dsp.ComplexBandpassDecimator - Extract a frequency subband using a one-sided (complex) bandpass

  decimator - MATLAB ([original](https://www.mathworks.com/help/dsp/ref/dsp.complexbandpassdecimator-system-object.html)) ([raw](?raw))

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 andBandwidth values.

To extract a frequency subband using a complex bandpass decimator:

Create the dsp.ComplexBandpassDecimator 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?

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

Creation

Syntax

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.

`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 toFs.

example

`bpdecim` = dsp.ComplexBandpassDecimator(`Name=Value`) sets properties using one or more name-value arguments. For example, to specify a decimation factor of 8, setDecimationFactor to 8.

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 therelease function unlocks them.

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

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

Center frequency of the desired band Fc, specified as a real scalar in Hz or in normalized frequency units (since R2024b).

If you set NormalizedFrequency to true, the center frequency value must be in the range (−1,1). If you setNormalizedFrequency to false, the center frequency value must be in the range (–Fs/2,Fs/2), where Fs is the value of the SampleRate property.

Tunable: Yes

Data Types: single | double

Filter design parameters, specified as:

"Decimation factor" –– The object specifies the decimation factor through theDecimation Factor property. The bandwidth of interest (BW) is computed using the following equation:
where
- Fs –– Sample rate specified through the 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:
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

To enable this property, setSpecification to "Decimation factor" or "Decimation factor and bandwidth".

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

Transition width of the filter TW, specified as a positive scalar in Hz or in normalized frequency units (since R2024b).

Width of the frequency band of interest BW, specified as a real positive scalar in Hz or in normalized frequency units (since R2024b).

Dependencies

To enable this property, setSpecification to"Bandwidth" or "Decimation factor and bandwidth".

Data Types: single | double

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

Dependencies

To enable this property, setSpecification to"Bandwidth" or "Decimation factor and bandwidth".

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 ifMixToBaseband 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 setMinimizeComplexCoefficients to false.

Since R2024b

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

true –– The center frequency, transition width, and bandwidth must be in the normalized frequency units (0 to 1).
When you set the NormalizedFrequency property totrue while creating the object and you do not set the frequency specifications, the object automatically sets the default values to normalized frequency units using the default sample rate of 44.1 kHz.
cbd = dsp.ComplexBandpassDecimator(NormalizedFrequency=true)
cbd =
dsp.ComplexBandpassDecimator with properties:
CenterFrequency: 0
Specification: "Decimation factor"
DecimationFactor: 2
StopbandAttenuation: 80
TransitionWidth: 0.0045
MinimizeComplexCoefficients: true
NormalizedFrequency: true

When you set the NormalizedFrequency property totrue after you create the object, you must specify the center frequency, transition width, and bandwidth in normalized units before you run the object algorithm.
cbd = dsp.ComplexBandpassDecimator
cbd =
dsp.ComplexBandpassDecimator with properties:
CenterFrequency: 0
Specification: "Decimation factor"
DecimationFactor: 2
StopbandAttenuation: 80
TransitionWidth: 100
MinimizeComplexCoefficients: true
NormalizedFrequency: false
SampleRate: 44100
To specify the normalized frequency values, setNormalizedFrequency totrue and manually convert the frequency values in Hz to the normalized values using the input sample rate in Hz and the interpolation factor. For example, if the input sample rate Fs is 44.1 kHz, the corresponding center frequency in normalized units is_CF_Hz/(Fs/2), the corresponding bandwidth in normalized units is_BW_Hz/(Fs/2), and the corresponding transition width in normalized units is_TW_Hz/(Fs/2).
cbd = dsp.ComplexBandpassDecimator;
cbd.NormalizedFrequency = true;
cbd.TransitionWidth = 100/(44100/2)
cbd =
dsp.ComplexBandpassDecimator with properties:
CenterFrequency: 0
Specification: "Decimation factor"
DecimationFactor: 2
StopbandAttenuation: 80
TransitionWidth: 0.0045
MinimizeComplexCoefficients: true
NormalizedFrequency: true

false –– The center frequency, bandwidth, and transition width values are in Hz. You can specify the input sample rate through theSampleRate property.

Data Types: logical

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

Dependencies

To enable this property, setNormalizedFrequency to false. (since R2024b)

Data Types: single | double

Usage

Syntax

Description

[y](#d126e262040) = bpdecim([x](#d126e261995)) 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 of size_P_-by-Q. The number of input rows_P_ can be arbitrary and does not have to be a multiple of the decimation factor.

This object supports variable-size input signals, that is, the frame length (number of rows) of the signal can change even when the object is locked. However, the number of channels (columns) must remain constant.

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.

When the input is of size P_-by-Q, and_P is not a multiple of the decimation factor_D_, the output signal has an upper bound size ofceil(P/D)-by-Q, where D is the decimation factor. If P is a multiple of the decimation factor, then the output is of size (P/D)-by-Q. 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:

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cost	Implementation cost of the complex bandpass decimator
freqz	Frequency response of the multirate multistage filter
info	Information about filter System object
visualize	Visualize filter stages
filterAnalyzer	Analyze filters with Filter Analyzer app

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

Create a dsp.ComplexBandpassDecimator object. Set the DecimationFactor to 12, center frequency to 0.2, and the NormalizedFrequency to true.

cbp = dsp.ComplexBandpassDecimator(12,0.2,NormalizedFrequency=true)

cbp = dsp.ComplexBandpassDecimator with properties:

            CenterFrequency: 0.2000
              Specification: 'Decimation factor'
           DecimationFactor: 12
        StopbandAttenuation: 80
            TransitionWidth: 0.0045
MinimizeComplexCoefficients: true
        NormalizedFrequency: true

Compute the implementation cost of cbp using the cost function.

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)")

Figure contains an axes object. The axes object with xlabel Frequency (Hz), ylabel h (dB) contains an object of type line.

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 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 = spectrumAnalyzer(SampleRate=Fs/D,... Method="welch",... YLimits=[-120 40],... FrequencyOffset=CF);

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

Visualize Filter Stages

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

Figure contains an axes object. The axes object with title Magnitude Response (dB), xlabel Frequency (Hz), ylabel Magnitude (dB) (normalized to 0 dB) contains 5 objects of type line. These objects represent Filter #1, Filter #2, Filter #3, Filter #4, Filter #5.

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
        NormalizedFrequency: false
                 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

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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 under these conditions:
- Input signal is complex-valued.
- Input signal has a data type of single ordouble.
  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.
In the code you generate from this object, the decimator output is a fixed-size signal if the input signal is fixed size and is a multiple of the decimation factor. If the input is not a multiple of the decimation factor or if the input is a variable-size signal, then the decimator output is of variable-size.

Version History

Introduced in R2018a

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The visualizeFilterStages function has been renamed tovisualize. Existing instances of this function continue to run. For new instances, use visualize.

The visualize function now launches a MATLAB® figure to visualize the filter stages of the complex bandpass decimator.

When you set the NormalizedFrequency property totrue, you must specify the center frequency, bandwidth, and the transition width in normalized frequency units (0 to 1). For more information, see theNormalizedFrequency property description.

This object supports an input signal with an arbitrary frame length, so the input frame length does not have to be a multiple of the decimation factor.