Discrete Transfer Fcn
Implement discrete transfer function
 Library:
Simulink / Discrete
HDL Coder / Discrete
HDL Coder / HDL Floating Point Operations
Description
The Discrete Transfer Fcn block implements the ztransform transfer function as follows:
$$H(z)=\frac{num(z)}{den(z)}=\frac{nu{m}_{0}{z}^{m}+nu{m}_{1}{z}^{m1}+\mathrm{...}+nu{m}_{m}}{de{n}_{0}{z}^{n}+de{n}_{1}{z}^{n1}+\mathrm{...}+de{n}_{n}}$$
where m+1 and n+1 are the number of numerator and denominator coefficients, respectively. num and den contain the coefficients of the numerator and denominator in descending powers of z. num can be a vector or matrix, while den must be a vector. The order of the denominator must be greater than or equal to the order of the numerator.
Specify the coefficients of the numerator and denominator polynomials in descending powers of z. This block lets you use polynomials in z to represent a discrete system, a method that control engineers typically use. Conversely, the Discrete Filter block lets you use polynomials in z^{1} (the delay operator) to represent a discrete system, a method that signal processing engineers typically use. The two methods are identical when the numerator and denominator polynomials have the same length.
The Discrete Transfer Fcn block applies the ztransform transfer function to each independent channel of the input. The Input processing parameter allows you to specify whether the block treats each column of the input as an individual channel (framebased processing) or each element of the input as an individual channel (samplebased processing). To perform framebased processing, you must have a DSP System Toolbox™ license.
Specifying Initial States
Use the Initial states parameter to specify initial filter states. To determine the number of initial states you must specify and how to specify them, use the following tables.
FrameBased Processing
Input  Number of Channels  Valid Initial States (Dialog Box)  Valid Initial States (Input Port) 

 1 


 N 


SampleBased Processing
Input  Number of Channels  Valid Initial States (Dialog Box)  Valid Initial States (Input Port) 

 1 


 N 


 K × N 


When the Initial states is a scalar, the block initializes all filter
states to the same scalar value. To initialize all states to zero, enter
0
. When the Initial states is a vector
or a matrix, each vector or matrix element specifies a unique initial state for a
corresponding delay element in a corresponding channel:
The vector length must equal the number of delay elements in the filter,
M = max(number of zeros, number of poles)
.The matrix must have the same number of rows as the number of delay elements in the filter,
M = max(number of zeros, number of poles)
. The matrix must also have one column for each channel of the input signal.
The following example shows the relationship between the initial filter output and the initial input and state. Given an initial input u_{1}, the first output y_{1} is related to the initial state [x_{1}, x_{2}] and initial input by as follows:
$$\begin{array}{l}y1=4x1\\ x2=1/2(u13x1)\end{array}$$
Ports
Input
u
— Input signal
scalar  vector  matrix
Input signal, specified as a scalar, vector, or matrix.
Data Types: single
 double
 int8
 int16
 int32
 fixed point
Num
— Numerator coefficients
scalar  vector  matrix
Coefficients of the numerator polynomial specified as a vector or matrix in descending powers of z. Use a row vector to specify the coefficients for a single numerator polynomial. Use a matrix to specify coefficients for multiple filters to be applied to the same input. Each matrix row represents a set of filter taps. The order of the denominator must be greater than or equal to the order of the numerator.
Dependencies
To enable this port, set Numerator Source to
Input port
.
Numerator and denominator coefficients must have the same complexity. They can have different word lengths and fraction lengths.
Data Types: single
 double
 int8
 int16
 int32
 fixed point
Den
— Denominator coefficients
scalar  vector  matrix
Coefficients of the denominator polynomial specified as a vector in descending powers of z. Use a row vector to specify the coefficients for a single denominator polynomial. Use a matrix to specify coefficients for multiple filters to be applied to the same input. Each matrix row represents a set of filter taps. The order of the denominator must be greater than or equal to the order of the numerator.
Dependencies
To enable this port, set Denominator Source
to Input port
.
Numerator and denominator coefficients must have the same complexity. They can have different word lengths and fraction lengths.
Data Types: single
 double
 int8
 int16
 int32
 fixed point
External reset
— External reset signal
scalar
External reset signal, specified as a scalar. When the specified trigger event occurs, the block resets the states to their initial conditions.
Tip
The icon for this port changes based on the value of the External reset parameter.
Dependencies
To enable this port, set External reset to
Rising
,
Falling
,
Either
,
Level
, or Level
hold
.
Limitations
The reset signal must be a scalar of type single, double, Boolean, or integer.
Fixedpoint data types, except for ufix1
, are not
supported.
Data Types: single
 double
 Boolean
 int8
 int16
 int32
 fixed point
x0
— Initial states
scalar  vector  matrix
Initial states, specified as a scalar, vector, or matrix. For more information about specifying states, see Specifying Initial States. States are complex when either the input or the coefficients are complex.
Dependencies
To enable this port, set Initial states
Source to Input
port
.
Data Types: single
 double
 int8
 int16
 int32
 fixed point
Output
Port_1
— Output signal
scalar  vector  matrix
Output signal specified as a scalar, vector, or matrix.
Data Types: single
 double
 int8
 int16
 int32
 fixed point
Parameters
Main
Numerator Source
— Source of numerator coefficients
Dialog
(default)  Input port
Specify the source of the numerator coefficients as
Dialog
or Input
port
.
Programmatic Use
Block Parameter:
NumeratorSource 
Type: character vector 
Values:
'Dialog'  'Input port' 
Default:
'Dialog'

Numerator Value
— Numerator coefficients
[1]
(default)  scalar  vector  matrix
Numerator coefficients of the discrete transfer function. To specify the coefficients,
set the Source to
Dialog
. Then, enter the coefficients in
Value as descending powers of
z. Use a row vector to specify the coefficients
for a single numerator polynomial. Use a matrix to specify coefficients
for multiple filters to be applied to the same input. Each matrix row
represents a set of filter taps.
Dependencies
To enable this parameter, set the Numerator
Source to Dialog
.
Programmatic Use
Block Parameter:
Numerator 
Type: character vector 
Values: scalar  vector  matrix 
Default:
'[1]'

Denominator Source
— Source of denominator coefficients
Dialog
(default)  Input port
Specify the source of the denominator coefficients as
Dialog
or Input
port
.
Programmatic Use
Block Parameter:
DenominatorSource 
Type: character vector 
Values:
'Dialog'  'Input port' 
Default:
'Dialog'

Denominator Value
— Denominator coefficients
[1 0.5]
(default)  scalar  vector  matrix
Denominator coefficients of the discrete transfer function. To specify
the coefficients, set the Source to
Dialog
. Then, enter the coefficients in
Value as descending powers of
z. Use a row vector to specify the coefficients
for a single denominator polynomial. Use a matrix to specify
coefficients for multiple filters to be applied to the same input. Each
matrix row represents a set of filter taps.
Dependencies
To enable this parameter, set the Denominator
Source to Dialog
.
Programmatic Use
Block Parameter:
Denominator 
Type: character vector 
Values: scalar  vector  matrix 
Default:
'[1 0.5]'

Initial states Source
— Source of initial states
Dialog
(default)  Input port
Specify the source of the initial states as
Dialog
or Input
port
.
Programmatic Use
Block Parameter:
InitialStatesSource 
Type: character vector 
Values:
'Dialog'  'Input port' 
Default:
'Dialog'

Initial states Value
— Initial filter states
0
(default)  scalar  vector  matrix
Specify the initial filter states as a scalar, vector, or matrix. To learn how to specify initial states, see Specifying Initial States.
Dependencies
To enable this parameter, set Initial states
Source to Dialog
.
Programmatic Use
Block Parameter:
InitialStates 
Type: character vector 
Values: scalar  vector  matrix 
Default:
'0'

External reset
— External state reset
None
(default)  Rising
 Falling
 Either
 Level
 Level hold
Specify the trigger event to use to reset the states to the initial conditions.
Reset Mode  Behavior 

None  No reset 
Rising  Reset on a rising edge 
Falling  Reset on a falling edge 
Either  Reset on either a rising or falling edge 
Level  Reset in either of these cases:

Level hold  Reset when the reset signal is nonzero at the current time step 
Programmatic Use
Block Parameter:
ExternalReset 
Type: character vector 
Values: 'None' 
'Rising'  'Falling' 
'Either'  'Level'  'Level
hold' 
Default: 'None' 
Input processing
— Sample or framebased processing
Elements as channels (sample
based)
(default)  Columns as channels (frame based)
Specify whether the block performs sample or framebased processing.
Elements as channels (sample based)
— Process each element of the input as an independent channel.Columns as channels (frame based)
— Process each column of the input as an independent channel.Note
Framebased processing requires a DSP System Toolbox license.
For more information, see Sample and FrameBased Concepts (DSP System Toolbox).
Programmatic Use
Block Parameter:
InputProcessing 
Type: character vector 
Values:
'Elements as channels (sample based)'  'Columns as
channels (frame based)' 
Default:
'Elements as channels (sample
based)' 
Optimize by skipping divide by leading denominator coefficient (a0)
— Skip divide by a0
off
(default)  on
Select when the leading denominator coefficient, a_{0}, equals 1. This parameter optimizes your code.
When you select this check box, the block does not perform a dividebya_{0} either in simulation or in the generated code. An error occurs if a_{0} is not equal to one.
When you clear this check box, the block is fully tunable during simulation, and performs a dividebya_{0} in both simulation and code generation.
Programmatic Use
Block Parameter:
a0EqualsOne

Type: character vector 
Values:
'off'  'on' 
Default:
'off'

Sample time (1 for inherited)
— Interval between samples
1
(default)  scalar  vector
Specify the time interval between samples. To inherit the sample time,
set this parameter to 1
. For more information, see
Specify Sample Time.
Programmatic Use
Block Parameter:
SampleTime 
Type: character vector 
Values: scalar  vector 
Default:
'1' 
Data Types
State
— State data type
Inherit: Same as input
(default)  int8
 int16
 int32
 int64
 fixdt(1,16,0)
 <data type expression>
Specify the state data type. You can set it to:
A rule that inherits a data type, for example,
Inherit: Same as input
A builtin integer, for example,
int8
A data type object, for example, a
Simulink.NumericType
objectAn expression that evaluates to a data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.
Numerator coefficients
— Numerator coefficient data type
Inherit: Inherit via internal
rule
(default)  int8
 int16
 int32
 int64
 fixdt(1,16)
 fixdt(1,16,0)
 <data type expression>
Specify the numerator coefficient data type. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
A builtin integer, for example,
int8
A data type object, for example, a
Simulink.NumericType
objectAn expression that evaluates to a data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.
Programmatic Use
Block Parameter:
NumCoeffDataTypeStr 
Type: character vector 
Values:
'Inherit: Inherit via internal rule'  'int8'  'int16'
 'int32'  'int64'  'fixdt(1,16)'  'fixdt(1,16,0)' 
'<data type expression>' 
Default:
'Inherit: Inherit via internal rule' 
Numerator coefficient minimum
— Minimum value of numerator coefficients
[]
(default)  scalar
Specify the minimum value that a numerator coefficient can have. The
default value is []
(unspecified). Simulink^{®} software uses this value to perform:
Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixedpoint data types
Programmatic Use
Block Parameter:
NumCoeffMin 
Type: character vector 
Values: scalar 
Default:
'[]' 
Numerator coefficient maximum
— Maximum value of numerator coefficients
[]
(default)  scalar
Specify the maximum value that a numerator coefficient can have. The
default value is []
(unspecified). Simulink software uses this value to perform:
Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixedpoint data types
Programmatic Use
Block Parameter:
NumCoeffMax 
Type: character vector 
Values: scalar 
Default:
'[]' 
Numerator product output
— Numerator product output data type
Inherit: Inherit via internal
rule
(default)  Inherit: Same as input
 int8
 int16
 int32
 int64
 fixdt(1,16,0)
 <data type expression>
Specify the product output data type for the numerator coefficients. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
A builtin data type, for example,
int8
A data type object, for example, a
Simulink.NumericType
objectAn expression that evaluates to a data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.
Programmatic Use
Block Parameter:
NumProductDataTypeStr 
Type: character vector 
Values:
'Inherit: Inherit via internal rule'  'Inherit: Same
as input'  'int8'  'int16'  'int32'  'int64' 
'fixdt(1,16,0)'  '<data type
expression>' 
Default:
'Inherit: Inherit via interal rule' 
Numerator accumulator
— Numerator accumulator data type
Inherit: Inherit via internal
rule
(default)  Inherit: Same as input
 Inherit: Same as product output
 int8
 int16
 int32
 int64
 fixdt(1,16,0)
 <data type expression>
Specify the accumulator data type for the numerator coefficients. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
A builtin data type, for example,
int8
A data type object, for example, a
Simulink.NumericType
objectAn expression that evaluates to a data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.
Programmatic Use
Block Parameter:
NumAccumDataTypeStr 
Type: character vector 
Values:
'Inherit: Inherit via internal rule'  'Inherit: Same
as input'  'Inherit: Same as product output'  'int8' 
'int16'  'int32'  'int64'  'fixdt(1,16,0)'  '<data
type expression>' 
Default:
'Inherit: Inherit via interal rule' 
Denominator coefficients
— Denominator coefficient data type
Inherit: Inherit via internal
rule
(default)  int8
 int16
 int32
 int64
 fixdt(1,16)
 fixdt(1,16,0)
 <data type expression>
Specify the denominator coefficient data type. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
A builtin integer, for example,
int8
A data type object, for example, a
Simulink.NumericType
objectAn expression that evaluates to a data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.
Programmatic Use
Block Parameter:
DenCoeffDataTypeStr 
Type: character vector 
Values:
'Inherit: Inherit via internal rule'  'int8'  'int16'
 'int32'  'int64'  'fixdt(1,16)'  'fixdt(1,16,0)' 
'<data type expression>' 
Default:
'Inherit: Same wordlength as input' 
Denominator coefficient minimum
— Minimum value of denominator coefficients
[]
(default)  scalar
Specify the minimum value that a denominator coefficient can have. The
default value is []
(unspecified). Simulink software uses this value to perform:
Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixedpoint data types
Programmatic Use
Block Parameter:
DenCoeffMin 
Type: character vector 
Values: scalar 
Default:
'[]' 
Denominator coefficient maximum
— Maximum value of denominator coefficients
[]
(default)  scalar
Specify the maximum value that a denominator coefficient can have. The
default value is []
(unspecified). Simulink software uses this value to perform:
Parameter range checking (see Specify Minimum and Maximum Values for Block Parameters)
Automatic scaling of fixedpoint data types
Programmatic Use
Block Parameter:
DenCoeffMax 
Type: character vector 
Values: scalar 
Default:
'[]' 
Denominator product output
— Denominator product output data type
Inherit: Inherit via internal
rule
(default)  Inherit: Same as input
 int8
 int16
 int32
 int64
 fixdt(1,16,0)
 <data type expression>
Specify the product output data type for the denominator coefficients. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
A builtin data type, for example,
int8
A data type object, for example, a
Simulink.NumericType
objectAn expression that evaluates to a data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.
Programmatic Use
Block Parameter:
DenProductDataTypeStr 
Type: character vector 
Values:
'Inherit: Inherit via internal rule'  'Inherit: Same
as input'  'int8'  'int16'  'int32'  'int64' 
'fixdt(1,16,0)'  '<data type
expression>' 
Default:
'Inherit: Inherit via interal rule' 
Denominator accumulator
— Denominator accumulator data type
Inherit: Inherit via internal
rule
(default)  Inherit: Same as input
 Inherit: Same as product output
 int8
 int16
 int32
 int64
 fixdt(1,16,0)
 <data type expression>
Specify the accumulator data type for the denominator coefficients. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
A builtin data type, for example,
int8
A data type object, for example, a
Simulink.NumericType
objectAn expression that evaluates to a data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.
Programmatic Use
Block Parameter:
DenAccumDataTypeStr 
Type: character vector 
Values:
'Inherit: Inherit via internal rule'  'Inherit: Same
as input'  'Inherit: Same as product output'  'int8' 
'int16'  'int32'  'int64'  'fixdt(1,16,0)'  '<data
type expression>' 
Default:
'Inherit: Inherit via interal rule' 
Output
— Output data type
Inherit: Inherit via internal
rule
(default)  Inherit: Same as input
 int8
 int16
 int32
 int64
 fixdt(1,16)
 fixdt(1,16,0)
 <data type expression>
Specify the output data type. You can set it to:
A rule that inherits a data type, for example,
Inherit: Inherit via internal rule
A builtin data type, for example,
int8
A data type object, for example, a
Simulink.NumericType
objectAn expression that evaluates to a data type, for example,
fixdt(1,16,0)
Click the Show data type assistant button to display the Data Type Assistant, which helps you set the data type attributes. For more information, see Specify Data Types Using Data Type Assistant.
Programmatic Use
Block Parameter:
OutDataTypeStr 
Type: character vector 
Values:
'Inherit: Inherit via internal rule'  'Inherit: Same
as input'  'int8'  'int16'  'int32'  'int64' 
'fixdt(1,16)'  'fixdt(1,16,0)'  '<data type
expression>' 
Default:
'Inherit: Inherit via interal rule' 
Output minimum
— Minimum value of output
[]
(default)  scalar
Specify the minimum value that the block can output. The default value
is []
(unspecified). Simulink uses this value to perform:
Simulation range checking (see Specify Signal Ranges)
Automatic scaling of fixedpoint data types
Programmatic Use
Block Parameter:
OutMin 
Type: character vector 
Values: scalar 
Default:
'[]' 
Output maximum
— Maximum value of output
[]
(default)  scalar
Specify the maximum value that the block can output. The default value
is []
(unspecified). Simulink uses this value to perform:
Simulation range checking (see Specify Signal Ranges)
Automatic scaling of fixedpoint data types
Programmatic Use
Block Parameter:
OutMax 
Type: character vector 
Values: scalar 
Default:
'[]' 
Lock data type settings against changes by the fixedpoint tools
— Prevent fixedpoint tools from overriding data types
off
(default)  on
Select this parameter to prevent the fixedpoint tools from overriding the data types you specify on this block. For more information, see Lock the Output Data Type Setting (FixedPoint Designer).
Programmatic Use
Block Parameter: LockScale 
Type: character vector 
Values: 'off'  'on' 
Default: 'off' 
Integer rounding mode
— Rounding mode for fixedpoint operations
Floor
(default)  Ceiling
 Convergent
 Nearest
 Round
 Simplest
 Zero
Specify the rounding mode for fixedpoint operations. For more information, see Rounding (FixedPoint Designer).
Block parameters always round to the nearest representable value. To control the rounding of a block parameter, enter an expression using a MATLAB^{®} rounding function into the mask field.
Programmatic Use
Block Parameter:
RndMeth 
Type: character vector 
Values:
'Ceiling'  'Convergent'  'Floor'  'Nearest'  'Round'  'Simplest' 
'Zero' 
Default:
'Floor' 
Saturate on integer overflow
— Method of overflow action
off
(default)  on
Specify whether overflows saturate or wrap.
Action  Rationale  Impact on Overflows  Example 

Select this check box ( 
Your model has possible overflow, and you want explicit saturation protection in the generated code. 
Overflows saturate to either the minimum or maximum value that the data type can represent. 
The maximum value that the 
Do not select this check box ( 
You want to optimize efficiency of your generated code. You want to avoid overspecifying how a block handles outofrange signals. For more information, see Troubleshoot Signal Range Errors. 
Overflows wrap to the appropriate value that is representable by the data type. 
The maximum value that the 
When you select this check box, saturation applies to every internal operation on the block, not just the output, or result. Usually, the code generation process can detect when overflow is not possible. In this case, the code generator does not produce saturation code.
Programmatic Use
Block Parameter: SaturateOnIntegerOverflow 
Type: character vector 
Values:
'off'  'on' 
Default: 'off' 
State Attributes
State name
— Unique name for block state
''
(default)  alphanumeric string
Use this parameter to assign a unique name to the block state. The default is ' '
. When this field is blank, no name is assigned. When using this parameter, remember these considerations:
A valid identifier starts with an alphabetic or underscore character, followed by alphanumeric or underscore characters.
The state name applies only to the selected block.
This parameter enables State name must resolve to Simulink signal object when you click Apply.
For more information, see C Code Generation Configuration for Model Interface Elements (Simulink Coder).
Programmatic Use
Block Parameter: StateName 
Type: character vector 
Values: unique name 
Default: '' 
State name must resolve to Simulink signal object
— Require state name resolve to a signal object
off
(default)  on
Select this check box to require that the state name resolves to a Simulink signal object.
Dependencies
To enable this parameter, specify a value for State name. This parameter appears only if you set the model configuration parameter Signal resolution to a value other than None
.
Programmatic Use
Block Parameter: StateMustResolveToSignalObject 
Type: character vector 
Values:
'off'  'on' 
Default: 'off' 
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

^{[a]} This block only supports signed fixedpoint data types. 
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.
HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.
This block has a single, default HDL architecture.
General  

ConstMultiplierOptimization  Canonical signed digit (CSD) or factored CSD optimization. The
default is 
ConstrainedOutputPipeline  Number of registers to place at
the outputs by moving existing delays within your design. Distributed
pipelining does not redistribute these registers. The default is

InputPipeline  Number of input pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is

OutputPipeline  Number of output pipeline stages
to insert in the generated code. Distributed pipelining and constrained
output pipelining can move these registers. The default is

Native Floating Point  

HandleDenormals  Specify whether you want HDL Coder to insert additional logic to handle denormal numbers in your design.
Denormal numbers are numbers that have magnitudes less than the smallest floatingpoint
number that can be represented without leading zeros in the mantissa. The default is

LatencyStrategy  Specify whether to map the blocks in your design to

MantissaMultiplyStrategy  Specify how to implement the mantissa multiplication operation during code generation.
By using different settings, you can control the DSP usage on the target FPGA device.
The default is 
Double data types are not supported for this block. Use single data types instead.
Frame, matrix, and vector input data types are not supported.
The leading denominator coefficient (a0) must be 1 or 1.
The Discrete Transfer Fcn block is excluded from the following optimizations:
Resource sharing
Distributed pipelining
PLC Code Generation
Generate Structured Text code using Simulink® PLC Coder™.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
This block only supports signed fixedpoint data types.
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