%% 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)