noisedm.html

交流 模糊控制 交流 模糊控制

<!--
This HTML is auto-generated from an m-file.
Your changes will be overwritten.
--><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:x-large">Adaptive Noise Cancellation</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">This is a demonstration of adaptive nonlinear noise cancellation using
the Fuzzy Logic Toolbox functions ANFIS and GENFIS1.
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Copyright 1994-2002 The MathWorks, Inc.
$Revision: 1.13 $
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Defined below is a hypothetical information signal x sampled
at 100Hz over 6 seconds.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">time = (0:0.01:6)';
x = sin(40./(time+0.01));
subplot(1,1,1)
plot(time, x)
title(<span style="color:#B20000">'Information Signal x'</span>)
xlabel(<span style="color:#B20000">'time'</span>)
ylabel(<span style="color:#B20000">'x'</span>)</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" vspace="5" hspace="5" src="noisedm_img_02_01.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Unfortunately, the information signal x cannot be measured
without an interference signal n2, which is generated from
another noise source n1 via a certain unknown nonlinear
process.
</p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">Shown in the window is the noise source n1.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">n1 = randn(size(time));
plot(time, n1)
title(<span style="color:#B20000">'Noise Source n1'</span>)
xlabel(<span style="color:#B20000">'time'</span>)
ylabel(<span style="color:#B20000">'n1'</span>)</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" vspace="5" hspace="5" src="noisedm_img_03_01.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">The interference signal n2 that appears in the measured
signal is assumed to be generated via an unknown nonlinear
equation:
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">n2(k) = 4*sin(n1(k))*n1(k-1)/(1+n1(k-1)^2)
</pre><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">This nonlinear characteristic is shown as a surface in the
window.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">domain = linspace(min(n1), max(n1), 20);
[xx, yy] = meshgrid(domain, domain);
zz = 4*sin(xx).*yy./(1+yy.^2);

surf(xx, yy, zz);
xlabel(<span style="color:#B20000">'n1(k)'</span>);
ylabel(<span style="color:#B20000">'n1(k-1)'</span>);
zlabel(<span style="color:#B20000">'n2(k)'</span>);
title(<span style="color:#B20000">'Unknown Channel Characteristics That Generate Interference'</span>);
axis([min(domain) max(domain) min(domain)  max(domain) min(zz(:)) max(zz(:))]);
set(gca, <span style="color:#B20000">'box'</span>, <span style="color:#B20000">'on'</span>);</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" vspace="5" hspace="5" src="noisedm_img_04_01.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">The noise source n1 and interference n2 are shown together.
Note that n2 is related to n1 via the highly nonlinear process
shown previously; it is hard to see if these two signals are
correlated in any way.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">n1d0 = n1;                            <span style="color:green">% n1 delay 0</span>
n1d1 = [0; n1d0(1:length(n1d0)-1)];   <span style="color:green">% n1 delay 1</span>
n2 = 4*sin(n1d0).*n1d1./(1+n1d1.^2);  <span style="color:green">% interference</span>
axis_limit = [min(time) max(time) min([n1;n2]) max([n1;n2])];
subplot(2,1,1)
plot(time, n1);
ylabel(<span style="color:#B20000">'noise n1'</span>); axis(axis_limit);
subplot(2,1,2)
plot(time, n2);
ylabel(<span style="color:#B20000">'interference n2'</span>); axis(axis_limit);</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" vspace="5" hspace="5" src="noisedm_img_05_01.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">The measured signal m is the sum of the original information
signal x and the interference n2. However, we do not  know
n2. The only signals available to us are the noise signal n1
and the measured signal m, and our task is to recover the
original information signal x. In the demo window is the
measured signal m that combines x and n2.
</p><pre xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="position: relative; left:30px">m = x + n2;             <span style="color:green">% measured signal</span>
subplot(1,1,1)
plot(time, m)
title(<span style="color:#B20000">'Measured Signal'</span>)
xlabel(<span style="color:#B20000">'time'</span>)
ylabel(<span style="color:#B20000">'m'</span>)</pre><img xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" vspace="5" hspace="5" src="noisedm_img_06_01.gif"><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd" style="color:#990000; font-weight:bold; font-size:medium; page-break-before: auto;"><a name=""></a></p><p xmlns:mwsh="http://www.mathworks.com/namespace/mcode/v1/syntaxhighlight.dtd">We will use the function ANFIS to identify the nonlinear
relationship between n1 and n2. Though n2 is not directly
available, we can take m as a "contaminated" version of n2