Filter Design Toolbox

adaptfilt.nlms

Construct a normalized LMS FIR adaptive filter object

Syntax

• ha = adaptfilt.nlms(l,step,leakage,offset,coeffs,states)
  

Description

ha = adaptfilt.nlms(l,step,leakage,offset,coeffs,states) constructs a normalized least-mean squares (NLMS) FIR adaptive filter object named ha.

Input Arguments

Entries in the following table describe the input arguments for adaptfilt.nlms.

Input Argument	Description
l	Adaptive filter length (the number of coefficients or taps) and it must be a positive integer. l defaults to 10.
step	NLMS step size. It must be a scalar between 0 and 2. Setting this step size value to one provides the fastest convergence. step defaults to 1.
leakage	NLMS leakage factor. It must be a scalar between zero and one. When it is less than one, a leaky NLMS algorithm results. leakage defaults to 1 (no leakage).
offset	Specifies an optional offset for the denominator of the step size normalization term. You must specify offset to be a scalar greater than or equal to zero. Nonzero offsets can help avoid a divide-by-near-zero condition that causes errors. Use this to avoid dividing by zero (or by very small numbers) when the square of the input data norm becomes very small (when the input signal amplitude becomes very small). When you omit it, offset defaults to zero.
coeffs	Vector composed of your initial filter coefficients. Enter a length l vector. coeffs defaults to a vector of zeros with length equal to the filter order.
states	Your initial adaptive filter states appear in the states vector. It must be a vector of length l-1. states defaults to a length l-1 vector with zeros for all of the elements.

adaptfilt.nlms Object Properties

In the syntax for creating the adaptfilt object, the input options are properties of the object you create. This table list all the properties for normalized LMS objects, their default values, and a brief description of the property.

Property	Range	Property Description
Algorithm	None	Reports the adaptive filter algorithm the object uses during adaptation
FilterLength	Any positive integer	Reports the length of the filter, the number of coefficients or taps
Coefficients	Vector of elements	Vector containing the initial filter coefficients. It must be a length l vector where l is the number of filter coefficients. coeffs defaults to length l vector of zeros when you do not provide the argument for input.
States	Vector of elements, data type double	Vector of the adaptive filter states. states defaults to a vector of zeros which has length equal to (l - 1).
StepSize		NLMS step size. It must be a scalar between zero and one. Setting this step size value to one provides the fastest convergence. step defaults to one.
Leakage		NLMS leakage factor. It must be a scalar between zero and one. When it is less than one, a leaky NLMS algorithm results. leakage defaults to 1 (no leakage).
Offset		Specifies an optional offset for the denominator of the step size normalization term. You must specify offset to be a scalar greater than or equal to zero. Nonzero offsets can help avoid a divide-by-near-zero condition that causes errors. Use this to avoid dividing by zero (or by very small numbers) when the square of the input data norm becomes very small (when the input signal amplitude becomes very small). When you omit it, offset defaults to zero.
ResetBeforeFiltering	off or on	Determine whether the filter states and coefficients get restored to their starting values for each filtering operation. The starting values are the values in place when you create the filter. ResetBeforeFiltering returns to zero any property value that the filter changes during processing. Property values that the filter does not change are not affected. Defaults to 'on'.
NumSamplesProcessed	Any integer	Returns the number of samples processed during filtering. Defaults to zero.

Example

To help you compare this algorithm's performance to other LMS-based algorithms, such as BLMS or LMS, this example demonstrates the NLMS adaptive filter in use to identify the coefficients of an unknown FIR filter of order equal to 32--an example used in other adaptive filter examples.

• x  = randn(1,500);     % Input to the filter
  b  = fir1(31,0.5);     % FIR system to be identified
  n  = 0.1*randn(1,500); % Observation noise signal
  d  = filter(b,1,x)+n;  % Desired signal
  mu = 1;                % NLMS step size
  offset = 50;           % NLMS offset
  ha = adaptfilt.nlms(32,mu,1,offset);
  [y,e] = filter(ha,x,d);
  subplot(2,1,1); plot(1:500,[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([b.',ha.coefficients.']);
  legend('Actual','Estimated'); 
  xlabel('Coefficient #'); ylabel('Coefficient Value'); grid on;
  

See Also

adaptfilt.ap, adaptfilt.ap2, adaptfilt.lms, adaptfilt.rls, adaptfilt.swrls

adaptfilt.lsl

adaptfilt.pbfdaf