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LMS Update

Estimate weights of LMS adaptive filter

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  • Library:

  • DSP System Toolbox / Filtering / Adaptive Filters

  • LMS Update block

Description

TheLMS Updateblock estimates the weights of an LMS adaptive filter. The block accepts the data and error as inputs and computes the filter weights based on the algorithm the block chooses. For more details on the algorithms, seeAlgorithms.

You can use this block to compute the adaptive filter weights in applications such as system identification, inverse modeling, and filtered-x LMS algorithms, which are used in acoustic noise cancellation. For more details, seeReferences.

Ports

Input

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数据自适应滤波器的输入。块accepts single-precision or double-precision floating point inputs. All inputs must be scalars and must have the same data type and precision.

Data Types:single|double
Complex Number Support:Yes

Error between the output signal and the desired signal.

Data Types:single|double
Complex Number Support:Yes

To enable this port, setStep size sourcetoInput port.

Data Types:single|double

When the input to this port is not zero, the block updates the filter weights. When the input to this port is 0, the filter weights do not change.

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

When the input to this port is not zero, the block resets the filter weights to their initial values. When the input to this port is 0, the filter weights do not change.

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

Output

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The length of the filter weights vector is the value in theFilter lengthparameter.

Data Types:single|double

Parameters

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The block uses one of the listed algorithms to compute the filter weights. For more details on the algorithms, seeAlgorithms.

Filter lengthspecifies the length of the weights vector the block generates through theWtsoutput port.

  • Property— Specify the filter adaptation size using theStep size (mu)parameter.

  • Input port— Pass filter adaptation size using theMuinput port.

Step size (mu)indicates the amount by which the filter weights are updated in each iteration. Choose an optimal step size so that the filter is stable and the convergence speed is optimal.

To enable this parameter, setStep size sourcetoProperty.

This parameter is tunable. You can change its value even during the simulation.

Leakage factor (0 to 1)prevents unbounded growth of the filter coefficients by reducing the drift of the coefficients from their optimum values. A leakage factor of1.0indicates no leakage. If you encounter coefficient drift, that is, large fluctuation about the optimum solution, decrease the leakage factor until the coefficient fluctuation becomes small.

This parameter is tunable. You can change its value even during the simulation.

This parameter specifies the initial value of the filter weights,w(n-1). The block uses this value to compute the weights,w(n), whenn = 1. For more details, seeAlgorithms.

When you select this check box, theAdaptinput port appears on the block. When the input to this port is greater than 0, the block updates the filter weights. When the input to this port is less than or equal to 0, the filter weights do not change.

When you select this check box, theResetinput port appears on the block. When the input to this port is greater than 0, the block resets the filter weights to their initial values. When the input to this port is less than or equal to 0, the filter weights do not change.

  • Code generation

    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.

Model Examples

Active Noise Control with Simulink Real-Time

Active Noise Control with Simulink Real-Time

设计一个实时usi有源噪声控制系统ng a Speedgoat® Simulink® Real-Time™ target.

Block Characteristics

Data Types

double|single

Direct Feedthrough

no

Multidimensional Signals

no

Variable-Size Signals

no

Zero-Crossing Detection

no

Algorithms

The block computes filter weight estimates using w ( n ) = α w ( n − 1 ) + f ( u ( n ) , e ( n ) , μ ) .

The function f ( u ( n ) , e ( n ) , μ ) is defined according to the LMS algorithm you specify through theAlgorithmparameter:

  • LMS— f ( u ( n ) , e ( n ) , μ ) = μ e ( n ) u * ( n )

  • Normalized LMS— f ( u ( n ) , e ( n ) , μ ) = μ e ( n ) u ∗ ( n ) ε + u H ( n ) u ( n )

    In theNormalized LMSalgorithm,εis a small positive constant that overcomes the potential numerical instability in the update of weights.

    For double-precision floating-point inputs,εis2.2204460492503131e-016. For single-precision floating-point inputs,εis1.192092896e-07. For fixed-point input,εis 0.

  • Sign-Error LMS— f ( u ( n ) , e ( n ) , μ ) = μ sign ( e ( n ) ) u * ( n )

  • Sign-Data LMS— f ( u ( n ) , e ( n ) , μ ) = μ e ( n ) sign ( u ( n ) ) , whereu(n) is real

  • Sign-Sign LMS— f ( u ( n ) , e ( n ) , μ ) = μ sign ( e ( n ) ) sign ( u ( n ) ) , whereu(n) is real

In the previous equations:

  • n— The current time index

  • u(n) — The vector of buffered input samples at stepn

  • u*(n) — The complex conjugate of the vector of buffered input samples at stepn

  • w(n) — The vector of filter weight estimates at stepn

  • e(n)— The estimation error at stepn

  • µ— The adaptation step size

  • α— The leakage factor (0 ≤ α ≤ 1)

References

[1] Madisetti, Vijay, and Douglas Williams. "Introduction to Adaptive Filters."The Digital Signal Processing Handbook.Boca Raton, FL: CRC Press, 1999.

[2] Akhtar, M. T., M. Abe, M. Kawamata. "Modified-filtered-x LMS algorithm based active noise control systems with improved online secondary-path modeling." IEEE Symposium on Circuits and Systems, 2004.

Extended Capabilities

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

See Also

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Topics

Introduced in R2016b

DSP System Toolbox Documentation

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