IIR Filter

Implement infinite impulse response (IIR) filter

• Library:

• Motor Control Blockset / Signal Management

• 

Description

The IIR Filter block implements a discrete first-order infinite impulse response (IIR) filter on the specified input signal. The block supports fixed-point and floating-point data types. The block is also optimized for code generation.

We recommend that you use fixed-step discrete solver for this block to enable code generation and ensure accurate simulation.

Equations

You can configure the IIR filter by using the filter coefficient ($$a$$) block parameter for a given cutoff frequency (f_c).

This equation describes computation of the filter coefficient from the cutoff frequency:

$a= \left( \frac{2\pi T_s{f}_c}{2\pi T_s{f}_c+1} \right)$

Alternatively, the block also computes the theoretical cutoff frequency for the given sample time using a filter coefficient:

$f_c= \left( \frac{a}{(1-a)\cdot 2\pi \cdot T_s} \right)$

Use the Filter type parameter to configure the block either as a low-pass or high-pass filter.

Low-pass filter:

$$y\left(k\right)=a\cdot x_k+(1-a)\cdot y_{k-1}$$

High-pass filter:

$$y\left(k\right)=(1-a)\cdot x_k- (1-a)\cdot x_{k-1}+(1-a)\cdot y_k$$

where:

• f_c is the cutoff frequency of the IIR filter.

• $$a$$ is the filter coefficient in the range (0, 1].

• $y\left(k\right)$ is the filtered output value at time $$k$$.

• $y_{k-1}$ is the filtered output value at time $k-1$.

• $x_k$ is the sampled input value at time $$k$$.

• $x_{k-1}$ is the filtered output value at time $k-1$.

• T_s is the sample time of the IIR Filter block.

Ports

Input

x — Sampled input signal

scalar

Sampled values of the raw input signal in the time domain.

Data Types: single | double | fixed point

Output

y — Filtered output signal

scalar

Filtered output signal returned by the IIR Filter block in the time domain.

Data Types: single | double | fixed point

Parameters

Filter type — IIR filter type

Low-pass (default) | High-pass

Type of the IIR filter.

Filter co-efficient — Filter coefficient of IIR filter

0.01 (default) | scalar in the range (0,1]

Filter coefficient of the IIR filter. The data type of this parameter is the same as that of the input signal. We suggest that you check the precision of the parameter value in this data type.

Display cutoff frequency — Display the cutoff frequency parameters

off (default) | on

Select this parameter for the block to display the Discrete step size (s) and Theoretical cutoff frequency (Hz) parameters.

Discrete step size (s) — Step size of discrete-time filter

50e-6 (default) | scalar

Step size of the discrete-time computation (in seconds) used by the IIR filter.

Dependencies

To display this parameter, select the Display cutoff frequency parameter.

Theoretical cutoff frequency (Hz) — Theoretical cutoff frequency of IIR filter

32.1525 | scalar

Theoretical cutoff frequency (in Hertz) of the IIR filter. This parameter is not configurable.

Dependencies

To display this parameter, select the Display cutoff frequency parameter.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Introduced in R2020a