# Documentation

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# maxstep

Maximum step size for adaptive filter convergence

`maxstep` will be removed in a future release. Use `dsp.LMSFilter` or `dsp.BlockLmsFilter` instead.

## Syntax

`mumax = maxstep(ha,x)[mumax,mumaxmse] = maxstep(ha,x)`

## Description

`mumax = maxstep(ha,x)` predicts a bound on the step size to provide convergence of the mean values of the adaptive filter coefficients. The columns of the matrix `x` contain individual input signal sequences. The signal set is assumed to have zero mean or nearly so.

`[mumax,mumaxmse] = maxstep(ha,x)` predicts a bound on the adaptive filter step size to provide convergence of the LMS adaptive filter coefficients in the mean-square sense. `maxstep` issues a warning when `ha.stepsize` is outside of the range 0 < `ha.stepsize` < `mumaxmse`/2.

`maxstep` is available for the following adaptive filter objects:

 Note   With `adaptfilt.nlms` filter objects, `maxstep` uses the following slightly different syntax:```mumax = maxstep(ha) [mumax,mumaxmse] = maxstep(ha)```The maximum step size for convergence is fully defined by the filter object `ha`. Matrix `x` is not necessary. If you include an `x` input matrix, MATLAB returns an error.

## Examples

Analyze and simulate a 32-coefficient (31st-order) LMS adaptive filter object. To demonstrate the adaptation process, run 2000 iterations and 50 trials.

```% Specify [numiterations,numexamples] = size(x); x = zeros(2000,50); d = x; obj = fdesign.lowpass('n,fc',31,0.5); hd = design(obj,'window'); % FIR filter to identified. coef = cell2mat(hd.coefficients); % Convert cell array to matrix. for k=1:size(x,2); % Create input and desired response signal % matrices. % Set the (k)th input to the filter. x(:,k) = filter(sqrt(0.75),[1 -0.5],sign(randn(size(x,1),1))); n = 0.1*randn(size(x,1),1); % (k)th observation noise signal. d(:,k) = filter(coef,1,x(:,k))+n; % (k)th desired signal end. end mu = 0.1; % LMS step size. ha = adaptfilt.lms(32,mu); [mumax,mumaxmse] = maxstep(ha,x); Warning: Step size is not in the range 0 < mu < mumaxmse/2: Erratic behavior might result. mumax mumax = 0.0623 mumaxmse mumaxmse = 0.0530```