FIR adaptive filter that uses BLMS
adaptfilt.blms will be removed in a future
ha = adaptfilt.blms(l,step,leakage,blocklen,coeffs,states)
ha = adaptfilt.blms(l,step,leakage,blocklen,coeffs,states) constructs
an FIR block LMS adaptive filter
the adaptive filter length (the number of coefficients or taps) and
must be a positive integer.
l defaults to 10.
step is the block LMS step size. You must
set step to a nonnegative scalar. You can use function
maxstep to determine a reasonable range
of step size values for the signals being processed. When unspecified,
leakage is the block LMS leakage factor.
It must be a scalar between 0 and 1. If you set leakage to be less
than one, you implement the leaky block LMS algorithm.
to 1 specifying no leakage in the adapting algorithm.
blocklen is the block length used. It must
be a positive integer and the signal vectors
be divisible by
blocklen. Larger block lengths
result in faster per-sample execution times but with poor adaptation
characteristics. When you choose
a power of 2, use
coeffs is a vector of initial filter coefficients.
it must be a length
l vector of zeros.
states contains a vector of your initial
filter states. It must be a length
l vector and
defaults to a length
l vector of zeros when you
do not include it in your calling function.
For information on how to run data through your adaptive filter
object, see the Adaptive Filter Syntaxes section of the reference
In the syntax for creating the
the input options are properties of the object created. This table
lists the properties for the adjoint LMS object, their default values,
and a brief description of the property.
Defines the adaptive filter algorithm the object uses during adaptation
Any positive integer
Reports the length of the filter, the number of coefficients or taps
Vector of elements
Vector containing the initial filter coefficients. It
must be a length
Vector of elements
Vector of the adaptive filter states.
Specifies the leakage parameter. Allows you to implement a leaky algorithm. Including a leakage factor can improve the results of the algorithm by forcing the algorithm to continue to adapt even after it reaches a minimum value. Ranges between 0 and 1.
Vector of length
Size of the blocks of data processed in each iteration
Sets the block LMS algorithm step size used for each
iteration of the adapting algorithm. Determines both how quickly and
how closely the adaptive filter converges to the filter solution.
Determine whether the filter states get restored to their
starting values for each filtering operation. The starting values
are the values in place when you create the filter.
Use an adaptive filter to identify an unknown 32nd-order FIR filter. In this example 500 input samples result in 500 iterations of the adaptation process. You see in the plot that follows the example code that the adaptive filter has determined the coefficients of the unknown system under test.
x = randn(1,500); % Input to the filter b = fir1(31,0.5); % FIR system to be identified no = 0.1*randn(1,500); % Observation noise signal d = filter(b,1,x)+no; % Desired signal mu = 0.008; % Block LMS step size n = 5; % Block length ha = adaptfilt.blms(32,mu,1,n); [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;
Based on looking at the figures here, the adaptive filter correctly identified the unknown system after 500 iterations, or fewer. In the lower plot, you see the comparison between the actual filter coefficients and those determined by the adaptation process.
Shynk, J.J.,"Frequency-Domain and Multirate Adaptive Filtering," IEEE® Signal Processing Magazine, vol. 9, no. 1, pp. 14-37, Jan. 1992.