LMS Adaptive Filter (DSP Blockset)

Compute filter estimates for an input using the normalized LMS adaptive filter algorithm.

Library

Adaptive Filters, in Filtering

Description

The LMS Adaptive Filter block implements an adaptive FIR filter using the stochastic gradient algorithm known as the normalized Least Mean-Square (LMS) algorithm:

The variables are as follows


Variable	Description
n	The current algorithm iteration
u(n)	The buffered input samples at step n
	The vector of filter-tap 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 unit-less adaptation constant

To overcome potential numerical instability in the tap-weight update, a small positive constant (a = 1e-10) has been added in the denominator.

To turn off normalization, deselect the Use normalization check box in the parameter dialog box. The block then computes the filter-tap estimate as

The block icon has port labels corresponding to the inputs and outputs of the LMS algorithm.


Block Ports	Corresponding Variables
`In`	u, the scalar input, which is internally buffered into the vector u(n) used by the algorithm
`Out`	y(n), the filtered scalar output
`Err`	e(n), the scalar estimation error
`Taps`	, the vector of filter-tap estimates

An optional Adapt input port is added when the Adapt input check box is selected in the dialog box. When this port is enabled, the block continuously adapts the filter coefficients while the Adapt input is nonzero. A zero-valued input to the Adapt port causes the block to stop adapting, and to hold the filter coefficients at their current values until the next nonzero Adapt input.

The FIR filter length parameter specifies the length of the filter that the LMS algorithm estimates. The Step size parameter corresponds to µ in the equations, and specifies how quickly the filter forgets past sample information. Typically, for convergence in the mean square, 0<µ<2. The Initial value of filter taps specifies the initial value

as a vector, or as a scalar to be repeated for all vector elements.

Dialog Box

FIR filter length: The length of the FIR filter.
Step-size: The step size, usually in the range (0,2).
Initial value of filter taps: The initial FIR filter coefficients.
Use normalization: Select or deselect normalization.
Adapt input: Enables the Adapt port.

References

Haykin, S. Adaptive Filter Theory. 3rd ed. Englewood Cliffs, NJ: Prentice Hall, 1996.