adaptncdemo.m

自适应滤波器设计是现在滤波器设计的重要一方面

%% Adaptive Noise Canceling (ANC) applied to Fetal Electrocardiography.
% This demonstration illustrates the application of adaptive filters to
% noise removal using adaptive noise canceling.  
%
%   Author(s): Scott C. Douglas
%   Copyright 1999-2005 The MathWorks, Inc.

%%
% In adaptive noise canceling, a measured signal d(n) contains two signals:
%        - an unknown signal of interest v(n)
%        - an interference signal u(n)
% The goal is to remove the interference signal from the measured
% signal by using a reference signal x(n) that is highly correlated with 
% the interference signal.  The example considered here is an application
% of adaptive filters to fetal electrocardiography, in which a maternal 
% heartbeat signal is adaptively removed from a fetal heartbeat sensor
% signal.  This example is adapted from Widrow, et al, "Adaptive noise 
% canceling:  Principles and applications," Proc. IEEE, vol. 63, no. 12, 
% pp. 1692-1716, December 1975.  

%% Creating the Maternal Heartbeat Signal
% In this example, we shall simulate the shapes of the electrocardiogram 
% for both the mother and fetus.  The following commands create an 
% electrocardiogram signal that a mother's heart might produce assuming
% a 4000 Hz sampling rate.  The heart rate for this signal is approximately
% 89 beats per minute, and the peak voltage of the signal is 3.5
% millivolts. 

x1 = 3.5*ecg(2700).';
y1 = sgolayfilt(kron(ones(1,13),x1),0,21);
n = 1:30000;
del = round(2700*rand(1));
mhb = y1(n + del);
t = 0.00025:0.00025:7.5;
plot(t,mhb);
axis([0 2.5 -4 4]);
grid;
xlabel('Time [sec]');
ylabel('Voltage [mV]');
title('Maternal Heartbeat Signal');


%% Creating the Fetal Heartbeat Signal
% The heart of a fetus beats noticeably faster than that of its mother, 
% with rates ranging from 120 to 160 beats per minute.  The amplitude of
% of the fetal electrocardiogram is also much weaker than that of the
% maternal electrocardiogram.  The following series of commands creates 
% an electrocardiogram signal corresponding to a heart rate of 139 beats
% per minute and a peak voltage of 0.25 millivolts. 

x2 = 0.25*ecg(1725);
y2 = sgolayfilt(kron(ones(1,20),x2),0,17);
del = round(1725*rand(1));
fhb = y2(n + del);
plot(t,fhb);
axis([0 2.5 -1 1]);
grid;
xlabel('Time [sec]');
ylabel('Voltage [mV]');
title('Fetal Heartbeat Signal');


%% The Measured Fetal Electrocardiogram
% The measured fetal electrocardiogram signal from the abdomen of the mother
% is usually dominated by the maternal heartbeat signal that propagates
% from the chest cavity to the abdomen.  We shall describe this propagation
% path as a linear FIR filter with 10 randomized coefficients.  In
% addition, we shall add a small amount of uncorrelated Gaussian noise to 
% simulate any broadband noise sources within the measurement.  Can you
% determine the fetal heartbeat rate by looking at this measured signal?   

Wopt = [0 1.0 -0.5 -0.8 1.0  -0.1 0.2 -0.3 0.6 0.1];
d = filter(Wopt,1,mhb) + fhb + 0.02*randn(size(mhb));
plot(t,d);
axis([0 2.5 -4 4]);
grid;
xlabel('Time [sec]');
ylabel('Voltage [mV]');
title('Measured Signal');


%% The Measured Maternal Electrocardiogram
% The maternal electrocardiogram signal is obtained from the chest of the
% mother. The goal of the adaptive noise canceler in this task is to
% adaptively remove the maternal heartbeat signal from the fetal
% electrocardiogram signal. The canceler needs a reference signal
% generated from a maternal electrocardiogram to perform this task.  Just
% like the fetal electrocardiogram signal, the maternal electrocardiogram
% signal will contain some additive broadband noise.

x = mhb + 0.02*randn(size(mhb));
plot(t,x);
axis([0 2.5 -4 4]);
grid;
xlabel('Time [sec]');
ylabel('Voltage [mV]');
title('Reference Signal');


%% Applying the Adaptive Noise Canceler
% The adaptive noise canceler can use most any adaptive procedure to
% perform its task.  For simplicity, we shall use the least-mean-square
% (LMS) adaptive filter with 15 coefficients and a step size of 0.00007.
% With these settings, the adaptive noise canceler converges reasonably
% well after a few seconds of adaptation--certainly a reasonable period 
% to wait given this particular diagnostic application.  

h = adaptfilt.lms(15,0.00007);
[y,e] = filter(h,x,d);
plot(t,d,'b',t,e,'r');
axis([0 7 -4 4]);
grid;
xlabel('Time [sec]');
ylabel('Voltage [mV]');
title('Convergence of Adaptive Noise Canceler');
legend('Measured Signal','Error Signal');


%% Recovering the Fetal Heartbeat Signal
% The output signal y(n) of the adaptive filter contains the estimated 
% maternal heartbeat signal, which is not the ultimate signal of interest.  
% What remains in the error signal e(n) after the system has converged is
% an estimate of the fetal heartbeat signal along with residual measurement
% noise.  Using the error signal, can you estimate the heart rate of the 
% fetus?

plot(t,e,'r');
axis([6 7.5 -0.5 0.5]);
grid;
xlabel('Time [sec]');
ylabel('Voltage [mV]');
title('Steady-State Error Signal');


displayEndOfDemoMessage(mfilename)