dsp.VariableBandwidthIIRFilter

Variable bandwidth IIR filter

Description

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

To filter each channel of the input:

1. Create the dsp.VariableBandwidthIIRFilter 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? (MATLAB).

Creation

Syntax

vbwIIR = dsp.VariableBandwidthIIRFilter

vbwIIR = dsp.VariableBandwidthIIRFilter(Name,Value)

Description

vbwIIR = dsp.VariableBandwidthIIRFilter returns a System object™, vbwIIR, which independently filters each channel of the input over successive calls to the algorithm. This System object uses a specified IIR filter implementation. The filter’s passband frequency may be tuned during the filtering operation. The variable bandwidth IIR filter is designed using the elliptical method. The filter is tuned using IIR spectral transformations based on allpass filters.

vbwIIR = dsp.VariableBandwidthIIRFilter(Name,Value) returns a variable bandwidth IIR filter System object, vbwIIR, 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

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 (MATLAB).

SampleRate — Input sample rate

44100 (default) | positive scalar

Specify the sampling rate of the input in Hertz as a finite numeric scalar. 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 — IIR filter order

8 (default) | positive integer

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

Data Types: double | single

PassbandFrequency — Filter passband frequency

512 (default) | positive scalar

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

Tunable: Yes

Dependencies

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

Data Types: double | single

PassbandRipple — Filter passband ripple

1 (default) | positive scalar

Specify the filter passband ripple as a real, positive scalar in decibels (dB). This property is non-tunable.

Data Types: double | single

StopbandAttenuation — Filter Stopband attenuation

60 (default) | positive scalar

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

Data Types: double | single

Usage

For versions earlier than R2016b, use the step function to run the System object algorithm. The arguments to step are the object you created, followed by the arguments shown in this section.

For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

Syntax

y = vbwIIR(x)

Description

y = vbwIIR(x) filters the real or complex input signal x using a variable bandwidth IIR filter to produce the output y. The variable bandwidth IIR 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.VariableBandwidthIIRFilter

freqz	Frequency response of filter
fvtool	Visualize frequency response of DSP filters
impz	Impulse response of discrete-time filter System object
info	Information about filter System object
coeffs	Filter coefficients
cost	Estimate cost for implementing filter System objects
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

Filtering Through a Variable Bandwidth Bandpass IIR Filter

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 examples shows you how to tune the center frequency and bandwidth of the IIR filter.

    Fs = 44100; % Input sample rate
    % Define a bandpass variable bandwidth IIR filter:
    vbwiir = dsp.VariableBandwidthIIRFilter('FilterType','Bandpass',...
                                          'FilterOrder',8,...
                                          '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 = vbwiir(x);
       % Transfer function estimation
       h = tfe(x,y);
       % plot transfer function
       aplot(20*log10(abs(h)))
       % Tune bandwidth and center frequency of the IIR filter
       if (i==250)
         vbwiir.CenterFrequency = 5000;
         vbwiir.Bandwidth = 2000;
       end
    end

Algorithms

This filter covers frequency transformations. A lowpass IIR prototype is designed, 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 prototype passband frequency is set to 0.5. If the FilterType property is 'Lowpass' or 'Highpass', the prototype’s order is equal to the value of FilterOrder. If the FilterType property is 'Bandpass' or 'Bandstop', the prototype filter order 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”, Proc. Inst. Elect. Eng. Vol. 117, No. 8, 1970, pp. 1585-1590.

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).