dsp.ParameterSmoother

Smooth input parameters using exponential smoothing

Since R2024a

Description

The dsp.ParameterSmoother System object™ gradually updates the input filter parameters until the parameters reach the desired value. The object uses a first-order IIR filter to smooth the parameters. For more information, see Parameter Smoothing.

To smooth input parameters:

1. Create the dsp.ParameterSmoother 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?

Creation

Syntax

paramSmoother = dsp.ParameterSmoother

paramSmoother = dsp.ParameterSmoother(numParam)

paramSmoother = dsp.ParameterSmoother(Name=Value)

Description

paramSmoother = dsp.ParameterSmoother returns a parameter smoother object with a smoothing factor of 0.6.

paramSmoother = dsp.ParameterSmoother(numParam) returns a parameter smoother object with the number of parameters specified in numParam.

paramSmoother = dsp.ParameterSmoother(Name=Value) returns a parameter smoother object with additional properties specified by one or more Name-Value arguments. For example, SmoothingMode='Smoothing time',SmoothingTime=2 sets the smoothing time to 2 seconds.

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.

NumParameters — Number of parameters

1 (default) | positive integer

Number of parameters, specified as a positive integer.

Tunable: Yes

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

SmoothingMode — Mode to use for smoothing

'Smoothing factor' (default) | 'Smoothing time'

Mode to use for smoothing, specified as one of these:

• 'Smoothing factor' –– Specify the smoothing factor through the SmoothingFactor property.

• 'Smoothing time' –– Specify the smoothing time through the SmoothingTime property.

For more information on these two modes, see Parameter Smoothing.

SmoothingFactor — Smoothing factor

0.6 (default) | scalar in the range [0, 1)

Smoothing factor α, specified as a scalar in the range [0, 1). When α = 0, the object does not smooth the parameters. As α approaches 1, smoothing and therefore the number of redesigns increase. For more information on the effect of α on smoothing, see Parameter Smoothing.

Tunable: Yes

Dependencies

To enable this property, set the SmoothingMode property to 'Smoothing factor'.

Data Types: single | double

SampleTime — Sample time of input parameters

1 (default) | positive scalar

Sample time T of the input parameters, specified as a positive scalar in seconds. This value determines the frequency with which the object updates the instantaneous values of the input parameters until the parameters reach the target value.

Dependencies

To enable this property, set the SmoothingMode property to 'Smoothing time'.

Data Types: single | double

SmoothingTime — Smoothing time in seconds

10 (default) | nonnegative scalar

Smoothing time τ in seconds, specified as a nonnegative scalar. This value indicates the time it takes for the parameter to change to exp(−T/τ)×current value + (1−exp(−T/τ))×target value, where T is the value you specify in the SampleTime property. For more information on the effect of τ on smoothing, see Parameter Smoothing.

Tunable: Yes

Dependencies

To enable this property, set the SmoothingMode property to 'Smoothing time'.

Data Types: single | double

Usage

Syntax

y = paramSmoother(x)

Description

y = paramSmoother(x) smoothes the input parameter x.

Input Arguments

x — Input parameter to smooth

scalar | vector | matrix

Input parameter to smooth, specified as a scalar, vector, or a matrix.

The number of input parameters must equal the value you specify in the NumParameters property.

Data Types: single | double

Output Arguments

y — Smoothed parameter

scalar | vector | matrix

Smoothed value of the parameter, returned as a scalar, vector, or a matrix. This is the instantaneous value of the parameter and it changes until the parameter reaches the target value.

The number of outputs the object returns equals the value you specify in the NumParameters property.

Data Types: single | double

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)

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

Design Second-Order Section Filter by Varying Smoothing Factor

Design and implement a second-order section filter using the designBandpassIIR function and the dsp.SOSFilter object. Vary the lower and higher 3-dB cutoff frequencies and the stopband attenuation of the filter. Smooth these parameters using the dsp.ParameterSmoother object. Vary the smoothing factor and note the change in how the object smooths these parameter values.

Set the target values of the three frequency specification parameters.

• Lower 3-dB cutoff frequency to 0.8 in normalized frequency units.

• Higher 3-dB cutoff frequency to 0.9 in normalized frequency units.

• Stopband attenuation to 120 dB.

F3dB1 = 0.8; 
F3dB2 = 0.9;
Astop = 120;

Initialize the dsp.ParameterSmoother object with a smoothing factor of 0.995. As the smoothing factor approaches 1, smoothing increases and the parameter values change more gradually.

smooth = dsp.ParameterSmoother(3,SmoothingFactor=0.995)

smooth = 
  dsp.ParameterSmoother with properties:

      NumParameters: 3
      SmoothingMode: 'Smoothing factor'
    SmoothingFactor: 0.9950

Initialize the dsp.SOSFilter object.

sosFilter = dsp.SOSFilter(CoefficientSource="Input port")

sosFilter = 
  dsp.SOSFilter with properties:

            Structure: 'Direct form II transposed'
    CoefficientSource: 'Input port'
       HasScaleValues: false

  Use get to show all properties

Initialize the spectrumAnalyzer object to plot the spectrum of the filter output. The two timescope objects plot the variation in the parameters with time and the target values of the parameters.

sa = spectrumAnalyzer(PlotAsTwoSidedSpectrum=false,...
    AveragingMethod="exponential",ForgettingFactor=0.7,...
    SampleRate=2);
tsFreq = timescope(SampleRate=2,...
    TimeSpanSource="property",TimeSpan=2999,...
    YLimits=[0 1],...
    ShowLegend=1,ChannelNames=["TargetF3dB1","TargetF3dB2","F3dB1","F3dB2"], ...
    Title="Smoothing Factor = 0.995");
tsAstop = timescope(SampleRate=2,...
    TimeSpanSource="property",TimeSpan=2999,...
    YLimits=[0 130],...
    ShowLegend=1,ChannelNames=["TargetAstop","Astop"],...
    Title="Smoothing Factor = 0.995");

Change the frequency specification parameters for a brief period during simulation. The dsp.ParameterSmoother object smooths the values when they change. The target frequency specification parameters changes abruptly, but the smoothed values change more gradually. Design the second-order section filter using the smoothed values. Pass a random signal to the filter and plot the output spectrum in the spectrum analyzer. Since the input is a random signal, the output spectrum shows the frequency response of the filter.

With each iteration, the time scope plots update with the changing values of the parameters. The frequency response of the filter updates accordingly in the spectrum analyzer.

for idx = 1:6000
    if idx == 2000
        F3dB1 = 0.5;
        F3dB2 = 0.7;
        Astop = 80;
    elseif idx == 4000
        F3dB1 = 0.8;
        F3dB2 = 0.9;
        Astop = 120;
    end
    [F3dB1S,F3dB2S,AstopS] = smooth(F3dB1,F3dB2,Astop);
    [b,a] = designBandpassIIR(HalfPowerFrequency1=F3dB1S,HalfPowerFrequency2=F3dB2S,StopbandAttenuation=AstopS,CascadeSectionsForm="sos");
    y = sosFilter(randn(1024,1),b,a);
    sa(y);
    tsFreq(F3dB1,F3dB2,F3dB1S,F3dB2S)
    tsAstop(Astop,AstopS)
end

Change Smoothing Factor

Change the smoothing factor of the dsp.ParameterSmoother object to 0.8 and rerun the simulation. The parameters change more abruptly and reach the target values very quickly since the smoothing factor is low.

Vary Smoothing Time of Gain in Speech Signal

Change the gain of a speech signal. Smooth the gain parameter by specifying the smoothing time. Smoothing time and smoothing factor are equivalent ways of specifying the smoothing behavior of the parameters. This example shows the effect of changing the smoothing time on the gain of the speech signal.

Initialize the dsp.ParameterSmoother object with a smoothing time of 2 seconds.

smooth = dsp.ParameterSmoother(1,SmoothingMode="Smoothing time",...
    SmoothingTime=2,SampleTime=1)

smooth = 
  dsp.ParameterSmoother with properties:

    NumParameters: 1
    SmoothingMode: 'Smoothing time'
       SampleTime: 1
    SmoothingTime: 2

Create an audio file reader to read a speech signal containing 1024 samples per frame.

afr = dsp.AudioFileReader

afr = 
  dsp.AudioFileReader with properties:

           Filename: '/mathworks/devel/bat/filer/batfs2566-0/Bdoc24b.2725827/build/runnable/matlab/toolbox/dsp/dsp/samples/speech_dft.mp3'
          PlayCount: 1
          ReadRange: [1 Inf]
    SamplesPerFrame: 1024
     OutputDataType: 'double'

  Use get to show all properties

Play the signal using the audioDeviceWriter object.

adw = audioDeviceWriter(SampleRate=afr.SampleRate)

adw = 
  audioDeviceWriter with properties:

        Device: 'Default'
    SampleRate: 22050

  Use get to show all properties

Visualize the variation in the gain parameter using the timescope object.

ts = timescope(ChannelNames=["Target Gain","Gain"],...
    TimeSpanSource="property",TimeSpan=100,...
    YLimits=[0 1.2],Title="Smoothing Time = 2 seconds");

Initialize the target gain to 1. Change the target gain to 0.1 for a brief period of the signal duration. The dsp.ParameterSmoother object smooths the gain value when it changes. The time scope shows the smoothing behavior. The target gain value changes abruptly, but the smoothed gain changes more gradually.

targetgain = 1;
for i = 1:100
    gainS = smooth(targetgain);
    y = gainS*afr();
    if i == 20
        targetgain = 0.1;
    elseif i == 70
        targetgain = 1;
    end
    adw(y);
    ts(targetgain,gainS)
end

Change Smoothing Time

Change the smoothing time to 4 seconds. Rerun the simulation with this new smoothing time value. The smoothing is more gradual and the parameter takes longer time to reach its target value.

More About

Parameter Smoothing

Parameter smoothing gradually changes the values of parameters until the desired value is reached.

The algorithm uses a first-order IIR filter to smooth the parameter.

$$g[n]=\alpha g[n-1]+\left(1-\alpha \right)t[n],$$

where:

• g[n] is the instantaneous value of the parameter.

• t[n] is the target value of the parameter.

• α is the smoothing factor. When α = 0, the algorithm does not smooth the parameters. As α approaches 1, smoothing and therefore the number of redesigns increase.

Effect of α on Parameter Smoothing

Assume that the initial current value of the parameter g[0] is 0 and the target value t[n] is 1.

Here is the progression of the smoothed parameter using these values.

g[1] = 1−α

g[2] = 1−α²

g[3] = 1−α³

g[n] = 1−αⁿ

Smoothing can also be expressed in terms of time by expressing α as exp(−nT/τ), where T is the sample time of the parameter (in seconds) and τ is the smoothing time (in seconds).

$$g[n]=e^{-nT/\tau }g[n-1]+\left(1-e^{-nT/\tau }\right)t[n]$$

Effect of τ on Parameter Smoothing

Assume that the initial current value of the parameter g[0] is 0 and the target value t[n] is 1. Also, assume that T divides τ perfectly.

Here is the progression of the smoothed parameter using these values.

In one time constant τ seconds, g[1] = 1−exp(−1) = 0.6321, the parameter reaches 63.21% of the target value.

In two time constants, g[2] = 1−exp(−2) = 0.8647, the parameter reaches 86.47 % of the target value.

In three time constants, g[3] = 1−exp(−3) = 0.9502, the parameter reaches approximately 95% of the target value.

Extended Capabilities

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

Version History

Introduced in R2024a