LMS Update
Estimate weights of LMS adaptive filter
 Library:
DSP System Toolbox / Filtering / Adaptive Filters
Description
The LMS Update block 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, see Algorithms.
You can use this block to compute the adaptive filter weights in applications such as system identification, inverse modeling, and filteredx LMS algorithms, which are used in acoustic noise cancellation. For more details, see References.
Ports
Input
Output
Parameters
Model Examples
Block Characteristics
Data Types 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

Algorithms
The block computes filter weight estimates using $$w(n)=\alpha w(n1)+f(u(n),e(n),\mu )$$.
The function $$f(u(n),e(n),\mu )$$ is defined according to the LMS algorithm you specify through the Algorithm parameter:
LMS
— $$f(u(n),e(n),\mu )=\mu e(n){u}^{*}(n)$$Normalized LMS
— $$f(u(n),e(n),\mu )=\mu e(n)\frac{{u}^{\ast}(n)}{\epsilon +{u}^{H}(n)u(n)}$$In the
Normalized LMS
algorithm, ε is a small positive constant that overcomes the potential numerical instability in the update of weights.For doubleprecision floatingpoint inputs, ε is
2.2204460492503131e016
. For singleprecision floatingpoint inputs, ε is1.192092896e07
. For fixedpoint input, ε is 0.SignError LMS
— $$f(u(n),e(n),\mu )=\mu \text{sign}(e(n)){u}^{*}(n)$$SignData LMS
— $$f(u(n),e(n),\mu )=\mu e(n)\text{sign}(u(n))$$, where u(n) is realSignSign LMS
— $$f(u(n),e(n),\mu )=\mu \text{sign}(e(n))\text{sign}(u(n))$$, where u(n) is real
In the previous equations:
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
e(n) — The estimation error at step n
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. "Modifiedfilteredx LMS algorithm based active noise control systems with improved online secondarypath modeling." IEEE Symposium on Circuits and Systems, 2004.