Variable Bandwidth FIR Filter

Design tunable bandwidth FIR filter

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Libraries:
DSP System Toolbox / Filtering / Filter Designs

Description

The Variable Bandwidth FIR Filter block filters each channel of the input signal over time using the specified FIR 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 FIR filter according to the filter parameters specified in the block dialog box. The output port properties, such as datatype, complexity, and dimension, are identical to the input port properties.

This block also supports SIMD code generation. For details, see Code Generation.

Examples

System Identification Using RLS Adaptive Filtering

Use a recursive least-squares (RLS) filter to identify an unknown system modeled with a lowpass FIR filter. Use the dynamic filter visualizer to compare the frequency response of the unknown and estimated systems. This example allows you to dynamically tune key simulation parameters using a user interface (UI). The example also shows you how to use MATLAB Coder™ to generate code for the algorithm and accelerate the speed of its execution.

Open Live Script

Ports

Input

x — Data input

vector | matrix

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 cutoff frequency from input port

• Specify center frequency from input port

• Specify bandwidth from input port

Data Types: single | double
Complex Number Support: Yes

Fcut — Filter cutoff frequency

positive scalar

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

Dependencies

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

Data Types: single | double

Fc — Filter center frequency

positive scalar

Specify the center frequency of the FIR 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

BW — Filter bandwidth

positive scalar

Specify the bandwidth of the FIR 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

Port_1 — Filtered output

vector | matrix

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

FIR filter order — FIR filter order

30 (default) | positive integer

Specify the order of the FIR filter as a positive integer scalar.

Filter type — Filter type

Lowpass (default) | Highpass | Bandpass | Bandstop

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

• Lowpass

• Highpass

• Bandpass

• Bandstop

Specify cutoff frequency from input port — Specify cutoff frequency from input port

off (default) | on

When you select this check box, specify the cutoff frequency through the Fcut port. When you clear this check box, specify the cutoff frequency in the block dialog box through the Filter cutoff frequency parameter.

Dependency

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

Filter cutoff frequency — Filter cutoff frequency

512 (default) | positive scalar

Specify the cutoff frequency of the FIR filter 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 cutoff 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 cutoff 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 cutoff frequency from input port parameter.

Specify center frequency from input port — Specify center frequency from input port

off (default) | on

When you select this check box, specify the center frequency 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.

Filter center frequency — Filter center frequency

44100/4 (default) | positive scalar

Specify the center frequency of the FIR filter 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.

Specify bandwidth from input port — Specify bandwidth from input port

off (default) | on

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

Dependency

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

Filter bandwidth — Filter bandwidth

7680 (default) | positive scalar

Specify the bandwidth of the FIR filter 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 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.

Window function — Window function

Hann (default) | Hamming | Chebyshev | Kaiser

Specify the window function used to design the FIR filter. You can set this parameter to:

• Hann

• Hamming

• Chebyshev

• Kaiser

Chebyshev window sidelobe attenuation (dB) — Chebyshev window sidelobe attenuation

60 (default) | positive scalar

Specify the sidelobe attenuation of the Chebyshev window as a real positive scalar.

Dependencies

To enable this parameter, set Window function to Chebyshev.

Kaiser window parameter — Kaiser window parameter

0.5 (default) | real scalar

Specify the Kaiser window parameter as a real scalar.

Dependencies

To enable this parameter, set Window function to Kaiser.

Sample rate mode — Mode to specify the input sample rate

Specify on dialog (default) | Inherit from input port | Use normalized frequency (0 to 1)

Since R2023a

Specify the input sample rate using one of these options:

• 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.

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

Input sample rate (Hz) — Input sample rate

44100 (default) | positive scalar

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)

View Filter Response — View Filter Response

button

Open the dynamic filter visualizer and display the magnitude response of the variable bandwidth FIR filter. The response is based on the parameters you select in the block dialog box. To update the magnitude response while the dynamic 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 Plot 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 dynamic filter visualizer interface and its tools, see dsp.DynamicFilterVisualizer.

Simulate using — Simulate using

Code generation (default) | Interpreted execution

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

• Code generation (default)

  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 simulation speed than Interpreted execution.

• Interpreted execution

  Simulate model using the MATLAB^®  interpreter. This option shortens startup time but has slower simulation speed than Code generation.

Block Characteristics

Data Types	double | single
Multidimensional Signals	No
Variable-Size Signals	Yes

Algorithms

FIR Transformations

All transformations assume a lowpass filter of length 2N+1.

Lowpass to Lowpass

Consider an ideal lowpass brickwall filter with normalized cutoff frequency ω_c1. By taking the inverse discrete Fourier transform of the ideal frequency response, and clipping the resulting sequence to length 2N+1, the impulse response is:

$$\begin{array}{l}forn=0\\ h_{LP}(n)=\frac{{\omega }_c}{\pi }.w(0)\\ for\text{ 1}\le \text{|n|}\le \text{N}\\ h_{LP}(n)=\frac{\sin ({\omega }_{c}n)}{\pi n}.w(n)\end{array}$$

where w(n) is the window vector. Tune the lowpass filter coefficients to a new cutoff frequency ω_c2 as follows:

$$\begin{array}{l}forn=0\\ h_{LP}(n)=\frac{{\omega }_{c2}}{\pi }.\omega (0)\\ for1\le \left|n\right|\le N\\ h_{LP}(n)=\frac{\sin ({\omega }_{c2}n)}{\pi n}.\omega (n)\end{array}$$

You do not need to recompute the window every time you tune the cutoff frequency.

Lowpass to Highpass

Assuming a lowpass filter with normalized 6-dB cutoff frequency ω_c, you can obtain a highpass filter with the same cutoff frequency by taking the complementary of the lowpass frequency response: H_HP(e^jω) = 1 − H_LP(e^jω)

Taking the inverse discrete Fourier transform of the above response, you have the following highpass filter coefficients:

$$\begin{array}{l}forn=0\\ h_{hp}(n)=1-h_{LP}(n)\\ for1\le \left|n\right|\le N\\ h_{hp}(n)=-h_{LP}(n)\end{array}$$

Lowpass to Bandpass

Obtain a bandpass filter centered at frequency ω₀ by shifting the lowpass response:

H_BP(e^jω) = H_LP(e^j(ω–ω₀)) + H_LP(e^{j(ω–ω₀)})

The bandwidth of the resulting bandpass filter is 2ω_c, as measured between the two cutoff frequencies of the bandpass filter. The equivalent bandpass filter coefficients are then:

$$\begin{array}{l}{h}_{BP}(n)=(e^{j{\omega }_{0}n}+e^{-j{\omega }_{0}n})h_{LP}(n)\\ \text{which can be written as:}\\ h_{BP}(n)=2\cos ({\omega }_{0}n)h_{LP}(n)\end{array}$$

Lowpass to Bandstop

You can transform a lowpass filter to a bandstop filter by combining the highpass and bandpass transformations. First make the filter bandpass by shifting the lowpass response, and then invert it to get a bandstop response centered at ω₀.

H_BS(e^jω) = 1 – (H_LP(e^{j(ω–ω₀)}) + H_LP(e^j(ω+ω₀)))

This yields the following coefficients:

$$\begin{array}{l}forn=0\\ h_{BS}(n)=1-2\cos ({\omega }_{0}n)h_{LP}(n)\\ for1\le \left|n\right|\le N\\ h_{BS}(n)=-2\cos ({\omega }_{0}n)h_{LP}(n)\end{array}$$

Generalized Transformation

You can combine these transformations to transform a lowpass filter to a lowpass, highpass, bandpass, or bandstop filter with arbitrary cutoffs.

For example, to transform a lowpass filter with cutoff ω_c1 to a highpass with cutoff ω_c2, you first apply the lowpass-to-lowpass transformation to get a lowpass filter with cutoff ω_c2, and then apply the lowpass-to-highpass transformation to get the highpass with cutoff ω_c2.

To get a bandpass filter with center frequency ω₀ and bandwidth β, we first apply the lowpass-to-lowpass transformation to go from a lowpass with cutoff ω_c to a lowpass with cutoff β/2, and then apply the lowpass-to-bandpass transformation to get the desired bandpass filter. You can use the same approach for a bandstop filter.

References

[1] Jarske, P., Y. Neuvo, and S. K. Mitra. "A Simple Approach to the Design of Linear Phase FIR Digital Filters with Variable Characteristics." Signal Processing 14, no. 4 *(1988): 313-326.

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

The Variable Bandwidth FIR Filter block supports SIMD code generation using Intel^® AVX2 code replacement library when the input signal has a data type of single or double.

The SIMD technology significantly improves the performance of the generated code. For more information, see SIMD Code Generation. To generate SIMD code from this block, see Use Intel AVX2 Code Replacement Library to Generate SIMD Code from Simulink Blocks.

Version History

Introduced in R2015a

R2023a: Support for normalized frequencies

When you set the Sample rate mode parameter to Use normalized frequency (0 to 1), you can specify the filter cutoff frequency, center frequency, and filter bandwidth in normalized frequency units (0 to 1).