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# Documentation

## LMS Filter: Noise Cancellation

This example shows how to generate HDL code from a MATLAB® design that implements an LMS filter. It also shows how to design a testbench that implements noise cancellation using this filter.

Introduction

The algorithm computes the filtered output, error and the filter weights for a given input and desired signal using the Least Mean Squares (LMS) algorithm. The LMS filter is then used to identify an FIR signal embedded in noise.

```design_name = 'mlhdlc_lms_fcn';
testbench_name = 'mlhdlc_lms_noise_canceler_tb';
```

Let us take a look at the MATLAB design

```type(design_name);
```
```%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% MATLAB Design: Adaptive Noise Canceler algorithm using Least Mean Square
% (LMS) filter implemented in MATLAB
%
% Key Design pattern covered in this example:
% (1) Use of function calls
% (2) Function inlining vs instantiation knobs available in the coder
% (3) Use of system objects in the testbench to stream test vectors into the design
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%#codegen

function [filtered_signal, y, fc] = mlhdlc_lms_fcn(input, desired, step_size, reset_weights)
%
% 'input'  : The signal from Exterior Mic which records the ambient noise.
% 'desired': The signal from Pilot's Mic which includes
%            original music signal and the noise signal
% 'err_sig': The difference between the 'desired' and the filtered 'input'
%            It represents the estimated music signal (output of this block)
%
% The LMS filter is trying to retrieve the original music signal ('err_sig')
% from Pilot's Mic by filtering the Exterior Mic's signal and using it to
% cancel the noise in Pilot's Mic. The coefficients/weights of the filter
% are updated(adapted) in real-time based on 'input' and 'err_sig'.

% register filter coefficients
persistent filter_coeff;
if isempty(filter_coeff)
filter_coeff = zeros(1, 40);
end

% Variable Filter
% call 'tapped_delay_fcn' function on path to create 40-step tapped delay
delayed_signal = mtapped_delay_fcn(input);

% apply filter coefficients
weight_applied = delayed_signal .* filter_coeff;

% call 'treesum' function on matlab path to sum up the results
filtered_signal = mtreesum_fcn(weight_applied);

% Output estimated Original Signal
td = desired;
tf = filtered_signal;

esig = td - tf;
y = esig;

% Update Weights
% call 'update_weight_fcn' function on matlab path to
% calculate the new weights
updated_weight = update_weight_fcn(step_size, esig, delayed_signal, ...
filter_coeff, reset_weights);

% update filter coefficients register
filter_coeff = updated_weight;

fc = filter_coeff;

function y = mtreesum_fcn(u)
%Implement the 'sum' function without a for-loop
%  y = sum(u);

%  The loop based implementation of 'sum' function is not ideal for
%  HDL generation and results in a longer critical path.
%  A tree is more efficient as it results in
%  delay of log2(N) instead of a delay of N delay

%  This implementation shows how to explicitly implement the vector sum in
%  a tree shape to enable hardware optimizations.

%  The ideal way to code this generically for any length of 'u' is to use
%  recursion but it is not currently supported by MATLAB Coder

% NOTE: To instruct MATLAB Coder to compile an external function,
% add the following compilation directive or pragma to the function code
%#codegen

% This implementation is hardwired for a 40tap filter.

level1 = vsum(u);
level2 = vsum(level1);
level3 = vsum(level2);
level4 = vsum(level3);
level5 = vsum(level4);
level6 = vsum(level5);
y = level6;

function output = vsum(input)

coder.inline('always');

vt = input(1:2:end);

for i = int32(1:numel(input)/2)
k = int32(i*2);
vt(i) = vt(i) + input(k);
end

output = vt;

function tap_delay = mtapped_delay_fcn(input)
% The Tapped Delay function delays its input by the specified number
% of sample periods, and outputs all the delayed versions in a vector
% form. The output includes current input

% NOTE: To instruct MATLAB Coder to compile an external function,
% add the following compilation directive or pragma to the function code
%#codegen

persistent u_d;
if isempty(u_d)
u_d = zeros(1,40);
end

u_d = [u_d(2:40), input];

tap_delay = u_d;

function weights = update_weight_fcn(step_size, err_sig, delayed_signal, filter_coeff, reset_weights)
% This function updates the adaptive filter weights based on LMS algorithm

%   Copyright 2007-2010 The MathWorks, Inc.

% NOTE: To instruct MATLAB Coder to compile an external function,
% add the following compilation directive or pragma to the function code
%#codegen

step_sig = step_size .* err_sig;
correction_factor = delayed_signal .* step_sig;
updated_weight = correction_factor + filter_coeff;

if reset_weights
weights = zeros(1,40);
else
weights = updated_weight;
end
```
```type(testbench_name);
```
```% returns an adaptive FIR filter System object,
% HLMS, that computes the filtered output, filter error and the filter
% weights for a given input and desired signal using the Least Mean
% Squares (LMS) algorithm.

clear('mlhdlc_lms_fcn');

hfilt2 = dsp.FIRFilter(...
'Numerator', fir1(10, [.5, .75]));
rng('default'); % always default to known state
x = randn(1000,1);                              % Noise
d = step(hfilt2, x) + sin(0:.05:49.95)';         % Noise + Signal

stepSize = 0.01;
reset_weights =false;

hSrc = dsp.SignalSource(x);
hDesiredSrc = dsp.SignalSource(d);

hOut = dsp.SignalSink;
hErr = dsp.SignalSink;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Call to the design
%%%%%%%%%%%%%%%%%%%%%%%%%%%%
while (~isDone(hSrc))
[y, e] = mlhdlc_lms_fcn(step(hSrc), step(hDesiredSrc), stepSize, reset_weights);
step(hOut, y);
step(hErr, e);
end

figure('Name', [mfilename, '_signal_plot']);
subplot(2,1,1), plot(hOut.Buffer), title('Noise + Signal');
subplot(2,1,2),plot(hErr.Buffer), title('Signal');
```

Create a New Folder and Copy Relevant Files

Execute the following lines of code to copy the necessary example files into a temporary folder.

```mlhdlc_demo_dir = fullfile(matlabroot, 'toolbox', 'hdlcoder', 'hdlcoderdemos', 'matlabhdlcoderdemos');
mlhdlc_temp_dir = [tempdir 'mlhdlc_lms_nc'];

% create a temporary folder and copy the MATLAB files
cd(tempdir);
[~, ~, ~] = rmdir(mlhdlc_temp_dir, 's');
mkdir(mlhdlc_temp_dir);
cd(mlhdlc_temp_dir);

copyfile(fullfile(mlhdlc_demo_dir, [design_name,'.m*']), mlhdlc_temp_dir);
copyfile(fullfile(mlhdlc_demo_dir, [testbench_name,'.m*']), mlhdlc_temp_dir);
```

Simulate the Design

It is always a good practice to simulate the design with the testbench prior to code generation to make sure there are no runtime errors.

```mlhdlc_lms_noise_canceler_tb
```

Creating a New Project From the Command Line

```coder -hdlcoder -new mlhdlc_lms_nc
```

Next, add the file 'mlhdlc_lms_fcn.m' to the project as the MATLAB Function and 'mlhdlc_lms_noise_canceler_tb.m' as the MATLAB Test Bench.

You can refer to Getting Started with MATLAB to HDL Workflow tutorial for a more complete tutorial on creating and populating MATLAB HDL Coder™ projects.

Run Fixed-Point Conversion and HDL Code Generation

Launch the Workflow Advisor from the Build tab and right click on the 'Code Generation' step and choose the option 'Run to selected task' to run all the steps from the beginning through the HDL code generation.

Examine the generated HDL code by clicking on the hyperlinks in the Code Generation Log window.

Clean up the Generated Files

You can run the following commands to clean up the temporary project folder.

```mlhdlc_demo_dir = fullfile(matlabroot, 'toolbox', 'hdlcoder', 'hdlcoderdemos', 'matlabhdlcoderdemos');
mlhdlc_temp_dir = [tempdir 'mlhdlc_lms_nc'];
clear mex;
cd (mlhdlc_demo_dir);
rmdir(mlhdlc_temp_dir, 's');
```