filt2block

Generate Simulink filter block

Syntax

filt2block(b,a)

filt2block(B,A,"ctf")

filt2block({B,A,g})

filt2block(d)

filt2block(sos)

filt2block(___,"subsystem")

filt2block(___,Name=Value)

Description

filt2block(b,a) generates a Discrete Filter (Simulink) block with numerator coefficients, b, and denominator coefficients, a.

• If a is a scalar or unspecified, then filt2block generates a Discrete FIR Filter (Simulink) block.

• If b has up to three elements and a has two or three elements, then the function generates a Second-Order Section Filter (DSP System Toolbox) block. You must have DSP System Toolbox™ installed to create a Second-Order Section Filter block. Otherwise, specify the "subsystem" argument to generate a subsystem block that implements the filter using basic blocks.

filt2block(B,A,"ctf") generates a Simulink^® block from a digital filter represented as Cascaded Transfer Functions (CTF) with numerator coefficients B and denominator coefficients A. (since R2026a)

Note

Specify the "ctf" option to disambiguate CTF numerator matrices B with six columns from second-order section matrix inputs, sos, when you specify A as a scalar or vector.

filt2block({B,A,g}) also specifies the scale values, g, across the CTF sections of the digital filter. (since R2026a)

filt2block(d) generates a Simulink block from a digitalFilter object, d.

The function generates a Discrete FIR Filter (Simulink) block if d is an FIR filter, a Discrete Filter (Simulink) block if d is an IIR filter without any second-order sections, a Second-Order Section Filter (DSP System Toolbox) block if d is an IIR filter with second-order sections, or a Subsystem (Simulink) block if d is a digital filter cascade or has coefficients in the CTF format.

filt2block(sos) generates a Second-Order Section Filter (DSP System Toolbox) block from an L-by-6 second-order sections matrix, sos. L is the number of sections and must be greater than or equal to 2.

filt2block(___,"subsystem") generates a Simulink subsystem block that implements the filter specified by any of the previous syntaxes using basic blocks, including Sum (Simulink), Gain (Simulink), and Delay (Simulink).

filt2block(___,Name=Value) uses additional options specified by one or more name-value arguments.

Examples

Generate Block from FIR Filter

Design a 30th-order FIR filter using the window method. Specify a cutoff frequency of π/4 rad/sample. Create a Simulink® block.

b = fir1(30,0.25);
filt2block(b)

Generate Block from IIR Filter

Design a third-order IIR Butterworth filter. Specify a cutoff frequency of π/4 rad/sample. Create a Simulink® block.

[b,a] = butter(3,0.25);
filt2block(b,a)

Generate FIR Filter with Direct Form I Transposed Structure

Design a 30th-order FIR filter using the window method. Specify a cutoff frequency of π/4 rad/sample. Create a Simulink® block with a direct form I transposed structure.

b = fir1(30,0.25);
filt2block(b,FilterStructure="directFormTransposed")

Generate IIR Filter with Direct Form I Structure

Design a 30th-order IIR Butterworth filter. Specify a cutoff frequency of π/4 rad/sample. Create a Simulink® block with a direct form I structure.

[B,A] = butter(30,0.25,"ctf");
filt2block(B,A,"ctf",FilterStructure="directForm1")

Generate Subsystem Block from Second-Order Section Matrix

Design a 15th-order Butterworth filter with a cutoff frequency of π/5 rad/sample. Obtain the filter in biquad form and generate a Simulink® subsystem block from the second order sections.

[z,p,k] = butter(15,0.2);
sos = zp2sos(z,p,k);
filt2block(sos,"subsystem")

Lowpass FIR Filter Block with Sample-Based Processing

Generate a Simulink® subsystem block that implements an FIR lowpass filter using sum, gain, and delay blocks. Specify the input processing to be elements as channels by specifying FrameBasedProcessing as false.

b = fir1(8,0.5);
filt2block(b,"subsystem",BlockName="Lowpass FIR", ...
              FrameBasedProcessing=false)

New Model with Highpass Elliptic Filter Block

Design a highpass elliptic filter with normalized stopband frequency 0.45 and normalized passband frequency 0.55. Specify a stopband attenuation of 40 dB and a passband ripple of 0.5 dB. Implement the filter as a Direct Form II structure, call it "HP", and place it in a new Simulink® model.

d = designfilt("highpassiir",DesignMethod="ellip", ...
               StopbandFrequency=0.45,PassbandFrequency=0.55, ...
               StopbandAttenuation=40,PassbandRipple=0.5);

filt2block(d,"subsystem",FilterStructure="directForm2", ...
             Destination="new",BlockName="HP")

Generate Subsystem Block from Digital Filter Cascade

Since R2026a

Design two digital filters with these specifications:

• A lowpass FIR filter with normalized passband and stopband frequencies of 0.65 and 0.80, respectively. The passband ripple is 1 dB and the stopband attenuation is 50 dB.

• A bandstop FIR filter with passband ripple of 1 dB and stopband attenuation of 50 dB. The normalized passband frequencies are 0.25 and 0.34. The normalized stopband frequencies are 0.36 and 0.45.

d1 = designfilt("lowpassfir", ...
    PassbandFrequency=0.65,StopbandFrequency=0.80, ...
    PassbandRipple=1,StopbandAttenuation=50);
d2 = designfilt("bandstopfir", ...
    PassbandFrequency1=0.25,StopbandFrequency1=0.34, ...
    StopbandFrequency2=0.36,PassbandFrequency2=0.45, ...
    PassbandRipple1=1,StopbandAttenuation=50, ...
    PassbandRipple2=1);

Cascade the lowpass FIR and bandstop FIR filters to form a digital filter cascade. Set the sample rate to 20 Hz.

d = cascade(d1,d2,SampleRate=20);

Implement the filter in a new Simulink® model.

filt2block(d)

Input Arguments

b, a — Transfer function coefficients

vectors

Transfer function coefficients, specified as vectors. b and a represent the numerator and denominator coefficients, respectively.

The filter coefficients are ordered in descending powers of z^–1 with the first element corresponding to the coefficient for z⁰.

Note

If a(1) is not equal to 1, then filt2block normalizes the filter coefficients by a(1). In this case, a(1) must be nonzero.

Example: b = fir1(30,0.25);

Example: [b,a] = butter(3,0.25,"high");

Data Types: single | double
Complex Number Support: Yes

sos — Second-order section matrix

K-by-6 matrix

Second order section matrix, specified as a K-by-6 matrix. Each row of the matrix contains the coefficients for a biquadratic rational function in z^–1. The Z-transform of the kth rational biquadratic system impulse response is

$$H_k(z)=\frac{B_k(1)+B_k(2)z^{-1}+B_k(3)z^{-2}}{A_k(1)+A_k(2)z^{-1}+A_k(3)z^{-2}}$$.

The coefficients in the kth row of the matrix, sos, are in this order:

$$\left[\begin{array}{cccccc}{B}_k(1)& B_k(2)& B_k(3)& A_k(1)& A_k(2)& A_k(3)\end{array}\right]$$.

The frequency response of the filter is its transfer function evaluated on the unit circle with z = e^j2πf.

Note

If any element of sos(:,4) is not equal to 1, then filt2block normalizes the filter coefficients by sos(:,4). In this case, sos(:,4) must be nonzero.

Example: s = [2 4 2 6 0 2;3 3 0 6 0 0] specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Data Types: single | double
Complex Number Support: Yes

d — Digital filter

digitalFilter object

Digital filter, specified as a digitalFilter object. Use designfilt to generate a digital filter based on frequency-response specifications.

Example: d = designfilt("lowpassiir",FilterOrder=3,HalfPowerFrequency=0.5) specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

B,A — Cascaded transfer function (CTF) coefficients

scalars | vectors | matrices

Cascaded transfer function (CTF) coefficients, specified as scalars, vectors, or matrices. B and A list the numerator and denominator coefficients of the cascaded transfer function, respectively.

B must be of size L-by-(m + 1) and A must be of size L-by-(n + 1), where:

• L represents the number of filter sections.

• m represents the order of the filter numerators.

• n represents the order of the filter denominators.

For more information about the cascaded transfer function format and coefficient matrices, see Specify Digital Filters in CTF Format.

Note

If any element of A(:,1) is not equal to 1, then filt2block normalizes the filter coefficients by A(:,1). In this case, A(:,1) must be nonzero.

Example: B = [2 4 2;3 3 0] and A = [6 0 2;6 0 0] specify a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Data Types: double | single
Complex Number Support: Yes

g — Scale values

scalar | vector

Scale values, specified as a real-valued scalar or as a real-valued vector with L + 1 elements, where L is the number of CTF sections. The scale values represent the distribution of the filter gain across sections of the cascaded filter representation.

The filt2block function applies a gain to the filter sections using the scaleFilterSections function depending on how you specify g:

• Scalar — The function distributes the gain uniformly across all filter sections.

• Vector — The function applies the first L gain values to the corresponding filter sections and distributes the last gain value uniformly across all filter sections.

Data Types: double | single

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Example: filt2block(d,"subsystem",BlockName="Lowpass FIR",FrameBasedProcessing=true) generates a Simulink block that implements a digital filter, d, where the block name is "Lowpass FIR" and the input processing is framed-based.

FilterStructure — Filter structure

character vector | string scalar

Filter structure, specified as a character vector or string scalar. Valid options for this argument depend on the filter type. The following table lists the valid filter structures for each filter type.

Filter Type	Filter Structures
FIR	"directForm" (default), "directFormTransposed", "directFormSymmetric", "directFormAntiSymmetric", "overlapAdd". Note The "overlapAdd" structure is available only when you omit "subsystem" and requires a DSP System Toolbox software license. For digital filter cascades or multisection CTF filters, filt2block does not support the "overlapAdd" filter structure.
IIR	"directForm2" (default), "directForm1", "directForm1Transposed", "directForm2Transposed" If the filter has second-order sections, then the function uses the "directForm2Transposed" filter structure by default.

Destination — Destination for Simulink filter block

"current" (default) | "new" | character vector | string scalar

Destination for the Simulink filter block, specified as a character vector or string scalar. You can add the filter block to your current model with "current", add the filter block to a new model with "new", or specify the name of an existing model.

Example: filt2block([1 2 1],Destination="MyModel",BlockName="New block")

Data Types: char | string

BlockName — Block name

character vector | string scalar

Block name, specified as a character vector or string scalar.

Data Types: char | string

OverwriteBlock — Overwrite block

false (default) | true

Overwrite block, specified as a logical false or true. If you use a value for BlockName that is the same as an existing block, the value of OverwriteBlock determines whether the block is overwritten.

Data Types: logical

MapCoefficientsToPorts — Map coefficients to ports

false (default) | true

Map coefficients to ports, specified as a logical false or true.

Data Types: logical

CoefficientNames — Coefficient variable names

cell array of character vectors | string array

Coefficient variable names, specified as a cell array of character vectors or a string array. This argument is applicable only when MapCoefficientsToPorts is true.

Valid options for this argument depend on the filter specifications. The following table lists the valid coefficient name for each filter specification.

Filter Specification	Coefficient Names
b	One-element array, consisting of the name for the numerator coefficients. Default: "Num"
b,a	Two-element array, consisting of the name for the numerator and denominator coefficients. Default: ["Num" "Den"]
sos	Two- or three-element array, consisting of one of these: Name for the numerator and denominator coefficients, if you specify a two-element array. To name the array of scale values, the function appends _g to the name specified for the numerator coefficients. Name for the numerator coefficients, denominator coefficients, and scale values, if you specify a three-element array. Default: ["Num" "Den" "g"]
d	For an FIR filter, see the b filter specification. For an IIR filter with at least one section that is not second-order, see the b,a filter specification. For an IIR filter using second-order sections, see the sos filter specification. For a digital filter cascade, the format for the coefficient names depends on the type of filter implementation along the stages: If d contains at least one stage that represents an IIR filter using second-order sections, see the sos filter specification. If d contains at least one stage that represents an IIR filter with at least one section that is not second-order, see the b,a filter specification. If all the stages in d are FIR filters, see the b filter specification.
B,A,"ctf"	Two-element array, consisting of the name for the numerator and denominator coefficients. If B and A represent an FIR filter, the function uses only the specified name for the numerator coefficients. If the filter has multiple CTF sections, the function appends _X where X is the CTF section number. If B and A represent an IIR filter with at least one section that is not second-order, the function uses the specified name for the numerator and denominator coefficients. If the filter has multiple CTF sections, the function appends _X where X is the CTF section number. If B and A represent an IIR filter using second-order sections, the function uses the specified name for the numerator and denominator coefficients. To name the array of scale values, the function appends _g to the name specified for the numerator coefficients. Default: ["Num" "Den"]
{B,A,g}	Three-element array, consisting of the name for the numerator coefficients, denominator coefficients, and scale values. If B and A represent an FIR filter, the function uses only the specified name for the numerator coefficients. If the filter has multiple CTF sections, the function appends _X where X is the CTF section number. If B and A represent an IIR filter with at least one section that is not second-order, the function uses only the specified name for the numerator and denominator coefficients. If the filter has multiple CTF sections, the function appends _X where X is the CTF section number. If B and A represent an IIR filter using second-order sections, the function uses the specified name for the numerator coefficients, denominator coefficients, and scale values. Default: ["Num" "Den" "g"]

Data Types: cell | string

FrameBasedProcessing — Option to choose between frame-based and sample-based processing

true (default) | false

Option to choose between frame-based and sample-based processing, specified as one of these:

• true — filt2block creates a block that performs frame-based processing.

• false — filt2block creates a block that performs sample-based processing.

To perform frame-based processing, you must have a DSP System Toolbox license. For more information, see Sample- and Frame-Based Concepts (DSP System Toolbox).

Data Types: logical

OptimizeZeros — Remove zero-gain blocks

true (default) | false

Remove zero-gain blocks, specified as a logical true or false.

To specify this argument, you must also specify the "subsystem" argument in the filt2block function call.

Data Types: logical

OptimizeOnes — Replace unity-gain blocks with direct connection

true (default) | false

Replace unity-gain blocks with direct connection, specified as a logical true or false.

To specify this argument, you must also specify the "subsystem" argument in the filt2block function call.

Data Types: logical

OptimizeNegativeOnes — Replace negative unity-gain blocks with sign change

true (default) | false

Replace negative unity-gain blocks with a sign change at the nearest block, specified as a logical true or false.

To specify this argument, you must also specify the "subsystem" argument in the filt2block function call.

Data Types: logical

OptimizeDelayChains — Replace cascaded delays with a single delay

true (default) | false

Replace cascaded delays with a single delay, specified as a logical true or false.

To specify this argument, you must also specify the "subsystem" argument in the filt2block function call.

Data Types: logical

More About

Cascaded Transfer Functions

Partitioning an IIR digital filter into cascaded sections improves its numerical stability and reduces its susceptibility to coefficient quantization errors. The cascaded form of a transfer function H(z) in terms of the L transfer functions H₁(z), H₂(z), …, H_L(z) is

$$H(z)={\displaystyle \prod _{l=1}^L{H}_l(z)}=H_1(z)\times H_2(z)\times \cdots \times H_L(z).$$

Specify Digital Filters in CTF Format

You can specify digital filters in the CTF format for analysis, visualization, and signal filtering. Specify a filter by listing its coefficients B and A. You can also include the filter scaling gain across sections by specifying a scalar or vector g.

Filter Coefficients

When you specify the coefficients as L-row matrices,

$$B=\left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1,m+1}\\ b_{21}& b_{22}& \cdots & b_{2,m+1}\\ ⋮& ⋮& \ddots & ⋮\\ b_{L1}& b_{L2}& \cdots & b_{L,m+1}\end{array}\right],A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1,n+1}\\ a_{21}& a_{22}& \cdots & a_{2,n+1}\\ ⋮& ⋮& \ddots & ⋮\\ a_{L1}& a_{L2}& \cdots & a_{L,n+1}\end{array}\right],$$

it is assumed that you have specified the filter as a sequence of L cascaded transfer functions, such that the full transfer function of the filter is

$$H\left(z\right)=\frac{b_{11}+b_{12}{z}^{-1}+\cdots +b_{1,m+1}{z}^{-m}}{a_{11}+a_{12}{z}^{-1}+\cdots +a_{1,n+1}{z}^{-n}}\times \frac{b_{21}+b_{22}{z}^{-1}+\cdots +b_{2,m+1}{z}^{-m}}{a_{21}+a_{22}{z}^{-1}+\cdots +a_{2,n+1}{z}^{-n}}\times \cdots \times \frac{b_{L1}+b_{L2}{z}^{-1}+\cdots +b_{L,m+1}{z}^{-m}}{a_{L1}+a_{L2}{z}^{-1}+\cdots +a_{L,n+1}{z}^{-n}},$$

where m ≥ 0 is the numerator order of the filter and n ≥ 0 is the denominator order.

• If you specify both B and A as vectors, it is assumed that the underlying system is a one-section IIR filter (L = 1), with B representing the numerator of the transfer function and A representing its denominator.

• If B is scalar, it is assumed that the filter is a cascade of all-pole IIR filters with each section having an overall system gain equal to B.

• If A is scalar, it is assumed that the filter is a cascade of FIR filters with each section having an overall system gain equal to 1/A.

Note

• To convert second-order section matrices to cascaded transfer functions, use the sos2ctf function.

• To convert a zero-pole-gain filter representation to cascaded transfer functions, use the zp2ctf function.

Coefficients and Gain

If you have an overall scaling gain or multiple scaling gains factored out from the coefficient values, you can specify the coefficients and gain as a cell array of the form {B,A,g}. Scaling filter sections is especially important when you work with fixed-point arithmetic to ensure that the output of each filter section has similar amplitude levels, which helps avoid inaccuracies in the filter response due to limited numeric precision.

The gain can be a scalar overall gain or a vector of section gains.

• If the gain is scalar, the value applies uniformly to all the cascade filter sections.

• If the gain is a vector, it must have one more element than the number of filter sections L in the cascade. Each of the first L scale values applies to the corresponding filter section, and the last value applies uniformly to all the cascade filter sections.

If you specify the coefficient matrices and gain vector as

$$B=\left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1,m+1}\\ b_{21}& b_{22}& \cdots & b_{2,m+1}\\ ⋮& ⋮& \ddots & ⋮\\ b_{L1}& b_{L2}& \cdots & b_{L,m+1}\end{array}\right],A=\left[\begin{array}{cccc}{a}_{11}& a_{12}& \cdots & a_{1,n+1}\\ a_{21}& a_{22}& \cdots & a_{2,n+1}\\ ⋮& ⋮& \ddots & ⋮\\ a_{L1}& a_{L2}& \cdots & a_{L,n+1}\end{array}\right],g=\left[\begin{array}{ccccc}{g}_1& g_2& \cdots & g_L& g_{\text{S}}\end{array}\right],$$

it is assumed that the transfer function of the filter system is

$$H\left(z\right)=g_{\text{S}}\left(g_1\frac{b_{11}+b_{12}{z}^{-1}+\cdots +b_{1,m+1}{z}^{-m}}{a_{11}+a_{12}{z}^{-1}+\cdots +a_{1,n+1}{z}^{-n}}\times g_2\frac{b_{21}+b_{22}{z}^{-1}+\cdots +b_{2,m+1}{z}^{-m}}{a_{21}+a_{22}{z}^{-1}+\cdots +a_{2,n+1}{z}^{-n}}\times \cdots \times g_L\frac{b_{L1}+b_{L2}{z}^{-1}+\cdots +b_{L,m+1}{z}^{-m}}{a_{L1}+a_{L2}{z}^{-1}+\cdots +a_{L,n+1}{z}^{-n}}\right).$$

References

[1] Lyons, Richard G. Understanding Digital Signal Processing. Upper Saddle River, NJ: Prentice Hall, 2004.

Version History

Introduced in R2013a

R2026a: Generate Simulink filter blocks using cascaded transfer functions

The filt2block function supports inputs in the cascaded transfer function (CTF) format.