Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

dsp.LMSFilter System object

Package: dsp

LMS adaptive filter

Description

The LMSFilter implements an adaptive FIR filter object that returns the filtered output, the error vector, and filter weights. The LMS filter uses one of five different LMS algorithms.

To implement the adaptive FIR filter object:

  1. Define and set up your adaptive FIR filter object. See Construction.

  2. Call step to implement the filter according to the properties of dsp.LMSFilter. The behavior of step is specific to each object in the toolbox.

    Note:   Starting in R2016b, instead of using the step method to perform the operation defined by the System object™, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations.

Construction

lms = dsp.LMSFilter returns an adaptive FIR filter object, lms, that computes the filtered output, filter error and the filter weights for a given input and desired signal using the Least Mean Squares (LMS) algorithm.

lms = dsp.LMSFilter('PropertyName', PropertyValue,...) returns an LMS filter object, lms, with each property set to the specified value.

lms = dsp.LMSFilter(LEN,'PropertyName',PropertyValue,...) returns an LMS filter object, lms, with the Length property set to LEN, and other specified properties set to the specified values.

Properties

Method

Method to calculate filter weights

Specify the method used to calculate filter weights as LMS, Normalized LMS, Sign-Error LMS, Sign-Data LMS, or Sign-Sign LMS. The default is LMS.

Length

Length of FIR filter weights vector

Specify the length of the FIR filter weights vector as a positive integer. The default is 32.

StepSizeSource

How to specify adaptation step size

Choose how to specify the adaptation step size factor as Property or Input port. The default is Property.

StepSize

Adaptation step size

Specify the adaptation step size factor as a nonnegative real number. For convergence of the normalized LMS method, set the step size greater than 0 and less than 2. This property only applies when the StepSizeSource property is Property. The default is 0.1. This property is tunable.

LeakageFactor

Leakage factor used in LMS filter

Specify the leakage factor as a real number between 0 and 1 inclusive. A leakage factor of 1 corresponds to no leakage in the adapting method. The default is 1. This property is tunable.

InitialConditions

Initial conditions of filter weights

Specify the initial values of the FIR filter weights as a scalar or vector of length equal to the Length property value. The default is 0.

AdaptInputPort

Enable weight adaptation

Specify when the LMS filter should adapt the filter weights. By default, the value of this property is false, and the object continuously updates the filter weights. When this property is set to true, an adaptation control input is provided to the step method. If the value of this input is nonzero, the object continuously updates the filter weights. If the input is zero, the filter weights remain at their current value.

WeightsResetInputPort

Enable weight reset

Specify when the LMS filter should reset the filter weights. By default, the value of this property is false, and the object does not reset the weights. When this property is set to true, a reset control input is provided to the step method, and the WeightsResetCondition property applies. The object resets the filter weights based on the values of the WeightsResetCondition property and the reset input to the step method.

WeightsResetCondition

Reset trigger setting for filter weights

Specify the event to reset the filter weights as Rising edge, Falling edge, Either edge, or Non-zero. The LMS filter resets the filter weights based on the values of this property and the reset input to the step method. This property only applies when the WeightsResetInputPort property is true. The default is Non-zero.

WeightsOutput

Enable returning filter weights

Specify how to output the adapted filter weights as one of the following:

  • 'Last' (default) — The object returns a column vector of weights corresponding to the last sample of the data frame. The length of the weights vector is the value given by the Length property.

  • 'All' — The object returns a FrameLength-by-Length matrix of weights. The matrix corresponds to the full sample-by-sample history of weights values for all FrameLength samples of the input values. Each row in the matrix corresponds to a set of LMS filter weights calculated for the corresponding input sample.

  • 'None' — This setting disables the weights output.

 Fixed-Point Properties

Methods

maxstepMaximum step size for LMS adaptive filter convergence
msepredPredicted mean-square error for LMS filter
msesimMean-squared error for LMS filter
resetReset filter states for LMS filter
stepApply LMS adaptive filter to input
Common to All System Objects
clone

Create System object with same property values

getNumInputs

Expected number of inputs to a System object

getNumOutputs

Expected number of outputs of a System object

isLocked

Check locked states of a System object (logical)

release

Allow System object property value changes

Examples

expand all

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).

lms1 = dsp.LMSFilter(11,'StepSize',0.01);
filt = dsp.FIRFilter; % System to be identified
filt.Numerator = fir1(10,.25);
x = randn(1000,1); % input signal

d = filt(x) + 0.01*randn(1000,1); % desired signal
[y,e,w] = lms1(x,d);

subplot(2,1,1);
plot(1:1000, [d,y,e]);
title('System Identification of an FIR filter');
legend('Desired', 'Output', 'Error');
xlabel('time index');
ylabel('signal value');
subplot(2,1,2);
stem([filt.Numerator.',w]);
legend('Actual','Estimated');
xlabel('coefficient #');
ylabel('coefficient value');

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).

Initialize the LMS filter with a length of 11 and step size of 0.05.

FrameSize = 100; NIter = 10;
lmsfilt2 = dsp.LMSFilter('Length',11,'Method','Normalized LMS', ...
    'StepSize',0.05);
firfilt2 = dsp.FIRFilter('Numerator', fir1(10,[.5, .75]));
sinewave = dsp.SineWave('Frequency',0.01, ...
    'SampleRate',1,'SamplesPerFrame',FrameSize);
TS = dsp.TimeScope('TimeSpan',FrameSize*NIter,'TimeUnits','Seconds',...
    'YLimits',[-3 3],'BufferLength',2*FrameSize*NIter, ...
    'ShowLegend',true,'ChannelNames', ...
    {'Noisy signal', 'Filtered signal'});

Pass the noisy input signal into the LMS filter and view the filtered output in the time scope.

for k = 1:NIter
    x = randn(FrameSize,1);       % Input signal
    d = firfilt2(x) + sinewave(); % Noise + Signal
    [y,e,w] = lmsfilt2(x,d);
    TS([d,e]);          % Noisy = channel 1; Filtered = channel 2
end

Note: This example runs only in R2017a or later. If you are using a release earlier than R2017a, the object does not output a full sample-by-sample history of filter weights. If you are using a release earlier than R2016b, replace each call to the function with the equivalent step syntax. For example, myObject(x) becomes step(myObject,x).

Initialize the dsp.LMSFilter System object™ and set the WeightsOutput property to 'All'. This setting enables the LMS filter to output a matrix of weights with dimensions [FrameLength Length], corresponding to the full sample-by-sample history of weights for all FrameLength samples of input values.

FrameSize = 15000;
lmsfilt3 = dsp.LMSFilter('Length',63,'Method','LMS', ...
    'StepSize',0.001,'LeakageFactor',0.99999, ...
    'WeightsOutput','All'); % full Weights history

w_actual = fir1(64,[0.5 0.75]);
firfilt3 = dsp.FIRFilter('Numerator',w_actual);
sinewave = dsp.SineWave('Frequency',0.01, ...
    'SampleRate',1,'SamplesPerFrame',FrameSize);

TS = dsp.TimeScope('TimeSpan',FrameSize,'TimeUnits','Seconds', ...
    'YLimits',[-0.25 0.75],'BufferLength',2*FrameSize, ...
    'ShowLegend',true,'ChannelNames', ...
    {'Coeff 33 Estimate','Coeff 34 Estimate','Coeff 35 Estimate', ...
    'Coeff 33 Actual','Coeff 34 Actual','Coeff 35 Actual'});

Run one frame and output the full adaptive weights history, w.

x = randn(FrameSize,1);       % Input signal
d = firfilt3(x) + sinewave(); % Noise + Signal
[~,~,w] = lmsfilt3(x,d);

Each row in w is a set of weights estimated for the respective input sample. Each column in w gives the complete history of a specific weight. Plot the actual weight and the entire history of the 33rd, 34th, and the 35th weight. In the plot, you can see that the estimated weight output eventually converges with the actual weight as the adaptive filter receives input samples and continues to adapt.

idxBeg = 33;
idxEnd = 35;
TS([w(:,idxBeg:idxEnd), repmat(w_actual(idxBeg:idxEnd),FrameSize,1)]);

Algorithms

This filter's algorithm is defined by the following equations.

y(n)=wT(n1)u(n)e(n)=d(n)y(n)w(n)=αw(n1)+f(u(n),e(n),μ)

The various LMS adaptive filter algorithms available in this System object are defined as:

  • LMS:

    f(u(n),e(n),μ)=μe(n)u*(n)

  • Normalized LMS:

    f(u(n),e(n),μ)=μe(n)u(n)ε+uH(n)u(n)

  • Sign-Error LMS:

    f(u(n),e(n),μ)=μsign(e(n))u*(n)

  • Sign-Data LMS:

    f(u(n),e(n),μ)=μe(n)sign(u(n))

    where u(n) is real.

  • Sign-Sign LMS:

    f(u(n),e(n),μ)=μsign(e(n))sign(u(n))

    where u(n) is real.

The variables are as follows:

VariableDescription

n

The current time index

u(n)

The vector of buffered input samples at step n

u*(n)

The complex conjugate of the vector of buffered input samples at step n

w(n)

The vector of filter weight estimates at step n

y(n)

The filtered output at step n

e(n)

The estimation error at step n

d(n)

The desired response at step n

µ

The adaptation step size

αThe leakage factor (0 < α ≤ 1)

Extended Capabilities

See Also

System Objects

Blocks

Introduced in R2012a

Was this topic helpful?