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Examples

System Identification Using RLS Adaptive Filtering

Use a recursive least-squares (RLS) filter to identify an unknown system modeled with a lowpass FIR filter. Use the dynamic filter visualizer to compare the frequency response of the unknown and estimated systems. This example allows you to dynamically tune key simulation parameters using a user interface (UI). The example also shows you how to use MATLAB Coder™ to generate code for the algorithm and accelerate the speed of its execution.

Open Live Script

Ports

Input

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x—Data input
vector | matrix

Specify the data input as a vector or a matrix. The block treats each column of the input signal as a separate channel. If the input is a two-dimensional signal, the first dimension represents the channel length (or frame size) and the second dimension represents the number of channels. If the input is a one-dimensional signal, then the block interprets it as having a single channel.

The block accepts variable-size input signals, that is, you can change the size of each input channel during simulation but you cannot change the number of channels.

这个港口是不知名的,直到你选择其中的一个parameters:

Specify cutoff frequency from input port
Specify center frequency from input port
Specify bandwidth from input port

Data Types:single|double
Complex Number Support:Yes

Fcut—Filter cutoff frequency
positive scalar

Specify the cutoff frequency of the FIR filter as a real positive scalar in Hzor in normalized frequency units(since R2023a).

Dependencies

To enable this port, select theSpecify cutoff frequency from input portparameter.

Data Types:single|double

Fc—Filter center frequency
positive scalar

Specify the center frequency of the FIR filter as a real positive scalar in Hzor in normalized frequency units(since R2023a).

Dependencies

To enable this port, select theSpecify center frequency from input portparameter.

Data Types:single|double

BW—Filter bandwidth
positive scalar

Specify the bandwidth of the FIR filter as a real positive scalar in Hzor in normalized frequency units(since R2023a).

Dependencies

To enable this port, select theSpecify bandwidth from input portparameter.

Data Types:single|double

Output

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Port_1—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:single|double
Complex Number Support:Yes

Parameters

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

Specify the order of the FIR filter as a positive integer scalar.

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

Specify the type of FIR filter. You can set this parameter to:

Lowpass
Highpass
Bandpass
Bandstop

Specify cutoff frequency from input port—Specify cutoff frequency from input port
`off`(default) |`on`

When you select this check box, specify the cutoff frequency through theFcutport. When you clear this check box, specify the cutoff frequency in the block dialog box through theFilter cutoff frequencyparameter.

Dependency

To enable this parameter, setFilter typetoLowpassorHighpass.

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

Specify the cutoff frequency of the FIR filter as a real positive scalar in Hzor in normalized frequency units(since R2023a).

If you set theSample rate modeparameter to:

Specify on dialogorInherit from input port——滤波器截止频率的值Hz and must be less than half the value of the input sample rate.
Use normalized frequency (0 to 1)——滤波器截止频率的值normalized frequency units. The value must be a positive scalar less than1.0.

(since R2023a)

Tunable:Yes

Dependencies

To enable this parameter:

SetFilter typetoLowpassorHighpass.
Clear theSpecify cutoff frequency from input portparameter.

Specify center frequency from input port—Specify center frequency from input port
`off`(default) |`on`

When you select this check box, specify the center frequency through theFcport. When you clear this check box, specify the center frequency in the block dialog box through theFilter center frequencyparameter.

Dependencies

To enable this parameter, setFilter typetoBandpassorBandstop.

Filter center frequency—Filter center frequency
44100/4 (default) | positive scalar

Specify the center frequency of the FIR filter as a real positive scalar in Hzor in normalized frequency units(since R2023a).

If you set theSample rate modeparameter to:

Specify on dialogorInherit from input port–– The value of the filter center frequency is in Hz and must be less than half the value of the input sample rate.
Use normalized frequency (0 to 1)–– The value of the filter center frequency is in normalized frequency units. The value must be a positive scalar less than1.0.

(since R2023a)

Tunable:Yes

Dependencies

To enable this parameter:

SetFilter typetoBandpassorBandstop.
Clear theSpecify center frequency from input portparameter.

Specify bandwidth from input port—Specify bandwidth from input port
`off`(default) |`on`

When you select this check box, specify the filter bandwidth through theBWport. When you clear this check box, specify the filter bandwidth in the block dialog box through theFilter bandwidthparameter.

Dependency

To enable this parameter, setFilter typetoBandpassorBandstop.

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

Specify the bandwidth of the FIR filter as a real positive scalar in Hzor in normalized frequency units(since R2023a).

If you set theSample rate modeparameter to:

Specify on dialogorInherit from input port–– The value of the filter bandwidth is in Hz and must be less than half the value of the input sample rate.
Use normalized frequency (0 to 1)–– The value of the filter bandwidth is in normalized frequency units. The value must be a positive scalar less than1.0.

(since R2023a)

Tunable:Yes

Dependencies

To enable this parameter:

SetFilter typetoBandpassorBandstop.
Clear theSpecify bandwidth from input portparameter.

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

Specify the window function used to design the FIR filter. You can set this parameter to:

Hann
Hamming
Chebyshev
Kaiser

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

Specify the sidelobe attenuation of the Chebyshev window as a real positive scalar.

Dependencies

To enable this parameter, setWindow functiontoChebyshev.

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

Specify the Kaiser window parameter as a real scalar.

Dependencies

To enable this parameter, setWindow functiontoKaiser.

Sample rate mode—Mode to specify the input sample rate
`Specify on dialog`(default) |`Inherit from input port`|`Use normalized frequency (0 to 1)`

Since R2023a

Specify the input sample rate using one of these options:

Specify on dialog–– Specify the input sample rate in the block dialog box using theInput sample rate (Hz)parameter.
Inherit from input port–– The block inherits the sample rate from the input signal asN/Ts, whereNis the frame size of the input signal andTsis the sample time of the input signal.
Use normalized frequency (0 to 1)–– Specify the filter cutoff frequency, center frequency, and the filter bandwidth in normalized frequency units (0 to 1).

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

Specify the sample rate of the input signal as a positive scalar in Hz.

Dependencies

To enable this parameter, set theSample rate modeparameter toSpecify on dialog.(since R2023a)

View Filter Response—View Filter Response
button

Open the dynamic filter visualizer and display the magnitude response of the variable bandwidth FIR filter. The response is based on the parameters you select in the block dialog box. To update the magnitude response while the dynamic filter visualizer is running, modify the parameters in the dialog box and clickApply.

You can configure the plot settings and the signal measurements from the interface of the visualizer.

On thePlottab, theConfigurationsection allows you to modify the plot settings.

Plot tab contains legend, magnitude phase button, and settings. Generate script, copy display and print sections are also in this tab.

On theMeasurementstab, you can measure the signal statistics, place data cursors, and display the peak values of the selected signal.

Measurements tab contains 3 sections - select channel, modify data cursor settings, and modify peak finder settings.

For more details on the dynamic filter visualizer interface and its tools, seedsp.DynamicFilterVisualizer.

Simulate using—Simulate using
`Code generation`(default) |`Interpreted execution`

Specify the type of simulation to run. You can set this parameter to:

Code generation(default)
Simulate model using generated C code. The first time you run a simulation, Simulink^®generates C code for the block. The C code is reused for subsequent simulations, as long as the model does not change. This option requires additional startup time but provides faster simulation speed thanInterpreted execution.
Interpreted execution
Simulate model using the MATLAB^®interpreter. This option shortens startup time but has slower simulation speed thanCode generation.

Block Characteristics

Data Types	`double`\|`single`
Multidimensional Signals	`No`
Variable-Size Signals	`Yes`

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. Tune the lowpass filter coefficients to a new cutoff frequency ω_c2as follows:

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

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:

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

Lowpass to Bandpass

Obtain a bandpass filter centered at frequency ω₀by 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

你可以将一个低通滤波器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:

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

Generalized Transformation

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_c1to 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 ω₀and bandwidth β, we first apply the lowpass-to-lowpass transformation to go from a lowpass with cutoff ω_cto 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.

Extended Capabilities

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

TheVariable Bandwidth FIR Filterblock supports SIMD code generation using Intel^®AVX2 technology when the input signal has a data type ofsingleordouble.

The SIMD technology significantly improves the performance of the generated code.

Version History

Introduced in R2015a

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R2023a:Support for normalized frequencies

When you set theSample rate modeparameter toUse normalized frequency (0 to 1), you can specify the filter cutoff frequency, center frequency, and filter bandwidth in normalized frequency units (0 to 1).

Variable Bandwidth FIR Filter

Description

Examples

System Identification Using RLS Adaptive Filtering

Ports

Input

x—Data inputvector | matrix

Fcut—Filter cutoff frequencypositive scalar

Dependencies

Fc—Filter center frequencypositive scalar

Dependencies

BW—Filter bandwidthpositive scalar

Dependencies

Output

Port_1—Filtered outputvector | matrix

Parameters

FIR filter order—FIR filter order30(default) | positive integer

Filter type—Filter typeLowpass(default) |Highpass|Bandpass|Bandstop

Specify cutoff frequency from input port—Specify cutoff frequency from input portoff(default) |on

Dependency

Filter cutoff frequency—Filter cutoff frequency512 (default) | positive scalar

Dependencies

Specify center frequency from input port—Specify center frequency from input portoff(default) |on

Dependencies

Filter center frequency—Filter center frequency44100/4 (default) | positive scalar

Dependencies

Specify bandwidth from input port—Specify bandwidth from input portoff(default) |on

Dependency

Filter bandwidth—Filter bandwidth7680 (default) | positive scalar

Dependencies

Window function—Window functionHann(default) |Hamming|Chebyshev|Kaiser

Chebyshev window sidelobe attenuation (dB)—Chebyshev window sidelobe attenuation60 (default) | positive scalar

Dependencies

Kaiser window parameter—Kaiser window parameter0.5 (default) | real scalar

Dependencies

Sample rate mode—Mode to specify the input sample rateSpecify on dialog(default) |Inherit from input port|Use normalized frequency (0 to 1)

Input sample rate (Hz)—Input sample rate44100 (default) | positive scalar

Dependencies

View Filter Response—View Filter Responsebutton

Simulate using—Simulate usingCode generation(default) |Interpreted execution

Block Characteristics

Algorithms

FIR Transformations

References

Extended Capabilities

C/C++ Code GenerationGenerate C and C++ code using Simulink® Coder™.

Version History

R2023a:Support for normalized frequencies

See Also

Objects

Blocks

x—Data input
vector | matrix

Fcut—Filter cutoff frequency
positive scalar

Fc—Filter center frequency
positive scalar

BW—Filter bandwidth
positive scalar

Port_1—Filtered output
vector | matrix

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

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

Specify cutoff frequency from input port—Specify cutoff frequency from input port
`off`(default) |`on`

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

Specify center frequency from input port—Specify center frequency from input port
`off`(default) |`on`

Filter center frequency—Filter center frequency
44100/4 (default) | positive scalar

Specify bandwidth from input port—Specify bandwidth from input port
`off`(default) |`on`

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

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

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

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

Sample rate mode—Mode to specify the input sample rate
`Specify on dialog`(default) |`Inherit from input port`|`Use normalized frequency (0 to 1)`

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

View Filter Response—View Filter Response
button

Simulate using—Simulate using
`Code generation`(default) |`Interpreted execution`

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