dsp.ComplexBandpassDecimator

Extract a frequency subband using a one-sided (complex) bandpass decimator

Description

The dsp.ComplexBandpassDecimator System object™ extracts a specific sub-band of frequencies using a one-sided, multistage, complex bandpass decimator. The object determines the bandwidth of interest using the specified CenterFrequency, DecimationFactor and Bandwidth values.

To extract a frequency subband using a complex bandpass decimator:

  1. Create the dsp.ComplexBandpassDecimator 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

bpdecim = dsp.ComplexBandpassDecimator
bpdecim = dsp.ComplexBandpassDecimator(d)
bpdecim = dsp.ComplexBandpassDecimator(d,Fc)
bpdecim = dsp.ComplexBandpassDecimator(d,Fc,Fs)
bpdecim = dsp.ComplexBandpassDecimator(Name,Value)

Description

bpdecim = dsp.ComplexBandpassDecimator creates a System object that filters each channel of the input over time using a one-sided, multistage, complex bandpass decimation filter. The object determines the bandwidth of interest using the default center frequency, decimation factor, and bandwidth values.

example

bpdecim = dsp.ComplexBandpassDecimator(d) creates a complex bandpass decimator object with the DecimationFactor property set to d.

example

bpdecim = dsp.ComplexBandpassDecimator(d,Fc) creates a complex bandpass decimator object with the DecimationFactor property set to d, and the CenterFrequency property set to Fc.

example

bpdecim = dsp.ComplexBandpassDecimator(d,Fc,Fs) creates a complex bandpass decimator object with the DecimationFactor property set to d, the CenterFrequency property set to Fc, and the SampleRate property set to Fs.

Example: dsp.ComplexBandpassDecimator(48e3/1e3,2e3,48e3);

bpdecim = dsp.ComplexBandpassDecimator(Name,Value) creates a complex bandpass decimator object with each specified property set to the specified value. Enclose each property name in quotes. You can use this syntax with any previous input argument combinations.

Example: dsp.ComplexBandpassDecimator(48e3/1e3,2e3,48e3,'CenterFrequency',1e3);

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 (MATLAB).

Center frequency of the desired band in Hz, specified as a real, finite numeric scalar in the range [-SampleRate/2, SampleRate/2].

Tunable: Yes

Data Types: single | double

Filter design parameters, specified as:

  • 'Decimation factor' –– The object specifies the decimation factor through the Decimation Factor property. The bandwidth of interest (BW) is computed using the following equation:

    BW=Fs/D

    where

    • Fs –– Sample rate specified through SampleRate property.

    • D –– Decimation factor.

  • 'Bandwidth' –– The object specifies the bandwidth through the Bandwidth property. The decimation factor (D) is computed using the following equation:

    D=floor(FsBW+TW)

    where

    • Fs –– Sample rate specified through SampleRate property.

    • BW –– Bandwidth of interest.

    • TW –– Transition width specified through the TransitionWidth property.

  • 'Decimation factor and bandwidth' –– The decimation factor and the bandwidth of interest are specified through the DecimationFactor and Bandwidth properties.

Factor by which to reduce the bandwidth of the input signal, specified as a positive integer. The frame size (number of rows) of the input signal must be a multiple of the decimation factor.

Dependencies

This property applies when you set Specification to either 'Decimation factor' or 'Decimation factor and bandwidth'.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Stopband attenuation of the filter in dB, specified as finite positive scalar.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Transition width of the filter in Hz, specified as a positive scalar.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Width of the frequency band of interest, specified as a real positive scalar in Hz.

Dependencies

This property applies when you set Specification to either 'Bandwidth' or 'Decimation factor and bandwidth'.

Data Types: single | double

Passband ripple of the filter, specified as a positive scalar in dB.

Dependencies

This property applies when you set Specification to either 'Bandwidth' or 'Decimation factor and bandwidth'.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Flag to minimize the number of complex filter coefficients, specified as:

  • true –– The first stage of the multistage filter is bandpass (complex coefficients) centered at the specified center frequency. The first stage is followed by a mixing stage that heterodynes the signal to DC. The remaining filter stages, all with real coefficients, follow.

  • false –– The input signal is first passed through the different stages of the multistage filter. All stages are bandpass (complex coefficients). The signal is then heterodyned to DC if MixToBaseband is true, and the frequency offset resulting from the decimation is nonzero.

Flag to mix the signal to baseband, specified as:

  • true –– The object heterodynes the filtered, decimated signal to DC. This mixing stage runs at the output sample rate of the filter.

  • false –– The object skips the mixing stage.

Dependencies

This property applies when you set MinimizeComplexCoefficients to false.

Sampling rate of the input signal in Hz, specified as a real positive scalar.

Data Types: single | double

Usage

Syntax

y = bpdecim(x)

Description

y = bpdecim(x) filters the real or complex input signal, x, to produce the output, y. The output contains the subband of frequencies specified by the System object properties. The System object filters each channel of the input signal independently over time. The frame size (first dimension) of x must be a multiple of the decimation factor.

Input Arguments

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Data input, specified as a vector or a matrix. The number of rows in the input must be a multiple of the decimation factor.

Data Types: single | double
Complex Number Support: Yes

Output Arguments

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Output of the complex bandpass decimator, returned as a vector or a matrix. The output contains the subband of frequencies specified by the System object properties. The number of rows (frame size) in the output signal is 1/D times the number of rows in the input signal, where D is the decimation factor. The number of channels (columns) does not change.

The data type of the output is same as the data type of the input. The output signal is always complex.

Data Types: single | double
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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costImplementation cost of the complex bandpass decimator
freqzFrequency response of the multirate multistage filter
infoInformation about filter System object
visualizeFilterStagesVisualize filter stages
stepRun System object algorithm
releaseRelease resources and allow changes to System object property values and input characteristics
resetReset internal states of System object

Examples

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Compute the implementation cost of a complex bandpass decimator using the cost function.

Create a dsp.ComplexBandpassDecimator object. Set the DecimationFactor to 12, the CenterFrequency to 5000 Hz, and the SampleRate to 44,100 Hz.

cbp = dsp.ComplexBandpassDecimator(12,5000,44100)
cbp = 
  dsp.ComplexBandpassDecimator with properties:

                CenterFrequency: 5000
                  Specification: 'Decimation factor'
               DecimationFactor: 12
            StopbandAttenuation: 80
                TransitionWidth: 100
    MinimizeComplexCoefficients: true
                     SampleRate: 44100

Compute the implementation cost of cbp using the cost function.

c = cost(cbp)
c = struct with fields:
                      NumCoefficients: 201
                            NumStates: 379
    RealMultiplicationsPerInputSample: 44.3333
          RealAdditionsPerInputSample: 43.8333

Compute the complex frequency response of a complex bandpass decimator using the freqz function.

Create a dsp.ComplexBandpassDecimator object. Set the DecimationFactor to 12, the CenterFrequency to 5000 Hz, and the SampleRate to 44100 Hz. Compute and display the frequency response.

cbp = dsp.ComplexBandpassDecimator(12,5000,44100);
[h,f] = freqz(cbp);
plot(f,20*log10(abs(h)))
grid on
xlabel('Frequency (Hz')
ylabel('h (dB)')

Filter an input signal through a complex bandpass decimator and visualize the filtered spectrum in a spectrum analyzer.

Initialization

Create a dsp.ComplexBandpassDecimator System object™ with center frequency set to 2000 Hz, bandwidth of interest set to 1000 Hz, and sample rate set to 48 kHz. The decimation factor is computed as the ratio of the sample rate to the bandwidth of interest. The input to the decimator is a sine wave with a frame length of 1200 samples with tones at 1625 Hz, 2000 Hz, and 2125 Hz. Create a dsp.SpectrumAnalyzer scope to visualize the signal spectrum.

Fs = 48e3;
CF = 2000;
BW = 1000;
D  =  Fs/BW;
FrameLength = 1200;
bpdecim = dsp.ComplexBandpassDecimator(D,CF,Fs);

sa = dsp.SpectrumAnalyzer('SampleRate',Fs/D,...
    'YLimits',[-120 40],...
    'FrequencyOffset',CF);

tones = [1625 2000 2125];
sin = dsp.SineWave('SampleRate',Fs,'Frequency',tones,...
    'SamplesPerFrame',FrameLength);

Visualize Filter Stages

Using the visualizeFilterStages function, you can visualize the response of each individual filter stage using FVTool.

visualizeFilterStages(bpdecim)

Display Filter info

The info function displays information about the bandpass decimator.

fprintf('%s',info(bpdecim))
Overall Decimation Factor       : 48
Bandwidth                       : 1000 Hz
Number of Filters               : 5
Real multiplications per Input Sample: 14.708333
Real additions per Input Sample      : 13.833333
Number of Coefficients               : 89
Filters:                         
   Filter 1:
   dsp.FIRDecimator     - Decimation Factor   : 2 
   Filter 2:
   dsp.FIRDecimator     - Decimation Factor   : 2 
   Filter 3:
   dsp.FIRDecimator     - Decimation Factor   : 2 
   Filter 4:
   dsp.FIRDecimator     - Decimation Factor   : 3 
   Filter 5:
   dsp.FIRDecimator     - Decimation Factor   : 2 

Stream In and Filter Signal

Construct a for-loop to run for 1000 iterations. In each iteration, stream in 1200 samples (one frame) of the noisy sine wave and apply the complex bandpass decimator on each frame of the input signal. Visualize the input and output spectrum in the spectrum analyzer, sa.

for index = 1:1000
    x = sum(sin(),2) +  1e-4*randn(FrameLength,1);
    z = bpdecim(x);
    sa(z);
end

The bandpass decimator with center frequency at 2000 Hz and a bandwidth of 1000 Hz passes the three sine wave tones at 1625 Hz, 2000 Hz, and 2125 Hz.

Change the center frequency of the decimator to 2400 Hz and filter the signal.

release(bpdecim);
bpdecim.CenterFrequency = 2400
bpdecim = 

  dsp.ComplexBandpassDecimator with properties:

                CenterFrequency: 2400
                  Specification: 'Decimation factor'
               DecimationFactor: 48
            StopbandAttenuation: 80
                TransitionWidth: 100
    MinimizeComplexCoefficients: true
                     SampleRate: 48000

Configure the spectrum analyzer to show the bandwidth of interest, [-1900, 2900] Hz.

release(sa)
sa.FrequencyOffset = 2400;

Stream in the data and filter the signal.

for index = 1:1000
    x = sum(sin(),2) +  1e-4 * randn(FrameLength,1);
    z = bpdecim(x);
    sa(z);
end

The tones at 2000 Hz and 2125 Hz are passed through the decimator, while the tone at 1625 Hz is filtered out.

Algorithms

The complex bandpass decimator is designed by applying a complex frequency shift transformation on a lowpass prototype filter. The lowpass prototype in this case is a multirate, multistage finite impulse response (FIR) filter. The desired frequency shift applies only to the first stage. Subsequent stages scale the desired frequency shift by their respective cumulative decimation factors. For details, see Complex Bandpass Filter Design and Zoom FFT.

Extended Capabilities

Introduced in R2018a