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:

Create the dsp.VariableBandwidthFIRFilter object and set its properties.
Call the object with arguments, as if it were a function.

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

Creation

Syntax

vbw = dsp.VariableBandwidthFIRFilter

vbw = dsp.VariableBandwidthFIRFilter(Name,Value)

Description

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

example

vbw = dsp.VariableBandwidthFIRFilter(Name,Value) returns a variable bandwidth FIR filter System object, vbw, with each property set to the specified value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN).

Properties

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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.

`SampleRate` — Input sample rate
`44100` (default) | positive scalar

Input sample rate, specified as a positive scalar in Hz. This property is non-tunable.

Data Types: double | single

`FilterType` — Filter type
`'Lowpass'` (default) | `'Highpass'` | `'Bandpass'` | `'Bandstop'`

Specify the type of the filter as one of 'Lowpass' | 'Highpass' | 'Bandpass' | 'Bandstop'. This property is non-tunable.

`FilterOrder` — FIR filter order
`30` (default) | positive integer

Specify the order of the FIR filter as a positive integer scalar. This property is non-tunable.

Data Types: double | single

`Window` — Window function
`'Hann'` (default) | `'Hamming'` | `'Chebyshev'` | `'Kaiser'`

Specify the window function used to design the FIR filter as one of 'Hann' | 'Hamming' | 'Chebyshev' | 'Kaiser'. This property is non-tunable.

`KaiserWindowParameter` — Kaiser window parameter
`0.5` (default) | real scalar

Specify the Kaiser window parameter as a real scalar. This property is non-tunable.

Dependencies

This property applies when you set the 'Window' property to 'Kaiser'.

Data Types: double | single

`CutoffFrequency` — Filter cutoff frequency
`512` (default) | positive scalar

Specify the filter cutoff frequency in Hz as a real, positive scalar, smaller than the SampleRate/2.

Tunable: Yes

Dependencies

This property applies if you set the FilterType property to 'Lowpass' or 'Highpass'.

Data Types: double | single

`CenterFrequency` — Filter center frequency
`11025` (default) | positive scalar

Specify the filter center frequency in Hz as a real, positive scalar, smaller than SampleRate/2.

Tunable: Yes

Dependencies

This property applies when you set the FilterType property to 'Bandpass' or 'Bandstop'.

Data Types: double | single

`Bandwidth` — Filter bandwidth
`7680` (default) | positive scalar

Specify the filter bandwidth in Hertz as a real, positive scalar, smaller than SampleRate/2.

Tunable: Yes

Dependencies

This property applies if you set the FilterType property to 'Bandpass' or 'Bandstop'.

Data Types: double | single

`SidelobeAttenuation` — Chebyshev window sidelobe attenuation
`60` (default) | positive scalar

Specify the Chebyshev window attenuation as a real, positive scalar in decibels (dB). This property is non-tunable.

Dependencies

This property applies if you set the Window property to 'Chebyshev'.

Data Types: double | single

Usage

Syntax

y = vbw(x)

Description

example

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

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`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

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`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)

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Specific to `dsp.VariableBandwidthFIRFilter`

`freqz`	Frequency response of discrete-time filter System object
`fvtool`	Visualize frequency response of DSP filters
`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

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

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Filtering Through a Variable Bandwidth Bandpass FIR Filter

Open Script

Note: This example runs only in R2016b or later. If you are using an earlier release, replace each call to the function with the equivalent step syntax. For example, myObject(x) becomes step(myObject,x).

This example shows you how to tune the center frequency and the bandwidth of the FIR filter.

Fs = 44100; % Input sample rate
% Define a bandpass variable bandwidth FIR filter:
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');
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

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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:

$\begin{array}{l} f o r n = 0 \\ h_{L P} (n) = \frac{ω_{c}}{π} . w (0) \\ f o r 1 \leq |n| \leq N \\ h_{L P} (n) = \frac{\sin (ω_{c} n)}{π n} . w (n) \end{array}$

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

$\begin{array}{l} f o r n = 0 \\ h_{L P} (n) = \frac{ω_{c 2}}{π} . ω (0) \\ f o r 1 \leq | n | \leq N \\ h_{L P} (n) = \frac{\sin (ω_{c 2} n)}{π n} . ω (n) \end{array}$

There is no 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, a highpass filter with the same cutoff frequency can be obtained 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, we get the following highpass filter coefficients:

$\begin{array}{l} f o r n = 0 \\ h_{h p} (n) = 1 - h_{L P} (n) \\ f o r 1 \leq | n | \leq N \\ h_{h p} (n) = - h_{L P} (n) \end{array}$

Lowpass to Bandpass

A bandpass filtered centered at frequency ω₀ can be obtained 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:

$\begin{array}{l} h_{B P} (n) = (e^{j ω_{0} n} + e^{- j ω_{0} n}) h_{L P} (n) \\ which can be written as: \\ h_{B P} (n) = 2 \cos (ω_{0} n) h_{L P} (n) \end{array}$

Lowpass to Bandstop

We can transform a lowpass filter to a bandstop filter by combining the highpass and bandpass transformations. That is, first make the filter bandpass by shifting the lowpass response, and then invert in 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:

$\begin{array}{l} f o r n = 0 \\ h_{B S} (n) = 1 - 2 \cos (ω_{0} n) h_{L P} (n) \\ f o r 1 \leq | n | \leq N \\ h_{B S} (n) = - 2 \cos (ω_{0} n) h_{L P} (n) \end{array}$

Generalized Transformation

The transformations highlighted above can be combined 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. The same approach can be applied to 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.

Documentation

dsp.VariableBandwidthFIRFilter

Description

Creation

Syntax

Description

Properties

SampleRate — Input sample rate 44100 (default) | positive scalar

FilterType — Filter type 'Lowpass' (default) | 'Highpass' | 'Bandpass' | 'Bandstop'

FilterOrder — FIR filter order 30 (default) | positive integer

Window — Window function 'Hann' (default) | 'Hamming' | 'Chebyshev' | 'Kaiser'

KaiserWindowParameter — Kaiser window parameter 0.5 (default) | real scalar

Dependencies

CutoffFrequency — Filter cutoff frequency 512 (default) | positive scalar

Dependencies

CenterFrequency — Filter center frequency 11025 (default) | positive scalar

Dependencies

Bandwidth — Filter bandwidth 7680 (default) | positive scalar

Dependencies

SidelobeAttenuation — Chebyshev window sidelobe attenuation 60 (default) | positive scalar

Dependencies

Usage

Syntax

Description

Input Arguments

x — Data input vector | matrix

Output Arguments

y — Filtered output vector | matrix

Object Functions

Specific to dsp.VariableBandwidthFIRFilter

Common to All System Objects

Examples

Filtering Through a Variable Bandwidth Bandpass FIR Filter

Algorithms

FIR Transformations

References

Extended Capabilities

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

See Also

Functions

Objects

Blocks

Topics

DSP System Toolbox Documentation

Support

`SampleRate` — Input sample rate
`44100` (default) | positive scalar

`FilterType` — Filter type
`'Lowpass'` (default) | `'Highpass'` | `'Bandpass'` | `'Bandstop'`

`FilterOrder` — FIR filter order
`30` (default) | positive integer

`Window` — Window function
`'Hann'` (default) | `'Hamming'` | `'Chebyshev'` | `'Kaiser'`

`KaiserWindowParameter` — Kaiser window parameter
`0.5` (default) | real scalar

`CutoffFrequency` — Filter cutoff frequency
`512` (default) | positive scalar

`CenterFrequency` — Filter center frequency
`11025` (default) | positive scalar

`Bandwidth` — Filter bandwidth
`7680` (default) | positive scalar

`SidelobeAttenuation` — Chebyshev window sidelobe attenuation
`60` (default) | positive scalar

`x` — Data input
vector | matrix

`y` — Filtered output
vector | matrix

Specific to `dsp.VariableBandwidthFIRFilter`

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