dsp.VariableBandwidthFIRFilter

Variable bandwidth FIR filter

Description

The dsp.VariableBandwidthFIRFilter object filters each channel of the input using FIR filter implementations. It does so while having the capability of tuning the bandwidth.

To filter each channel of the input:

1. Create the dsp.VariableBandwidthFIRFilter object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

This object supports C/C++ code generation and SIMD code generation under certain conditions. For more information, see Code Generation.

Creation

Syntax

vbw = dsp.VariableBandwidthFIRFilter

vbw = dsp.VariableBandwidthFIRFilter(Name=Value)

Description

vbw = dsp.VariableBandwidthFIRFilter returns a variable bandwidth FIR filter object which independently filters each channel of the input over successive calls to the object. The filter cutoff frequency can be tuned during the filtering operation. The variable bandwidth FIR filter is designed using the window method.

vbw = dsp.VariableBandwidthFIRFilter(Name=Value) returns a variable bandwidth FIR filter with additional properties specified by one or more Name-Value pair arguments. Name is the property name and Value is the corresponding value. For example, FilterOrder=50 sets the filter order to 50.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

FilterOrder — FIR filter order

30 (default) | even positive integer

FIR filter order, specified as an even positive integer. This property is nontunable.

Data Types: double | single

FilterType — Type of filter response

'Lowpass' (default) | 'Highpass' | 'Bandpass' | 'Bandstop'

Type of filter response, specified as one of these options:

• 'Lowpass'

• 'Highpass'

• 'Bandpass'

• 'Bandstop'

CutoffFrequency — Filter cutoff frequency

512 (default) | positive scalar

Filter cutoff frequency, specified as a real positive scalar in Hz or in normalized frequency units (since R2023a).

If you set the NormalizedFrequency property to:

• false –– The value of the cutoff frequency is in Hz. The value must be less than half the SampleRate property value.

• true –– The value of the 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 property, set FilterType to 'Lowpass' or 'Highpass'.

Data Types: double | single

Window — Window function

'Hann' (default) | 'Hamming' | 'Chebyshev' | 'Kaiser'

Window function used to design the FIR filter, specified as one of these options:

• 'Hann'

• 'Hamming'

• 'Chebyshev'

• 'Kaiser'

KaiserWindowParameter — Kaiser window parameter

0.5 (default) | real scalar

Kaiser window parameter, specified as a real scalar.

Dependencies

To enable this property, set the Window property to 'Kaiser'.

Data Types: double | single

CenterFrequency — Center frequency of filter

11025 (default) | positive scalar

Center frequency of filter, specified as a real positive scalar in Hz or in normalized frequency units (since R2023a).

If you set the NormalizedFrequency property to:

• false –– The value of the center frequency is in Hz. The value must be less than half the SampleRate property value.

• true –– The value of the 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 property, set the FilterType property to 'Bandpass' or 'Bandstop'.

Data Types: double | single

Bandwidth — Filter bandwidth

7680 (default) | positive scalar

Filter bandwidth, specified as a real positive scalar in Hz or in normalized frequency units (since R2023a).

If you set the NormalizedFrequency property to:

• false –– The value of the filter bandwidth is in Hz. The value must be less than half the SampleRate property value.

• true –– 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 property, set the FilterType property to 'Bandpass' or 'Bandstop'.

Data Types: double | single

SidelobeAttenuation — Chebyshev window sidelobe attenuation

60 (default) | positive scalar

Chebyshev window sidelobe attenuation, specified as a real positive scalar in dB.

Dependencies

To enable this property, set the Window property to 'Chebyshev'.

Data Types: double | single

NormalizedFrequency — Flag to set frequencies in normalized units

false (default) | true

Since R2023a

Flag to set frequencies in normalized units, specified as one of these values:

• true –– The filter cutoff frequency, center frequency, and the filter bandwidth must be in the normalized frequency units and less than 1.0.

• false –– The filter cutoff frequency, center frequency, and the filter bandwidth are in Hz. You can specify the input sample rate through the SampleRate property.

Data Types: logical

SampleRate — Input sample rate

44100 (default) | positive scalar

Input sample rate, specified as a positive scalar in Hz.

Dependency

To enable this property, set NormalizedFrequency to false. (since R2023a)

Data Types: double | single

Usage

Syntax

y = vbw(x)

Description

y = vbw(x) filters the input signal x using the variable bandwidth FIR filter to produce the output y. The variable bandwidth FIR filter object operates on each channel, which means the object filters every column of the input signal independently over successive calls to the algorithm.

Input Arguments

x — Data input

vector | matrix

Data input, specified as a vector or a matrix. This object also accepts variable-size inputs. Once the object is locked, you can change the size of each input channel, but you cannot change the number of channels.

Data Types: double | single
Complex Number Support: Yes

Output Arguments

y — 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: double | single
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object™ as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to dsp.VariableBandwidthFIRFilter

freqz	Frequency response of discrete-time filter System object
filterAnalyzer	Analyze filters with Filter Analyzer app
impz	Impulse response of discrete-time filter System object
info	Information about filter System object
coeffs	Returns the filter System object coefficients in a structure
cost	Estimate cost of implementing filter System object
grpdelay	Group delay response of discrete-time filter System object
outputDelay	Determine output delay of single-rate or multirate filter

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Filtering Through a Variable Bandwidth Bandpass FIR Filter

Tune the center frequency and the bandwidth of the FIR bandpass filter. Filter a sinusoidal signal through this filter.

Define a bandpass variable bandwidth FIR filter. Specify an input sample rate of 44100 Hz. Initialize a dsp.TransferFunctionEstimator object to estimate the transfer function of the filter from the input and output signals. To visualize the transfer function, initialize a dsp.ArrayPlot object.

Fs = 44100; 
vbw = dsp.VariableBandwidthFIRFilter(FilterType='Bandpass',...
    FilterOrder=100,...
    SampleRate=Fs,...
    CenterFrequency=1e4,...
    Bandwidth=4e3);
tfe = dsp.TransferFunctionEstimator(FrequencyRange='onesided');
aplot = dsp.ArrayPlot(PlotType='Line',...
    XOffset=0,...
    YLimits=[-120 5], ...
    SampleIncrement=44100/1024,...
    YLabel='Frequency Response (dB)',...
    XLabel='Frequency (Hz)',...
    Title='System Transfer Function');

Generate a sine wave signal with a frame length of 1024. Tune the bandwidth and the center frequency of the filter. Pass the signal through this filter. Estimate the transfer function of the filter using the input and the generated output. Plot the system transfer function using an array plot.

FrameLength = 1024;
sine = dsp.SineWave(SamplesPerFrame=FrameLength);
for i=1:500
    % Generate input
    x = sine() + randn(FrameLength,1);
    % Pass input through the filter
    y = vbw(x);
    % Transfer function estimation
    h = tfe(x,y);
    % Plot transfer function
    aplot(20*log10(abs(h)))
    % Tune bandwidth and center frequency of the FIR filter
    if (i==250)
        vbw.CenterFrequency = 5000;
        vbw.Bandwidth = 2000;
    end
end

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. Vol. 14, Issue 4, June 1988, pp. 313-326.

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

See System Objects in MATLAB Code Generation (MATLAB Coder).

This object also 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 object, see Use Intel AVX2 Code Replacement Library to Generate SIMD Code from MATLAB Algorithms.

Version History

Introduced in R2014a

R2023a: Support for normalized frequencies

When you set the NormalizedFrequency property to true, you can specify the filter cutoff frequency, center frequency, and the filter bandwidth in normalized frequency units (0 to 1).

When you set the NormalizedFrequency property to true while creating the object, the frequency values are automatically set to normalized frequency units using the default sample rate of 44100 Hz.

vbFIRFilter = dsp.VariableBandwidthFIRFilter(NormalizedFrequency=true)

vbFIRFilter = 
  dsp.VariableBandwidthFIRFilter with properties:

            FilterOrder: 30
             FilterType: 'Lowpass'
        CutoffFrequency: 0.0232
                 Window: 'Hann'
    NormalizedFrequency: true

When you set the NormalizedFrequency property to true after you create the object, the frequencies must be manually set to the normalized frequency values before you run the object algorithm.

vbFIRFilter = dsp.VariableBandwidthFIRFilter

vbFIRFilter = 
  dsp.VariableBandwidthFIRFilter with properties:

            FilterOrder: 30
             FilterType: 'Lowpass'
        CutoffFrequency: 512
                 Window: 'Hann'
    NormalizedFrequency: false
             SampleRate: 44100

To specify the normalized frequency values, set NormalizedFrequency to true and manually convert the frequency values in Hz to normalized values using the input sample rate in Hz. For example, if the input sample rate is 44100 Hz, the corresponding values in normalized units are computed using these equations.

vbFIRFilter.NormalizedFrequency = true;
vbFIRFilter.CutoffFrequency = 512/(44100/2)

vbFIRFilter = 
  dsp.VariableBandwidthFIRFilter with properties:

            FilterOrder: 30
             FilterType: 'Lowpass'
        CutoffFrequency: 0.0232
                 Window: 'Hann'
    NormalizedFrequency: true