Filter Design Toolbox

Examples of Adaptive Filters That Use LMS Algorithms

This section provides introductory examples using some of the least mean squares (LMS) adaptive filter functions in the toolbox.

The Filter Design Toolbox provides many adaptive filter design functions that use the LMS algorithms to search for the optimal solution to the adaptive filter, including:

• adaptfilt.lms--implement the LMS algorithm to solve the Weiner-Hopf equation and find the filter coefficients for an adaptive filter.
• adaptfilt.nlms--implement the normalized variation of the LMS algorithm to solve the Weiner-Hopf equation and determine the filter coefficients of an adaptive filter.
• adaptfilt.sd--implement the sign-data variation of the LMS algorithm to solve the Weiner-Hopf equation and determine the filter coefficients of an adaptive filter. The correction to the filter weights at each iteration depends on the sign of the input x(k).
• adaptfilt.se--implement the sign-error variation of the LMS algorithm to solve the Weiner-Hopf equation and determine the filter coefficients of an adaptive filter. The correction applied to the current filter weights for each successive iteration depends on the sign of the error, e(k).
• adaptfilt.ss--implement the sign-sign variation of the LMS algorithm to solve the Weiner-Hopf equation and determine the filter coefficients of an adaptive filter. The correction applied to the current filter weights for each successive iteration depends on both the sign of x(k) and the sign of e(k).

To demonstrate the differences and similarities between the various LMS algorithms supplied in the toolbox, the LMS and NLMS adaptive filter examples use the same filter for the unknown system. In this case, the unknown filter is one of the filters used in the examples from gremez Examples--the constrained lowpass filter.

• [b,err,res]=gremez(12,[0 0.4 0.5 1], [1 1 0 0], [1 0.2],...
  {'w' 'c'});
  

From the figure you see that the filter is indeed lowpass and constrained to 0.2 ripple in the stopband. With this as the baseline, the adaptive LMS filter examples use the adaptive LMS algorithms and their initialization functions, to identify this filter in a system identification role. To review the general model for system ID mode, look at System Identification for the layout.

For the sign variations of the LMS algorithm, the examples use noise cancellation as the demonstration application, as opposed to the system identification application used in the LMS examples.

Algorithms

adaptfilt.lms Example--System Identification