Main Content

Variable Bandwidth IIR Filter

Design tunable bandwidth IIR filter

expand all in page
  • Variable Bandwidth IIR Filter block

Libraries:
DSP System Toolbox / Filtering / Filter Designs

Description

The Variable Bandwidth IIR Filter block filters each channel of the input signal over time using the IIR filter specifications. This block offers tunable filter design parameters, which enable you to tune the filter characteristics while the simulation is running.

The block designs the IIR filter according to the filter parameters set in the block dialog box. The output port properties, such as datatype, complexity, and dimension, are identical to the input port properties.

Examples

Tunable Lowpass Filtering of Noisy Input in Simulink

Tunable Lowpass Filtering of Noisy Input in Simulink

Filter a noisy chirp signal with a lowpass filter that has a tunable passband frequency. The filter in this example is designed using a Variable Bandwidth IIR Filter block with Filter type set to Lowpass. This type of filter enables you to change the passband frequency during simulation without having to redesign the whole filter. The filter algorithm recomputes the filter coefficients whenever the passband frequency changes.

Ports

Input

expand all

Specify the data input as a vector or a matrix. The block treats each column of the input signal as a separate channel. If the input is a two-dimensional signal, the first dimension represents the channel length (or frame size) and the second dimension represents the number of channels. If the input is a one-dimensional signal, then the block interprets it as having a single channel.

The block accepts variable-size input signals, that is, you can change the size of each input channel during simulation but you cannot change the number of channels.

This port is unnamed until you select one of these parameters:

  • Specify passband frequency from input port

  • Specify center frequency from input port

  • Specify bandwidth from input port

Data Types: single | double
Complex Number Support: Yes

Specify the passband frequency of the IIR filter as a real positive scalar in Hz or in normalized frequency units (since R2023a).

Dependencies

To enable this port, select the Specify passband frequency from input port parameter.

Data Types: single | double

Specify the center frequency of the IIR filter as a real positive scalar in Hz or in normalized frequency units (since R2023a).

Dependencies

To enable this port, select the Specify center frequency from input port parameter.

Data Types: single | double

Specify the bandwidth of the IIR filter as a real positive scalar in Hz or in normalized frequency units (since R2023a).

Dependencies

To enable this port, select the Specify bandwidth from input port parameter.

Data Types: single | double

Output

expand all

Filtered output, returned as a vector or a matrix. The size, data type, and complexity of the output signal matches that of the input signal.

Data Types: single | double
Complex Number Support: Yes

Parameters

expand all

Specify the type of IIR filter. You can set this parameter to:

  • Lowpass

  • Highpass

  • Bandpass

  • Bandstop

Specify the order of the IIR filter as a positive integer.

When you select this check box, specify the filter passband frequency through the Fp port. When you clear this check box, specify the passband frequency in the block dialog box through the Filter passband frequency parameter.

Dependency

To enable this parameter, set Filter type to Lowpass or Highpass.

Specify the filter passband frequency as a real, positive scalar in Hz or in normalized frequency units (since R2023a).

If you set the Sample rate mode parameter to:

  • Specify on dialog or Inherit from input port –– The value of the filter passband frequency is in Hz and must be less than half the value of the input sample rate.

  • Use normalized frequency (0 to 1) –– The value of the filter passband frequency is in normalized frequency units. The value must be a positive scalar less than 1.0.

(since R2023a)

Tunable: Yes

Dependencies

To enable this parameter:

  • Set Filter type to Lowpass or Highpass.

  • Clear the Specify passband frequency from input port parameter.

When you select this check box, specify the center frequency of the IIR filter through the Fc port. When you clear this check box, specify the center frequency in the block dialog box through the Filter center frequency parameter.

Dependencies

To enable this parameter, set Filter type to Bandpass or Bandstop.

Specify the filter center frequency as a real positive scalar in Hz or in normalized frequency units (since R2023a).

If you set the Sample rate mode parameter to:

  • Specify on dialog or Inherit from input port –– The value of the filter center frequency is in Hz and must be less than half the value of the input sample rate.

  • Use normalized frequency (0 to 1) –– The value of the filter center frequency is in normalized frequency units. The value must be a positive scalar less than 1.0.

(since R2023a)

Tunable: Yes

Dependencies

To enable this parameter:

  • Set Filter type to Bandpass or Bandstop.

  • Clear the Specify center frequency from input port parameter.

When you select this check box, specify the bandwidth of the IIR filter through the BW port. When you clear this check box, specify the filter bandwidth in the block dialog box through the Filter bandwidth parameter.

Dependencies

To enable this parameter, set Filter type to Bandpass or Bandstop.

Specify the filter bandwidth as a positive scalar in Hz or in normalized frequency units (since R2023a).

If you set the Sample rate mode parameter to:

  • Specify on dialog or Inherit from input port –– The value of the filter bandwidth is in Hz and must be less than half the value of the input sample rate.

  • Use normalized frequency (0 to 1) –– The value of the filter bandwidth is in normalized frequency units. The value must be a positive scalar less than 1.0.

(since R2023a)

Tunable: Yes

Dependencies

To enable this parameter:

  • Set Filter type to Bandpass or Bandstop.

  • Clear the Specify bandwidth from input port parameter.

Specify the filter passband ripple as a real, positive scalar.

Specify the filter stopband attenuation as a real, positive scalar.

Since R2023a

Specify the input sample rate using one of these options:

  • Use normalized frequency (0 to 1) –– Specify the filter passband frequency, center frequency, and the filter bandwidth in normalized frequency units (0 to 1).

  • Specify on dialog –– Specify the input sample rate in the block dialog box using the Input sample rate (Hz) parameter.

  • Inherit from input port –– The block inherits the sample rate from the input signal as N / Ts, where N is the frame size of the input signal and Ts is the sample time of the input signal.

Specify the sample rate of the input signal as a positive scalar in Hz.

Dependencies

To enable this parameter, set the Sample rate mode parameter to Specify on dialog. (since R2023a)

Clicking this button opens the filter visualizer and displays the magnitude response of the variable bandwidth IIR filter. The response is based on the parameters you select in the block parameters dialog box. To update the magnitude response while the filter visualizer is running, modify the parameters in the dialog box and click Apply.

You can configure the plot settings and the signal measurements from the interface of the visualizer.

On the Scope tab, the Configuration section allows you to modify the plot settings. On the Measurements tab, you can measure the signal statistics, place data cursors, and display the peak values of the selected signal.

For more details on the filter visualizer interface and its tools, see Configure Filter Visualizer.

Dependencies

To enable this button, do not specify any filter specifications from the input port.

Specify the type of simulation to run. You can set this parameter to:

  • Interpreted execution –– Simulate model using the MATLAB® interpreter. This option shortens startup time.

  • Code generation –– Simulate model using generated C code. The first time you run a simulation, Simulink® generates C code for the block. The C code is reused for subsequent simulations as long as the model does not change. This option requires additional startup time but provides faster subsequent simulations.

Block Characteristics

Data Types

double | single

Multidimensional Signals

No

Variable-Size Signals

Yes

Algorithms

This filter covers frequency transformations. The algorithm designs a lowpass IIR prototype using the elliptical method by specifying its order, passband frequency, passband ripple, and stopband attenuation. The passband ripple and stopband attenuation are equal to the values of the PassbandRipple and StopbandAttenuation properties. The algorithm sets the prototype passband frequency to 0.5. If the FilterType property is 'Lowpass' or 'Highpass', the order of the prototype filter is equal to the value of FilterOrder. If the FilterType property is 'Bandpass' or 'Bandstop', the order of the prototype filter is equal to FilterOrder/2. The prototype is a Direct Form II Transposed cascade of second-order sections (Biquad filter). The prototype is transformed into the desired filter using the algorithms used in Digital Frequency Transformations. Each prototype SOS section is transformed separately. When FilterType is 'Lowpass' or 'Highpass', the resulting filter remains a Direct Form II Transposed cascade of second order sections. If the FilterType is 'Bandpass' or 'Bandstop', the resulting filter is a cascade of Direct Form II Transposed cascade of fourth order sections.

References

[1] A. G. Constantinides. "Spectral Transformations for Digital Filters." Proceedings of the Institution of Electrical Engineers 117, no. 8 (1970):1585-1590.

Extended Capabilities

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

Version History

Introduced in R2015a

expand all

See Also

Blocks

Objects