given vector of section coefficients , function allpass2wdf calculates the corresponding vector so that

where or .

As a result, the following formulas are used:

for the first order:
for the second order:
for the fourth order: