Property Reference (Filter Design Toolbox)

Filter Design Toolbox

FilterStructure

The FilterStructure property values are specified as one of the following strings indicating the quantized filter architecture:

'

FilterStructure Property Name
Filter Description

'antisymmetricfir'
Antisymmetric finite impulse response (FIR). Even and odd forms.

'df1'
Direct form I.

'df1t'
Direct form I transposed.

'df2'
Direct form II.

'df2t'
Direct form II transposed. Default filter structure.

'fir'
Direct form FIR .

'firt'
Direct form FIR transposed.

'latcallpass'
Lattice allpass.

'latticeca'
Lattice coupled-allpass.

'latticecapc'
Lattice coupled-allpass power-complementary.

'latticear'
Lattice autoregressive (AR).

'latticema'
Lattice moving average (MA) minimum phase.

'latcmax'
Lattice moving average (MA) maximum phase.

'latticearma'
Lattice ARMA.

'statespace'
Single-input/single-output state-space.

'symmetricfir'
Symmetric FIR. Even and odd forms.

Default value: 'df2t'

FilterStructure Property Name	Filter Description
`'antisymmetricfir'`	Antisymmetric finite impulse response (FIR). Even and odd forms.
`'df1'`	Direct form I.
`'df1t'`	Direct form I transposed.
`'df2'`	Direct form II.
`'df2t'`	Direct form II transposed. Default filter structure.
`'fir'`	Direct form FIR .
`'firt'`	Direct form FIR transposed.
'`latcallpass`'	Lattice allpass.
`'latticeca'`	Lattice coupled-allpass.
`'latticecapc'`	Lattice coupled-allpass power-complementary.
`'latticear'`	Lattice autoregressive (AR).
`'latticema'`	Lattice moving average (MA) minimum phase.
`'latcmax'`	Lattice moving average (MA) maximum phase.
`'latticearma'`	Lattice ARMA.
`'statespace'`	Single-input/single-output state-space.
`'symmetricfir'`	Symmetric FIR. Even and odd forms.

Remarks: The syntax for entering values for the ReferenceCoefficients property is constrained by the FilterStructure property value. See Table 11-4: Syntax for Assigning Reference Filter Coefficients (Single Section), for information on how to enter these coefficients for each filter architecture.

Quantized Filter Structures

You can choose among several different filter structures when you create a quantized filter. You can also specify filters with single or multiple cascaded sections of the same type. Because quantization is a nonlinear process, different filter structures produce different results.

You specify the filter structure by assigning a value to the FilterStructure property. See the function reference listings for qfilt and set for information on setting property values.

The FilterStructure property value constrains the syntax you can use for specifying the filter reference coefficients. For details on the syntax to use for specifying a filter with either a single section, or multiple (L) cascaded sections, see Table 11-4, Syntax for Assigning Reference Filter Coefficients (Single Section), and Table 11-5, Syntax for Assigning Reference Filter Coefficients (L Sections).

The figures in the following subsections of this chapter serve as a visual aid to help you determine how to enter the reference filter coefficients for each filter structure. Each subsection contains a simple example for constructing a filter of a given structure.

For clarity, the scale factors appear outside the filter structure, labeled s(1) and s(2) for the input and output factors.

Direct Form Antisymmetric FIR Filter Structure (Odd Order)

The following figure depicts a direct form antisymmetric FIR filter structure that directly realizes a fifth-order antisymmetric FIR filter. The filter coefficients are labeled b(i), i = 1, ..., 6, and the initial and final state values in filtering are labeled z(i).

Use the string 'antisymmetricfir' for the value of the FilterStructure property to design a quantized filter with this structure.

Example -- Specifying an Odd-Order Direct Form Antisymmetric FIR Filter Structure. Specify a fifth-order direct form antisymmetric FIR filter structure for a quantized filter Hq with the following code.

b = [-0.008 0.06 -0.44 0.44 -0.06 0.008];
Hq = qfilt('antisymmetricfir',{b});

Antisymmetric FIR Filter Structure (Even Order)

The following figure depicts a direct form antisymmetric FIR filter structure that directly realizes a fourth-order antisymmetric FIR filter. The filter coefficients are labeled b(i), i = 1, ..., 5, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'antisymmetricfir' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying an Even-Order Direct Form Antisymmetric FIR Filter Structure. You can specify a fourth-order direct form antisymmetric FIR filter structure for a quantized filter Hq with the following code.

b = [-0.01 0.1 0.0 -0.1 0.01];
Hq = qfilt('antisymmetricfir',{b});

Direct Form I Filter Structure

The following figure depicts a direct form I filter structure that directly realizes a transfer function with a second-order numerator and denominator. The numerator coefficients are labeled b(i), the denominator coefficients are labeled a(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'df1' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Direct Form I Filter Structure. You can specify a second-order direct form I structure for a quantized filter Hq with the following code.

b = [0.3 0.6 0.3];
a = [1 0 0.2];
Hq = qfilt('df1',{b,a});

Direct Form I Transposed Filter Structure

The following figure depicts a direct form I transposed filter structure that directly realizes a transfer function with a second-order numerator and denominator. The numerator coefficients are labeled b(i), the denominator coefficients are labeled a(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'df1t' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Direct Form I Transposed Filter Structure. You can specify a second-order direct form I transposed filter structure for a quantized filter Hq with the following code.

b = [0.3 0.6 0.3];
a = [1 0 0.2];
Hq = qfilt('df1t',{b,a});

Direct Form II Filter Structure

The following figure depicts a direct form II filter structure that directly realizes a transfer function with a second-order numerator and denominator. The numerator coefficients are labeled b(i), the denominator coefficients are labeled a(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'df2' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Direct Form II Filter Structure. You can specify a second-order direct form II filter structure for a quantized filter Hq with the following code.

b = [0.3 0.6 0.3];
a = [1 0 0.2];
Hq = qfilt('df2',{b,a});

Direct Form II Transposed Filter Structure

The following figure depicts a direct form II transposed filter structure that directly realizes a transfer function with a second-order numerator and denominator. The numerator coefficients are labeled b(i), the denominator coefficients are labeled a(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'df2t' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Direct Form II Transposed Filter Structure. You can specify a second-order direct form II transposed filter structure for a quantized filter Hq with the following code.

b = [0.3 0.6 0.3];
a = [1 0 0.2];
Hq = qfilt('df2t',{b,a});

Direct Form Finite Impulse Response (FIR) Filter Structure

The following figure depicts a direct form finite impulse response (FIR) filter structure that directly realizes a second-order FIR filter. The filter coefficients are labeled b(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'fir' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Direct Form FIR Filter Structure. You can specify a second-order direct form FIR filter structure for a quantized filter Hq with the following code.

b = [0.05 0.9 0.05];
Hq = qfilt('fir',{b});

Direct Form FIR Transposed Filter Structure

The following figure depicts a direct form finite impulse response (FIR) transposed filter structure that directly realizes a second-order FIR filter. The filter coefficients are labeled b(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'firt' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Direct Forn FIR Transposed Filter Structure. You can specify a second-order direct form FIR transposed filter structure for a quantized filter Hq with the following code.

b = [0.05 0.9 0.05];
Hq = qfilt('firt',{b});

Lattice Allpass Filter Structure

The following figure depicts a lattice allpass filter structure. The pictured structure directly realizes third-order lattice allpass filters. The filter reflection coefficients are labeled k1(i), i = 1, 2, 3. The states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'latcallpass' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Lattice Allpass Filter Structure. You can specify a third-order lattice allpass filter structure for a quantized filter Hq with the following code.

k = [.66 .7 .44];
Hq = qfilt('latcallpass',{k});

Lattice Moving Average Maximum Phase Filter Structure

The following figure depicts a lattice moving average maximum phase filter structure that directly realizes a third-order lattice moving average (MA) filter with maximum phase. The filter reflection coefficients are labeled k1(i), i = 1, 2, 3. The states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'latcmax' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Lattice Moving Average Maximum Phase Filter Structure. You can specify a fourth-order lattice MA maximum phase filter structure for a quantized filter Hq with the following code.

k = [.66 .7 .44 .33];
Hq = qfilt('latcmax',{k});

Lattice Coupled-Allpass Filter Structure

The following figure depicts a lattice coupled-allpass filter structure. The filter is composed of two third-order allpass lattice filters. The filter reflection coefficients for the first filter are labeled k1(i), i = 1, 2, 3. The filter reflection coefficients for the second filter are labeled k2(i), i = 1, 2, 3. The unity gain complex coupling coefficient is beta. The states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'latticeca' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Lattice Coupled-Allpass Filter Structure. You can specify a third-order lattice coupled allpass filter structure for a quantized filter Hq with the following code.

k1 = [0.9511 + 0.3088i; 0.7511 + 0.1158i]
k2 = 0.7502 - 0.1218i
beta = 0.1385 + 0.9904i
Hq = qfilt('latticeca',{k1,k2,beta});

Lattice Coupled-Allpass Power Complementary Filter Structure

The following figure depicts a lattice coupled-allpass power complementary filter structure. The filter is composed of two third-order allpass lattice filters. The filter reflection coefficients for the first filter are labeled k1(i), i = 1, 2, 3. The filter reflection coefficients for the second filter are labeled k2(i), i = 1, 2, 3. The unity gain complex coupling coefficient is beta. The states used for initial and final state values in filtering are labeled z(i). The resulting filter transfer function is the power-complementary transfer function of the coupled allpass lattice filter (formed from the same coefficients).

Use the string 'latticecapc' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a Lattice Coupled-Allpass Power Complementary Filter Structure. Specify a third-order lattice coupled-allpass power complementary filter structure for a quantized filter Hq with the following code.

k1 = [0.9511 + 0.3088i; 0.7511 + 0.1158i]
k2 = 0.7502 - 0.1218i
beta = 0.1385 + 0.9904i
Hq = qfilt('latticecapc',{k1,k2,beta});

Lattice Autoregressive (AR) Filter Structure

The following figure depicts a lattice autoregressive (AR) filter structure that directly realizes a third-order lattice AR filter. The filter reflection coefficients are labeled k(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'latticear' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying an Lattice AR Filter Structure. You can specify a third-order lattice AR filter structure for a quantized filter Hq with the following code.

k = [.66 .7 .44];
Hq = qfilt('latticear',{k});

Lattice Moving Average (MA) Filter Structure

The following figure depicts a lattice moving average (MA) filter structure that directly realizes a third-order lattice MA filter. The filter reflection coefficients are labeled k(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'latticema' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying an Lattice MA Filter Structure. You can specify a third-order lattice MA filter structure for a quantized filter Hq with the following code.

k = [.66 .7 .44];
Hq = qfilt('latticema',{k});

Lattice Autoregressive Moving Average (ARMA) Filter Structure

The following figure depicts a lattice autoregressive moving average (ARMA) filter structure that directly realizes a fourth-order lattice ARMA filter. The filter reflection coefficients are labeled k(i), i = 1, ..., 4, the ladder coefficients are labeled v(i), i = 1, 2, 3, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'latticearma' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying an Lattice ARMA Filter Structure. You can specify a fourth-order lattice ARMA filter structure for a quantized filter Hq with the following code.

k = [.66 .7 .44 .66];
v = [1 0 0];
Hq = qfilt('latticearma',{k,v});

State-Space Filter Structure

State-space models with input sequence x_k and output sequence y_k have the following form.

If the states z_k are vectors of length n, then the matrices A, B, C, and D are n-by-n, n-by-1, 1-by-n, and 1-by-1 respectively.

Use the string 'statespace' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying a State-Space Filter Structure. You can specify a second-order state-space filter structure for a quantized filter Hq with the following code.

[A,B,C,D] = butter(2,0.5);
Hq = qfilt('statespace',{A,B,C,D});

Direct Form Symmetric FIR Filter Structure (Odd Order)

The following figure depicts a direct form symmetric FIR filter structure that directly realizes a fifth-order direct form symmetric FIR filter. The filter coefficients are labeled b(i), i = 1, ..., 6, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'symmetricfir' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying an Odd-Order Direct Form Symmetric FIR Filter Structure. You can specify a fifth-order direct form symmetric FIR filter structure for a quantized filter Hq with the following code.

b = [-0.008 0.06 0.44 0.44 0.06 -0.008];
Hq = qfilt('symmetricfir',{b});

Direct Form Symmetric FIR Filter Structure (Even Order)

The following figure depicts a direct form symmetric FIR filter structure that directly realizes a fourth-order direct form symmetric FIR filter. The filter coefficients are labeled b(i), i = 1, ..., 5, and the states (used for initial and final state values in filtering) are labeled z(i).

Use the string 'symmetricfir' to specify the value of the FilterStructure property for a quantized filter with this structure.

Example -- Specifying an Even-Order Direct Form Symmetric FIR Filter Structure. You can specify a fourth-order direct form symmetric FIR filter structure for
a quantized filter Hq with the following code.

b = [-0.01 0.1 0.8 0.1 -0.01];
Hq = qfilt('symmetricfir',{b});

CoefficientFormat InputFormat