RLS Adaptive Filter (DSP Blockset)

Compute filter estimates for an input using the RLS adaptive filter algorithm.

Library

Adaptive Filters, in Filtering

Description

The RLS Adaptive Filter block recursively computes the least-squares estimate (RLS) of the FIR filter coefficients based on an externally generated error signal.

The corresponding RLS filter is expressed in matrix form as

where

^-1 denotes the inverse exponential weighting. The variables are as follows


Variable	Description
n	The current algorithm iteration
u(n)	The buffered input samples at step n
P(n)	The inverse correlation matrix at step n
k(n)	The gain vector 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
	The memory weighting factor

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

Note that the implementation of the algorithm in the block does not precisely parallel the above equations; symmetry of the inverse correlation matrix P(n) is exploited to decrease the total number of computations by a factor of two.

The FIR filter length parameter specifies the length of the filter that the RLS algorithm estimates. The Memory weighting factor corresponds to

in the equations, and specifies how quickly the filter "forgets" past sample information. Setting

=1 specifies an infinite memory; typically, 0.95

1.

The Initial value of filter taps specifies the initial value

as a vector, or as a scalar to be repeated for all vector elements. The initial value of P(n) is

where

is specified by the Initial input variance estimate parameter.

Dialog Box

FIR filter length: The length of the FIR filter.
Memory weighting factor: The exponential weighting factor, in the range [0,1]. A value of 1 specifies an infinite memory.
Initial value of filter taps: The initial FIR filter coefficients.
Initial input variance estimate: The initial value of 1/P(n).
Adapt input: Enables the Adapt port.

References

Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1989.

Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.