Discrete Transfer Fcn
Discrete transfer function.
Description
Block Discrete Transfer Fcn realises the transfer function of the -transform as follows:
,
where
-
and are the number of coefficients in the numerator and denominator, respectively;
-
and - coefficients of numerator and denominator in descending order ;
The values of and can be a vector or a matrix. The order of the denominator must be greater than or equal to the order of the numerator.
The coefficients of the numerator and denominator polynomials are specified in descending order of degree . The block allows polynomials in to be used to represent a discrete system; this approach is more common in control systems. Conversely, the block Discrete Transfer Fcn allows polynomials in (delay operator) to be used to represent a discrete system; this approach is typically used in digital signal processing (DSP). When the numerator and denominator polynomials have the same length, the two approaches are equivalent.
The block Discrete Transfer Fcn applies the transfer function -transform to each independent input channel.
The block icon displays the discrete transfer function given the parameters Numerator coefficients и *Denominator coefficients*If the size of the block icon does not accommodate the entire expression, is displayed.
Specifying initial states
Use the parameters *Initial states*parameter to specify the initial states of the block. The specified initial states are the initial conditions of the delay blocks used in a filter bigram that implements a discrete transfer function.
If the value of parameters Initial states is a scalar, the block initialises all filter states with the same scalar value. To initialise all states with zero, enter 0.
If the value is a Initial states - is a vector or matrix, each element of the vector or matrix specifies a unique initial state for the corresponding delay element in the corresponding channel:
-
The length of the vector must be equal to the number of delay elements in the filter, .
-
The matrix must have as many rows as the number of delay elements in the filter, . The matrix must also have one column for each channel of the input signal.
The following example shows the relationship between the initial output data of the filter and the initial input data and state. Given the initial input , the first output is related to the initial state ] and the initial input as follows:
,
.
Ports
Input
#
u
—
input signal
scalar | vector | matrix
Details
Input signal. Scalar, vector or matrix.
| Data types |
|
| Complex numbers support |
No |
Output
#
OUT_1
—
output signal
scalar | vector | matrix
Details
Output signal. Scalar, vector or matrix.
| Data types |
|
| Complex numbers support |
No |
Parameters
Main
#
Numerator coefficients —
numerator coefficients
Scalar / array of real numbers
Details
Numerator coefficients of the discrete transfer function.
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |
#
Denominator coefficients —
denominator coefficients
Scalar / array of real numbers
Details
Denominator coefficients of the discrete transfer function.
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |
#
Initial states —
initial values
Scalar / array of real numbers
Details
Initial values. Scalar, vector or matrix.
| Default value |
|
| Program usage name |
|
| Tunable |
Yes |
| Evaluatable |
Yes |
#
Sample time —
interval between calculation steps
SampleTime (real number / vector of two real numbers)
Details
Specify the parameters Sample time as a non-negative number. To inherit the discrete step of the system, set the value of this parameters to -1.
| Default value |
|
| Program usage name |
|
| Tunable |
No |
| Evaluatable |
Yes |