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John K. Luebs
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.DS_Store
/.build
/Packages
xcuserdata/
DerivedData/
.swiftpm/configuration/registries.json
.swiftpm/xcode/package.xcworkspace/contents.xcworkspacedata
.netrc
*.class

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{
"originHash" : "bf0b92ec2751ab82eed76f0b5f4c42d45557a303569895153367fd1d19d1045a",
"pins" : [
{
"identity" : "swift-algorithms",
"kind" : "remoteSourceControl",
"location" : "https://github.com/apple/swift-algorithms",
"state" : {
"revision" : "f6919dfc309e7f1b56224378b11e28bab5bccc42",
"version" : "1.2.0"
}
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{
"identity" : "swift-numerics",
"kind" : "remoteSourceControl",
"location" : "https://github.com/apple/swift-numerics.git",
"state" : {
"revision" : "0a5bc04095a675662cf24757cc0640aa2204253b",
"version" : "1.0.2"
}
}
],
"version" : 3
}

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// swift-tools-version: 6.0
// The swift-tools-version declares the minimum version of Swift required to build this package.
import PackageDescription
let package = Package(
name: "EcgSynKit",
products: [
// Products define the executables and libraries a package produces, making them visible to other packages.
.library(
name: "EcgSynKit",
targets: ["EcgSynKit"]),
],
dependencies: [
.package(url: "https://github.com/apple/swift-algorithms", from: "1.2.0"),
// .package(url: "https://github.com/AudioKit/KissFFT.git", from: "1.0.0")
.package(path: "./KissFFT/")
],
targets: [
// Targets are the basic building blocks of a package, defining a module or a test suite.
// Targets can depend on other targets in this package and products from dependencies.
.target(
name: "EcgSynKit",
dependencies: [
.product(name: "Algorithms", package: "swift-algorithms"),
.product(name: "KissFFT", package: "kissfft")
]),
.testTarget(
name: "EcgSynKitTests",
dependencies: ["EcgSynKit"]
),
]
)

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import Algorithms
import Foundation
import KissFFT
struct Parameters {
/// The number of beats to simulate.
let numBeats: Int = 256
/// The ECG sampling frequency in Hz.
let sfEcg: Int = 256
/// The internal sampling frequency in Hz.
var sfInternal: Int = 512
/// The mean heart rate in beats per minute.
let hrMean: Double = 60.0
/// The standard deviation of the heart rate.
let hrStd: Double = 1.0
/// The ratio of power between low and high frequencies.
let lfhfRatio: Double = 0.5
/// The ECT amplitude in mV.
let amplitude: Double = 1.4
/// RNG seed value.
let seed: Int = 0
/// Amplitude of the noise.
let aNoise: Double = 0.0
/// The angle of each attractor (P, Q, R, S, T) around the limit cycle, in radians.
let theta: [Double] = [-60, -15, 0, 15, 90].map { $0 * .pi / 180 }
/// Widths of the attractors (P, Q, R, S, T).
let a: [Double] = [1.2, -5, 30, -7.5, 0.75]
/// The position of attractors (P, Q, R, S, T) above or below the z=0 plane.
let b: [Double] = [0.25, 0.1, 0.1, 0.1, 0.4]
/// Mayer wave frequency in Hz.
let flo = 0.1
/// flo standard deviation.
let flostd = 0.01
/// Respiratory rate frequency in Hz.
let fhi = 0.25
/// fhi standard deviation.
let fhistd = 0.01
}
/// Compute fft or inverse (based on sign) of vector data, where [i] is real and [i+1] is imaginary, i starts
/// from 0.
func fft(data: inout [Double], isign: Int) {
let isign = Double(isign)
let n = data.count
var j = 0
for i in stride(from: 0, to: n, by: 2) {
if j > i {
data.swapAt(j, i)
data.swapAt(j + 1, i + 1)
}
var m = n / 2
while m >= 2, j >= m {
j -= m
m /= 2
}
j += m
}
var mmax = 2
while mmax < n {
let istep = 2 * mmax
let theta = isign * (2.0 * .pi / Double(mmax))
let wtemp = sin(0.5 * theta)
let wpr = -2.0 * wtemp * wtemp
let wpi = sin(theta)
var wr = 1.0
var wi = 0.0
for m in stride(from: 0, to: mmax, by: 2) {
for i in stride(from: m, to: n, by: istep) {
let j = i + mmax
let tempr = wr * data[j] - wi * data[j + 1]
let tempi = wr * data[j + 1] + wi * data[j]
data[j] = data[i] - tempr
data[j + 1] = data[i + 1] - tempi
data[i] += tempr
data[i + 1] += tempi
}
let wrtemp = wr
wr = wr * wpr - wi * wpi + wr
wi = wi * wpr + wrtemp * wpi + wi
}
mmax = istep
}
}
func rrprocess(params: Parameters, nrr: Int) -> [Double] {
let w1 = 2.0 * .pi * params.flo
let w2 = 2.0 * .pi * params.fhi
let c1 = 2.0 * .pi * params.flostd
let c2 = 2.0 * .pi * params.fhistd
let sig2 = 1.0
let sig1 = params.lfhfRatio
let rrmean = 60.0 / params.hrMean
let rrstd = 60.0 * params.hrStd / (params.hrMean * params.hrMean)
let sf = Double(params.sfInternal)
let df = sf / Double(nrr)
var swc = (0 ..< nrr / 2 + 1).map {
let w = df * Double($0) * 2.0 * .pi
let dw1 = w - w1
let dw2 = w - w2
let hw = sig1 * exp(-dw1 * dw1 / (2.0 * c1 * c1)) / sqrt(2.0 * .pi * c1 * c1)
+ sig2 * exp(-dw2 * dw2 / (2.0 * c2 * c2)) / sqrt(2.0 * .pi * c2 * c2)
let sw = (sf / 2.0) * sqrt(hw)
let ph = 2.0 * .pi * Double.random(in: 0.0 ..< 1.0)
return kiss_fft_cpx(r: sw * cos(ph), i: sw * sin(ph))
}
swc[0].i = 0.0
swc[nrr / 2].i = 0.0
let fft = kiss_fftr_alloc(Int32(nrr), 1, nil, nil)
let outptr = UnsafeMutablePointer<Double>.allocate(capacity: nrr)
kiss_fftri(fft, swc, outptr)
var rr = (0 ..< nrr).map { outptr[$0] * (1.0 / Double(nrr)) }
outptr.deallocate()
let xstd = stdev(rr)
let ratio = rrstd / xstd
for i in 0 ..< nrr {
rr[i] = rr[i] * ratio + rrmean
}
return rr
}
func stdev(_ data: [Double]) -> Double {
let n = Double(data.count)
let mean = data.reduce(0.0, +) / n
return sqrt(data.lazy.map { ($0 - mean) * ($0 - mean) }.reduce(0.0, +) / (n - 1))
}
func compute(params: Parameters) {
// adjust extrema parameters for mean heart rate
let hrFact = sqrt(params.hrMean / 60)
let hrFact2 = sqrt(hrFact)
let bi = params.b.map { $0 * hrFact }
/// XXX: Discrepancy here between Java/C and Matlab, the former uses 1.0 for ti[4] adjustment.
let ti = zip([hrFact2, hrFact, 1, hrFact, hrFact2], params.theta).map(*)
let ai = params.a
let x0 = SIMD3<Double>(1.0, 0.0, 0.04) // XXX: Convert to init from vector3d
let rseed = params.seed
// calculate time scales
let h = 1.0 / Double(params.sfInternal)
let tstep = 1.0 / Double(params.sfEcg)
// calculate length of the RR time series
let rrmean = (60.0 / params.hrMean)
let numRr = Int(pow(2.0, ceil(log2(Double(params.numBeats * params.sfInternal) * rrmean))))
var rr = [Double](repeating: 0.0, count: numRr)
// TODO: check sfInternal is integer multple of sfEcg
// define frequency parameters for rr process
}

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import Testing
@testable import EcgSynKit
@testable import KissFFT
@Test func fftTest () {
// Write your test here and use APIs like `#expect(...)` to check expected conditions.
let p = Parameters()
let rr = rrprocess(params: p, nrr: 131072)
//fft(data: &a, isign: -1)
//print("out: \(rr)")
}

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<html>
<head><title>Index of /static/published-projects/ecgsyn/1.0.0/C/</title></head>
<body>
<h1>Index of /static/published-projects/ecgsyn/1.0.0/C/</h1><hr><pre><a href="../">../</a>
<a href="linux/">linux/</a> 12-Apr-2019 17:35 -
<a href="solaris/">solaris/</a> 12-Apr-2019 17:35 -
<a href="src/">src/</a> 12-Apr-2019 17:35 -
<a href="windows/">windows/</a> 12-Apr-2019 17:35 -
<a href="index.shtml">index.shtml</a> 12-Apr-2019 17:35 4274
</pre><hr></body>
</html>

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<!--#set var="TITLE" value="Compiling and using the C version of ECGSYN"-->
<!--#include virtual="/head.shtml"-->
<h2>Compiling ECGSYN</h2>
<p>
Sources for the C version of <a href="../">ECGSYN</a> are <a
href="src/">here</a>. Note, however, that two additional files are required in
order to compile ECGSYN. These files (<tt>dfour1.c</tt> and <tt>ran1.c</tt>)
are those included in <a href="http://www.nr.com" target="other">Numerical
Recipes in C</a>. Before attempting to compile ECGSYN, obtain these two files
from Numerical Recipes in C and place them in the same directory as the other
sources. (These files are not provided here because they cannot be freely
redistributed.)
<p>
If you cannot obtain <tt>dfour1.c</tt> and <tt>ran1.c</tt>, several
alternatives are available, including ready-to-run executable versions of
ECGSYN for <a href="linux/">GNU/Linux</a>, <a href="solaris/">Solaris</a>, and
<a href="windows/">MS-Windows</a>, as well as <a
href="../Matlab/">Matlab/Octave</a> and <a href="../Java/">Java</a>
implementations of ECGSYN.
<p>
On most platforms, including GNU/Linux, MacOS X, and Unix, compile ECGSYN
by typing
<pre>
make
</pre>
in a terminal window. This will also work under MS-Windows if you have
installed the free <a href="http://www.cygwin.com" target="other">Cygwin/gcc
development toolkit</a>. If you wish to use another compiler under MS-Windows,
you are on your own.
<h2>Running ECGSYN</h2>
<p>
The executable version is named <tt>ecgsyn</tt> (or, under MS-Windows,
<tt>ecgsyn.exe</tt>). Once you have this file, move it into any directory in
your PATH and run it by typing
<pre>
ecgsyn
</pre>
in a terminal window. You may add options (switches) to the '<tt>ecgsyn</tt>'
command; the option '<tt>$</tt>', as in
<pre>
ecgsyn $
</pre>
starts ECGSYN in interactive mode, as shown below:
<pre>
>> ecgsyn $
ECGSYN: A program for generating a realistic synthetic ECG
Copyright (c) 2003 by Patrick McSharry & Gari Clifford. All rights reserved.
O Name of output data file "ecgsyn.dat"
n Approximate number of heart beats 256
s ECG sampling frequency [Hz] 256
S Internal Sampling frequency [Hz] 256
a Amplitude of additive uniform noise [mV] 0
h Heart rate mean [bpm] 60
H Heart rate standard deviation [bpm] 1
f Low frequency [Hz] 0.1
F High frequency [Hz] 0.25
v Low frequency standard deviation [Hz] 0.01
V High frequency standard deviation [Hz] 0.01
q LF/HF ratio 0.5
R Seed 1
(Type ? for Help)
->
</pre>
<p>
At the prompt, you can then type <tt>?</tt> for help, or simply specify each
parameter that you want to change by typing the corresponding option letter (in
the first column above) followed by a space and the new value, then
&lt;enter&gt;. To review the current settings, enter a blank line. After you
have modified all the parameters you want, type = followed by &lt;enter&gt; to
run the program. You may also specify the parameters in a file called
<tt>ecgsyn.opt</tt>, which is automatically read (if it exists) the next time
you run the program.
<p>
Any of the options can also be entered directly on the command line, by
prefixing the option letter with '<tt>-</tt>', as in:
<pre>
ecgsyn -h 80 -n 100
</pre>
(which would create output at a mean heart rate of 80 bpm, lasting for about
100 beats).
<p>
The source files <tt>opt.c</tt> and <tt>opt.h</tt> provide the option
interpreter for ECGSYN; they were written by James Theiler. For additional
information, and for the most recent version of <tt>opt</tt>, see
<a href="http://nis-www.lanl.gov/~jt/Software/"
target="other"><tt>http://nis-www.lanl.gov/~jt/Software/</tt></a>.
<h2>Interpreting ECGSYN's output</h2>
<p>
Unless you have changed the name of the output file with the '<tt>O</tt>'
parameter, you will find the synthetic ECG written to a text file called
<tt>ecgsyn.dat</tt>. Click <a href="../sample-output/">here</a> for a sample
of ECGSYN output and for a description of the format of this file.
<hr>
<!--#include virtual="/footer.shtml"-->
</body>
</html>

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<!--#set var="TITLE" value="ECGSYN for GNU/Linux"-->
<!--#include virtual="/head.shtml"-->
<p>
The executable <tt>ecgsyn</tt> file in this directory was compiled from
these <a href="../src/">ECGSYN sources</a> with gcc 2.96 under Red Hat
Linux 7.2. It is known to work under Red Hat Linux 7.1, 7.2, 7.3, 8, and 9,
and may also work under other versions of GNU/Linux.

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<html>
<head><title>Index of /static/published-projects/ecgsyn/1.0.0/C/linux/</title></head>
<body>
<h1>Index of /static/published-projects/ecgsyn/1.0.0/C/linux/</h1><hr><pre><a href="../">../</a>
<a href="HEADER.shtml">HEADER.shtml</a> 12-Apr-2019 17:35 371
<a href="ecgsyn">ecgsyn</a> 12-Apr-2019 17:35 46457
</pre><hr></body>
</html>

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<!--#set var="TITLE" value="ECGSYN for Solaris"-->
<!--#include virtual="/head.shtml"-->
<p>
The executable <tt>ecgsyn</tt> file in this directory was compiled from
these <a href="../src/">ECGSYN sources</a> with gcc 3.1 under SunOS 5.8
(Solaris 8).

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<html>
<head><title>Index of /static/published-projects/ecgsyn/1.0.0/C/solaris/</title></head>
<body>
<h1>Index of /static/published-projects/ecgsyn/1.0.0/C/solaris/</h1><hr><pre><a href="../">../</a>
<a href="HEADER.shtml">HEADER.shtml</a> 12-Apr-2019 17:35 253
<a href="ecgsyn">ecgsyn</a> 12-Apr-2019 17:35 43854
</pre><hr></body>
</html>

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ECGSYN: A program for generating a realistic synthetic ECG
Copyright (C) 2003 by Patrick McSharry & Gari Clifford. All rights reserved.
Compiling ECGSYN
================
This directory contains sources for the C version of ECGSYN. Note, however,
that two additional files are required in order to compile ECGSYN. These
files (dfour1.c and ran1.c) are those included in Numerical Recipes in C
(http://www.nr.com/). Before attempting to compile ECGSYN, obtain these
two files from Numerical Recipes in C and place them in this directory.
(These files are missing from this directory because they cannot be freely
redistributed.)
If you cannot obtain dfour1.c and ran1.c, several alternatives are available,
including ready-to-run executable versions of ECGSYN for GNU/Linux, Solaris,
and MS-Windows (see the directory above this one), as well as Matlab/Octave
and Java implementations of ECGSYN. See http://www.physionet.org/ for details.
On most platforms, including GNU/Linux, MacOS X, and Unix, compile ECGSYN
by typing
make
in a terminal window. This will also work under MS-Windows if you have
installed the free Cygwin/gcc development toolkit (http://www.cygwin.com/).
If you wish to use another compiler under MS-Windows, you are on your own.
Running ECGSYN
==============
The executable version is named 'ecgsyn' (or, under MS-Windows, 'ecgsyn.exe').
Once you have this file, move it into any directory in your PATH and run
it by typing
ecgsyn
in a terminal window. You may add options (switches) to the 'ecgsyn' command;
the option '$', as in
ecgsyn $
starts 'ecgsyn' in interactive mode, as shown below:
>> ecgsyn $
ECGSYN: A program for generating a realistic synthetic ECG
Copyright (c) 2003 by Patrick McSharry & Gari Clifford. All rights reserved.
O Name of output data file "ecgsyn.dat"
n Approximate number of heart beats 256
s ECG sampling frequency [Hz] 256
S Internal Sampling frequency [Hz] 256
a Amplitude of additive uniform noise [mV] 0
h Heart rate mean [bpm] 60
H Heart rate standard deviation [bpm] 1
f Low frequency [Hz] 0.1
F High frequency [Hz] 0.25
v Low frequency standard deviation [Hz] 0.01
V High frequency standard deviation [Hz] 0.01
q LF/HF ratio 0.5
R Seed 1
(Type ? for Help)
->
At the prompt, you can then type ? for help, or simply specify each parameter
above that you want to change by typing the corresponding option letter (in the
first column above) followed by a space and the new value, then <enter>. To
review the current settings, enter a blank line. After you have modified all
the parameters you want, type = followed by <enter> to run the program. You may
also specify the parameters in a file called ecgsyn.opt, which is automatically
read (if it exists) the next time you run the program.
Any of the options can also be entered directly on the command line, by
prefixing the option letter with '-', as in:
ecgsyn -h 80 -n 100
(which would create output at a mean heart rate of 80 bpm, lasting for about
100 beats).
The source files opt.c and opt.h provide the option interpreter for ecgsyn;
they were written by James Theiler. For additional information, and for the
most recent version of 'opt', see http://nis-www.lanl.gov/~jt/Software/.
Interpreting ECGSYN's output
============================
Unless you have changed the name of the output file with the 'O' parameter,
you will find the synthetic ECG written to a text file called ecgsyn.dat,
which contains three columns:
* the time in seconds
* the ECG amplitude in millivolts
* markers to indicate the locations of the waveform peaks:
0 - (no peak)
1 - Top of P-wave
2 - Q-point
3 - Peak of R-wave
4 - S-point
5 - Peak of T-wave
To convert the ECG output into PhysioBank (WFDB) format, use a command
such as
wrsamp -F 256 -o synth -x 200 1 <ecgsyn.dat
(assuming you have not changed the default sampling frequency of 256 Hz).
This command produces a record named 'synth' (a signal file named 'synth.dat'
and a header file named 'synth.hea'), which can be read by other PhysioToolkit
applications. 'wrsamp' is part of the WFDB software package; see
http://www.physionet.org/physiotools/wfdb.shtml for details.
Further information
===================
The most recent version of this software can always be obtained from
http://www.physionet.org/physiotools/ecgsyn/
See IEEE Transactions on Biomedical Engineering, 50(3),289-294, March 2003.
Authors: P. McSharry (patrick AT mcsharry DOT net)
G. Clifford (gari AT mit DOT edu)

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# file: Makefile
# 'make' description file for compiling ecgsyn
CFILES = ecgsyn.c opt.c dfour1.c ran1.c
CFLAGS = -O
ecgsyn: $(CFILES) opt.h
$(CC) $(CFLAGS) -o ecgsyn $(CFILES) -lm
dfour1.c ran1.c:
@echo "To compile ecgsyn, first get copies of dfour1.c and ran1.c"
@echo "(from Numerical Recipes in C) and place them in this directory."
@echo "Then type:"
@echo " make ecgsyn"
@exit 1
clean:
rm -f *~ *.o *.obj

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/* 09 Oct 2003 "ecgsyn.c" */
/* */
/* Copyright (c)2003 by Patrick McSharry & Gari Clifford, All Rights Reserved */
/* See IEEE Transactions On Biomedical Engineering, 50(3),289-294, March 2003.*/
/* Contact P. McSharry (patrick AT mcsharry DOT net) or */
/* G. Clifford (gari AT mit DOT edu) */
/* */
/* This program is free software; you can redistribute it and/or modify */
/* it under the terms of the GNU General Public License as published by */
/* the Free Software Foundation; either version 2 of the License, or */
/* (at your option) any later version. */
/* */
/* This program is distributed in the hope that it will be useful, */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the */
/* GNU General Public License for more details. */
/* */
/* You should have received a copy of the GNU General Public License */
/* along with this program; if not, write to the Free Software Foundation */
/* Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA */
/* */
/* ecgsyn.m and its dependents are freely availble from Physionet - */
/* http://www.physionet.org/ - please report any bugs to the authors above. */
#include <stdio.h>
#include <math.h>
#include <stdlib.h>
#include "opt.h"
#define PI (2.0*asin(1.0))
#define SWAP(a,b) tempr=(a);(a)=(b);(b)=tempr
#define MIN(a,b) (a < b ? a : b)
#define MAX(a,b) (a > b ? a : b)
#define PI (2.0*asin(1.0))
#define OFFSET 1
#define ARG1 char*
#define IA 16807
#define IM 2147483647
#define AM (1.0/IM)
#define IQ 127773
#define IR 2836
#define NTAB 32
#define NDIV (1+(IM-1)/NTAB)
#define EPS 1.2e-7
#define RNMX (1.0-EPS)
/*--------------------------------------------------------------------------*/
/* DEFINE PARAMETERS AS GLOBAL VARIABLES */
/*--------------------------------------------------------------------------*/
char outfile[100]="ecgsyn.dat";/* Output data file */
int N = 256; /* Number of heart beats */
int sfecg = 256; /* ECG sampling frequency */
int sf = 256; /* Internal sampling frequency */
double Anoise = 0.0; /* Amplitude of additive uniform noise*/
double hrmean = 60.0; /* Heart rate mean */
double hrstd = 1.0; /* Heart rate std */
double flo = 0.1; /* Low frequency */
double fhi = 0.25; /* High frequency */
double flostd = 0.01; /* Low frequency std */
double fhistd = 0.01; /* High frequency std */
double lfhfratio = 0.5; /* LF/HF ratio */
int Necg = 0; /* Number of ECG outputs */
int mstate = 3; /* System state space dimension */
double xinitial = 1.0; /* Initial x co-ordinate value */
double yinitial = 0.0; /* Initial y co-ordinate value */
double zinitial = 0.04; /* Initial z co-ordinate value */
int seed = 1; /* Seed */
long rseed;
double h;
double *rr,*rrpc;
double *ti,*ai,*bi;
/* prototypes for externally defined functions */
void dfour1(double data[], unsigned long nn, int isign);
float ran1(long *idum);
/*---------------------------------------------------------------------------*/
/* ALLOCATE MEMORY FOR VECTOR */
/*---------------------------------------------------------------------------*/
double *mallocVect(long n0, long nx)
{
double *vect;
vect=(double *)malloc((size_t) ((nx-n0+1+OFFSET)*sizeof(double)));
if (!vect){
printf("Memory allocation failure in mallocVect");
}
return vect-n0+OFFSET;
}
/*---------------------------------------------------------------------------*/
/* FREE MEMORY FOR MALLOCVECT */
/*---------------------------------------------------------------------------*/
void freeVect(double *vect, long n0, long nx)
{
free((ARG1) (vect+n0-OFFSET));
}
/*---------------------------------------------------------------------------*/
/* MEAN CALCULATOR */
/*---------------------------------------------------------------------------*/
double mean(double *x, int n)
/* n-by-1 vector, calculate mean */
{
int j;
double add;
add = 0.0;
for(j=1;j<=n;j++) add += x[j];
return (add/n);
}
/*---------------------------------------------------------------------------*/
/* STANDARD DEVIATION CALCULATOR */
/*---------------------------------------------------------------------------*/
double stdev(double *x, int n)
/* n-by-1 vector, calculate standard deviation */
{
int j;
double add,mean,diff,total;
add = 0.0;
for(j=1;j<=n;j++) add += x[j];
mean = add/n;
total = 0.0;
for(j=1;j<=n;j++)
{
diff = x[j] - mean;
total += diff*diff;
}
return (sqrt(total/(n-1)));
}
/*--------------------------------------------------------------------------*/
/* WRITE VECTOR IN A FILE */
/*--------------------------------------------------------------------------*/
void vecfile(char filename[], double *x, int n)
{
int i;
FILE *fp;
fp = fopen(filename,"w");
for(i=1;i<=n;i++) fprintf(fp,"%e\n",x[i]);
fclose(fp);
}
/*--------------------------------------------------------------------------*/
/* INTERP */
/*--------------------------------------------------------------------------*/
void interp(double *y, double *x, int n, int r)
{
int i,j;
double a;
for(i=1;i<=n-1;i++)
{
for(j=1;j<=r;j++)
{
a = (j-1)*1.0/r;
y[(i-1)*r+j] = (1.0-a)*x[i] + a*x[i+1];
}
}
}
/*--------------------------------------------------------------------------*/
/* GENERATE RR PROCESS */
/*--------------------------------------------------------------------------*/
void rrprocess(double *rr, double flo, double fhi,
double flostd, double fhistd, double lfhfratio,
double hrmean, double hrstd, double sf, int n)
{
int i,j;
double c1,c2,w1,w2,sig1,sig2,rrmean,rrstd,xstd,ratio;
double df,dw1,dw2,*w,*Hw,*Sw,*ph0,*ph,*SwC;
w = mallocVect(1,n);
Hw = mallocVect(1,n);
Sw = mallocVect(1,n);
ph0 = mallocVect(1,n/2-1);
ph = mallocVect(1,n);
SwC = mallocVect(1,2*n);
w1 = 2.0*PI*flo;
w2 = 2.0*PI*fhi;
c1 = 2.0*PI*flostd;
c2 = 2.0*PI*fhistd;
sig2 = 1.0;
sig1 = lfhfratio;
rrmean = 60.0/hrmean;
rrstd = 60.0*hrstd/(hrmean*hrmean);
df = sf/n;
for(i=1;i<=n;i++) w[i] = (i-1)*2.0*PI*df;
for(i=1;i<=n;i++)
{
dw1 = w[i]-w1;
dw2 = w[i]-w2;
Hw[i] = sig1*exp(-dw1*dw1/(2.0*c1*c1))/sqrt(2*PI*c1*c1)
+ sig2*exp(-dw2*dw2/(2.0*c2*c2))/sqrt(2*PI*c2*c2);
}
for(i=1;i<=n/2;i++) Sw[i] = (sf/2.0)*sqrt(Hw[i]);
for(i=n/2+1;i<=n;i++) Sw[i] = (sf/2.0)*sqrt(Hw[n-i+1]);
/* randomise the phases */
for(i=1;i<=n/2-1;i++) ph0[i] = 2.0*PI*ran1(&rseed);
ph[1] = 0.0;
for(i=1;i<=n/2-1;i++) ph[i+1] = ph0[i];
ph[n/2+1] = 0.0;
for(i=1;i<=n/2-1;i++) ph[n-i+1] = - ph0[i];
/* make complex spectrum */
for(i=1;i<=n;i++) SwC[2*i-1] = Sw[i]*cos(ph[i]);
for(i=1;i<=n;i++) SwC[2*i] = Sw[i]*sin(ph[i]);
/* calculate inverse fft */
dfour1(SwC,n,-1);
/* extract real part */
for(i=1;i<=n;i++) rr[i] = (1.0/n)*SwC[2*i-1];
xstd = stdev(rr,n);
ratio = rrstd/xstd;
for(i=1;i<=n;i++) rr[i] *= ratio;
for(i=1;i<=n;i++) rr[i] += rrmean;
freeVect(w,1,n);
freeVect(Hw,1,n);
freeVect(Sw,1,n);
freeVect(ph0,1,n/2-1);
freeVect(ph,1,n);
freeVect(SwC,1,2*n);
}
/*--------------------------------------------------------------------------*/
/* THE ANGULAR FREQUENCY */
/*--------------------------------------------------------------------------*/
double angfreq(double t)
{
int i;
i = 1 + (int)floor(t/h);
return 2.0*PI/rrpc[i];
}
/*--------------------------------------------------------------------------*/
/* THE EXACT NONLINEAR DERIVATIVES */
/*--------------------------------------------------------------------------*/
void derivspqrst(double t0,double x[],double dxdt[])
{
int i,k;
double a0,w0,r0,x0,y0,z0;
double t,dt,dt2,*xi,*yi,zbase;
k = 5;
xi = mallocVect(1,k);
yi = mallocVect(1,k);
w0 = angfreq(t0);
r0 = 1.0; x0 = 0.0; y0 = 0.0; z0 = 0.0;
a0 = 1.0 - sqrt((x[1]-x0)*(x[1]-x0) + (x[2]-y0)*(x[2]-y0))/r0;
for(i=1;i<=k;i++) xi[i] = cos(ti[i]);
for(i=1;i<=k;i++) yi[i] = sin(ti[i]);
zbase = 0.005*sin(2.0*PI*fhi*t0);
t = atan2(x[2],x[1]);
dxdt[1] = a0*(x[1] - x0) - w0*(x[2] - y0);
dxdt[2] = a0*(x[2] - y0) + w0*(x[1] - x0);
dxdt[3] = 0.0;
for(i=1;i<=k;i++)
{
dt = fmod(t-ti[i],2.0*PI);
dt2 = dt*dt;
dxdt[3] += -ai[i]*dt*exp(-0.5*dt2/(bi[i]*bi[i]));
}
dxdt[3] += -1.0*(x[3] - zbase);
freeVect(xi,1,k);
freeVect(yi,1,k);
}
/*--------------------------------------------------------------------------*/
/* RUNGA-KUTTA FOURTH ORDER INTEGRATION */
/*--------------------------------------------------------------------------*/
void drk4(double y[], int n, double x, double h, double yout[],
void (*derivs)(double, double [], double []))
{
int i;
double xh,hh,h6,*dydx,*dym,*dyt,*yt;
dydx=mallocVect(1,n);
dym=mallocVect(1,n);
dyt=mallocVect(1,n);
yt=mallocVect(1,n);
hh=h*0.5;
h6=h/6.0;
xh=x+hh;
(*derivs)(x,y,dydx);
for (i=1;i<=n;i++) yt[i]=y[i]+hh*dydx[i];
(*derivs)(xh,yt,dyt);
for (i=1;i<=n;i++) yt[i]=y[i]+hh*dyt[i];
(*derivs)(xh,yt,dym);
for (i=1;i<=n;i++) {
yt[i]=y[i]+h*dym[i];
dym[i] += dyt[i];
}
(*derivs)(x+h,yt,dyt);
for (i=1;i<=n;i++)
yout[i]=y[i]+h6*(dydx[i]+dyt[i]+2.0*dym[i]);
freeVect(dydx,1,n);
freeVect(dym,1,n);
freeVect(dyt,1,n);
freeVect(yt,1,n);
}
/*--------------------------------------------------------------------------*/
/* DETECT PEAKS */
/*--------------------------------------------------------------------------*/
double detectpeaks(double *ipeak, double *x, double *y, double *z, int n)
{
int i,j,j1,j2,jmin,jmax,d;
double thetap1,thetap2,thetap3,thetap4,thetap5;
double theta1,theta2,d1,d2,zmin,zmax;
/* use globally defined angles for PQRST */
thetap1 = ti[1];
thetap2 = ti[2];
thetap3 = ti[3];
thetap4 = ti[4];
thetap5 = ti[5];
for(i=1;i<=n;i++) ipeak[i] = 0.0;
theta1 = atan2(y[1],x[1]);
for(i=1;i<n;i++)
{
theta2 = atan2(y[i+1],x[i+1]);
if( (theta1 <= thetap1) && (thetap1 <= theta2) )
{
d1 = thetap1 - theta1;
d2 = theta2 - thetap1;
if(d1 < d2) ipeak[i] = 1.0;
else ipeak[i+1] = 1.0;
}
else if( (theta1 <= thetap2) && (thetap2 <= theta2) )
{
d1 = thetap2 - theta1;
d2 = theta2 - thetap2;
if(d1 < d2) ipeak[i] = 2.0;
else ipeak[i+1] = 2.0;
}
else if( (theta1 <= thetap3) && (thetap3 <= theta2) )
{
d1 = thetap3 - theta1;
d2 = theta2 - thetap3;
if(d1 < d2) ipeak[i] = 3.0;
else ipeak[i+1] = 3.0;
}
else if( (theta1 <= thetap4) && (thetap4 <= theta2) )
{
d1 = thetap4 - theta1;
d2 = theta2 - thetap4;
if(d1 < d2) ipeak[i] = 4.0;
else ipeak[i+1] = 4.0;
}
else if( (theta1 <= thetap5) && (thetap5 <= theta2) )
{
d1 = thetap5 - theta1;
d2 = theta2 - thetap5;
if(d1 < d2) ipeak[i] = 5.0;
else ipeak[i+1] = 5.0;
}
theta1 = theta2;
}
/* correct the peaks */
d = (int)ceil(sfecg/64);
for(i=1;i<=n;i++)
{
if( ipeak[i]==1 || ipeak[i]==3 || ipeak[i]==5 )
{
j1 = MAX(1,i-d);
j2 = MIN(n,i+d);
jmax = j1;
zmax = z[j1];
for(j=j1+1;j<=j2;j++)
{
if(z[j] > zmax)
{
jmax = j;
zmax = z[j];
}
}
if(jmax != i)
{
ipeak[jmax] = ipeak[i];
ipeak[i] = 0;
}
}
else if( ipeak[i]==2 || ipeak[i]==4 )
{
j1 = MAX(1,i-d);
j2 = MIN(n,i+d);
jmin = j1;
zmin = z[j1];
for(j=j1+1;j<=j2;j++)
{
if(z[j] < zmin)
{
jmin = j;
zmin = z[j];
}
}
if(jmin != i)
{
ipeak[jmin] = ipeak[i];
ipeak[i] = 0;
}
}
}
}
/*--------------------------------------------------------------------------*/
/* MAIN PROGRAM */
/*---------------------------------------------------------------------------*/
main(argc,argv)
int argc;
char **argv;
{
/* First step is to register the options */
optregister(outfile,CSTRING,'O',"Name of output data file");
optregister(N,INT,'n',"Approximate number of heart beats");
optregister(sfecg,INT,'s',"ECG sampling frequency [Hz]");
optregister(sf,INT,'S',"Internal Sampling frequency [Hz]");
optregister(Anoise,DOUBLE,'a',"Amplitude of additive uniform noise [mV]");
optregister(hrmean,DOUBLE,'h',"Heart rate mean [bpm]");
optregister(hrstd,DOUBLE,'H',"Heart rate standard deviation [bpm]");
optregister(flo,DOUBLE,'f',"Low frequency [Hz]");
optregister(fhi,DOUBLE,'F',"High frequency [Hz]");
optregister(flostd,DOUBLE,'v',"Low frequency standard deviation [Hz]");
optregister(fhistd,DOUBLE,'V',"High frequency standard deviation [Hz]");
optregister(lfhfratio,DOUBLE,'q',"LF/HF ratio");
optregister(seed,INT,'R',"Seed");
opt_title_set("ECGSYN: A program for generating a realistic synthetic ECG\n"
"Copyright (c) 2003 by Patrick McSharry & Gari Clifford. All rights reserved.\n");
getopts(argc,argv);
dorun();
}
/*--------------------------------------------------------------------------*/
/* DORUN PART OF PROGRAM */
/*--------------------------------------------------------------------------*/
int dorun()
{
int i,j,k,q,Nrr,Nt,Nts;
double *x,tstep,tecg,rrmean,qd,hrfact,hrfact2;
double *xt,*yt,*zt,*xts,*yts,*zts;
double timev,*ipeak,zmin,zmax,zrange;
FILE *fp;
void (*derivs)(double, double [], double []);
/* perform some checks on input values */
q = (int)rint(sf/sfecg);
qd = (double)sf/(double)sfecg;
if(q != qd) {
printf("Internal sampling frequency must be an integer multiple of the \n");
printf("ECG sampling frequency!\n");
printf("Your current choices are:\n");
printf("ECG sampling frequency: %d Hertz\n",sfecg);
printf("Internal sampling frequency: %d Hertz\n",sf);
exit(1);}
/* declare and initialise the state vector */
x=mallocVect(1,mstate);
x[1] = xinitial;
x[2] = yinitial;
x[3] = zinitial;
/* declare and define the ECG morphology vectors (PQRST extrema parameters) */
ti=mallocVect(1,5);
ai=mallocVect(1,5);
bi=mallocVect(1,5);
/* P Q R S T */
ti[1]=-60.0; ti[2]=-15.0; ti[3]=0.0; ti[4]=15.0; ti[5]=90.0;
ai[1]=1.2; ai[2]=-5.0; ai[3]=30.0; ai[4]=-7.5; ai[5]=0.75;
bi[1]=0.25; bi[2]=0.1; bi[3]=0.1; bi[4]=0.1; bi[5]=0.4;
/* convert angles from degrees to radians */
for(i=1;i<=5;i++) ti[i] *= PI/180.0;
/* adjust extrema parameters for mean heart rate */
hrfact = sqrt(hrmean/60.0);
hrfact2 = sqrt(hrfact);
for(i=1;i<=5;i++) bi[i] *= hrfact;
ti[1]*=hrfact2; ti[2]*=hrfact; ti[3]*=1.0; ti[4]*=hrfact; ti[5]*=1.0;
/* calculate time scales */
h = 1.0/sf;
tstep = 1.0/sfecg;
printf("ECGSYN: A program for generating a realistic synthetic ECG\n"
"Copyright (c) 2003 by Patrick McSharry & Gari Clifford. All rights reserved.\n"
"See IEEE Transactions On Biomedical Engineering, 50(3), 289-294, March 2003.\n"
"Contact P. McSharry (patrick@mcsharry.net) or G. Clifford (gari@mit.edu)\n");
printf("Approximate number of heart beats: %d\n",N);
printf("ECG sampling frequency: %d Hertz\n",sfecg);
printf("Internal sampling frequency: %d Hertz\n",sf);
printf("Amplitude of additive uniformly distributed noise: %g mV\n",Anoise);
printf("Heart rate mean: %g beats per minute\n",hrmean);
printf("Heart rate std: %g beats per minute\n",hrstd);
printf("Low frequency: %g Hertz\n",flo);
printf("High frequency std: %g Hertz\n",fhistd);
printf("Low frequency std: %g Hertz\n",flostd);
printf("High frequency: %g Hertz\n",fhi);
printf("LF/HF ratio: %g\n",lfhfratio);
/* initialise seed */
rseed = -seed;
/* select the derivs to use */
derivs = derivspqrst;
/* calculate length of RR time series */
rrmean = (60/hrmean);
Nrr = (int)pow(2.0, ceil(log10(N*rrmean*sf)/log10(2.0)));
printf("Using %d = 2^%d samples for calculating RR intervals\n",
Nrr,(int)(log10(1.0*Nrr)/log10(2.0)));
/* create rrprocess with required spectrum */
rr = mallocVect(1,Nrr);
rrprocess(rr, flo, fhi, flostd, fhistd, lfhfratio, hrmean, hrstd, sf, Nrr);
vecfile("rr.dat",rr,Nrr);
/* create piecewise constant rr */
rrpc = mallocVect(1,2*Nrr);
tecg = 0.0;
i = 1;
j = 1;
while(i <= Nrr)
{
tecg += rr[j];
j = (int)rint(tecg/h);
for(k=i;k<=j;k++) rrpc[k] = rr[i];
i = j+1;
}
Nt = j;
vecfile("rrpc.dat",rrpc,Nt);
printf("Printing ECG signal to file: %s\n",outfile);
/* integrate dynamical system using fourth order Runge-Kutta*/
xt = mallocVect(1,Nt);
yt = mallocVect(1,Nt);
zt = mallocVect(1,Nt);
timev = 0.0;
for(i=1;i<=Nt;i++)
{
xt[i] = x[1];
yt[i] = x[2];
zt[i] = x[3];
drk4(x, mstate, timev, h, x, derivs);
timev += h;
}
/* downsample to ECG sampling frequency */
xts = mallocVect(1,Nt);
yts = mallocVect(1,Nt);
zts = mallocVect(1,Nt);
j=0;
for(i=1;i<=Nt;i+=q)
{
j++;
xts[j] = xt[i];
yts[j] = yt[i];
zts[j] = zt[i];
}
Nts = j;
/* do peak detection using angle */
ipeak = mallocVect(1,Nts);
detectpeaks(ipeak, xts, yts, zts, Nts);
/* scale signal to lie between -0.4 and 1.2 mV */
zmin = zts[1];
zmax = zts[1];
for(i=2;i<=Nts;i++)
{
if(zts[i] < zmin) zmin = zts[i];
else if(zts[i] > zmax) zmax = zts[i];
}
zrange = zmax-zmin;
for(i=1;i<=Nts;i++) zts[i] = (zts[i]-zmin)*(1.6)/zrange - 0.4;
/* include additive uniformly distributed measurement noise */
for(i=1;i<=Nts;i++) zts[i] += Anoise*(2.0*ran1(&rseed) - 1.0);
/* output ECG file */
fp = fopen(outfile,"w");
for(i=1;i<=Nts;i++) fprintf(fp,"%f %f %d\n",(i-1)*tstep,zts[i],(int)ipeak[i]);
fclose(fp);
printf("Finished ECG output\n");
freeVect(x,1,mstate);
freeVect(rr,1,Nrr);
freeVect(rrpc,1,2*Nrr);
freeVect(ti,1,5);
freeVect(ai,1,5);
freeVect(bi,1,5);
freeVect(xt,1,Nt);
freeVect(yt,1,Nt);
freeVect(zt,1,Nt);
freeVect(xts,1,Nt);
freeVect(yts,1,Nt);
freeVect(zts,1,Nt);
freeVect(ipeak,1,Nts);
/* END OF DORUN */
}

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<html>
<head><title>Index of /static/published-projects/ecgsyn/1.0.0/C/src/</title></head>
<body>
<h1>Index of /static/published-projects/ecgsyn/1.0.0/C/src/</h1><hr><pre><a href="../">../</a>
<a href="00README">00README</a> 12-Apr-2019 17:35 4672
<a href="Makefile">Makefile</a> 12-Apr-2019 17:35 426
<a href="ecgsyn.c">ecgsyn.c</a> 12-Apr-2019 17:35 20586
<a href="opt.c">opt.c</a> 12-Apr-2019 17:35 56582
<a href="opt.h">opt.h</a> 12-Apr-2019 17:35 5237
</pre><hr></body>
</html>

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/*
opt.h version 3.17 - User Include File for options package.
OPT is a subroutine library which facilitates the convenient
input of parameters to a C or C++ program. Parameters are parsed
from a command line, with further facilities for reading options
from files, from environment strings, or from an interactive
environment. The aim of the opt package is to permit programs to
be both user- and programmer- friendly. The package attempts to
on the one hand provide a direct and relatively full-featured
input interface to the ultimate user of the program, and at the
same time impose a minimal amount of work on the programmer to
"attach" the package to his or her software. A texinfo file is
part of the distribution; or you can view the html documentation at:
http://nis-www.lanl.gov/~jt/Software/opt/opt_toc.html
Download the lastest version of the source code from:
http://nis-www.lanl.gov/~jt/Software/
opt is available to the public under the GNU General Public License:
http://www.gnu.org/copyleft/gpl.html
This SOFTWARE has been authored by an employee of the University of
California, operator of the Los Alamos National Laboratory under
Contract No. W-7405-ENG-36 with the U.S. Department of Energy. The
U.S. Government has rights to use, reproduce, and distribute this
SOFTWARE. The public may copy, distribute, prepare derivative works
and publicly display this SOFTWARE without charge, provided that this
Notice and any statement of authorship are reproduced on all
copies. Neither the Government nor the University makes any warranty,
express or implied, or assumes any liability or responsibility for the
use of this SOFTWARE. If SOFTWARE is modified to produce derivative
works, such modified SOFTWARE should be clearly marked, so as not to
confuse it with the version available from LANL.
*/
#ifndef _OPT_H
#define _OPT_H /* Signal that this header file has been included */
/*
* These are delimiter characters
*/
#define DELIM '-' /* option delimiter character */
#define ALTDELIM '/' /* alternate delimiter character */
#define OPTFROMFILE '@' /* denotes options are in a file */
#define OPTTOFILE '%' /* says to put options in a file */
#define DOCUMENT '-' /* write document to file */
#define INTERACT '$' /* Flags interactive menu */
#define HELPCH '?' /* Help character */
/*
* These are not available on command line
* But may be invoked from a file
*/
#define IGNOREEOL ';' /* Ignore until the end of line */
#define RUN '=' /* Says to just run to completion */
#define QUITCH '.' /* Quit character */
/*
* These are not available on command line or from a file
* But may be invoked from the menu
*/
#define BANG '!' /* Shell escape character */
#define ADDITIONAL_OPTS '+' /* Additional options */
typedef enum {
INT, UNSINT, LONG, CHAR,
INTLEVEL,
FLOAT, DOUBLE,
FLAG, NEGFLAG, ABSFLAG, ABSNEGFLAG,
VSTRING, CSTRING, UNDELIMV, UNDELIMC
}
opt_TYPE;
typedef int (*PFI)();
#define OPT_EXT ".opt" /* standard options file extension */
#ifndef TRUE
#define TRUE 1
#define FALSE 0
#endif
#ifndef ARGCHECK
#ifdef __TURBOC__
#define ARGCHECK
#endif /* __TURBOC__ */
#ifdef __cplusplus
#define ARGCHECK
#endif /* __cplusplus */
#endif /* ARGCHECK */
#ifdef ARGCHECK
extern int opt_register(char *,opt_TYPE,char,char *);
extern void opt_usage_set(char *);
extern void opt_title_set(char *);
extern void opt_verify_set(PFI);
extern void opt_doc_set(PFI);
extern void opt_quit_set(PFI);
extern void opt_run_set(PFI);
extern void opt_help_setf(PFI);
extern void opt_help_set(char,char *);
extern void opt_ufilter_set(PFI);
extern void opt_dfilter_set(PFI);
extern void opt_env_set(char *);
extern void opt_default_set(char *);
#if DISABLE_VARARGS
extern void opt_errmess(char *);
extern void opt_message(char *);
extern void opt_warning(char *);
extern void opt_fatal(char *);
#else
extern void opt_errmess();
extern void opt_message();
extern void opt_warning();
extern void opt_fatal();
#endif /* DISABLE_VARARGS */
extern void opt_abort_run(void);
extern int opt_begin_run(PFI);
extern int getopts(int,char **);
#else
extern int opt_register();
extern void opt_usage_set();
extern void opt_title_set();
extern void opt_verify_set();
extern void opt_doc_set();
extern void opt_quit_set();
extern void opt_run_set();
extern void opt_help_setf();
extern void opt_help_set();
extern void opt_help_set();
extern void opt_ufilter_set();
extern void opt_dfilter_set();
extern void opt_env_set();
extern void opt_default_set();
extern void opt_errmess();
extern void opt_message();
extern void opt_warning();
extern void opt_fatal();
extern void opt_abort_run();
extern int opt_begin_run();
extern int getopts();
#endif /* ARGCHECK */
/*********************************
* Macro's for registering options
*/
#define optregister(val,typ,c,str) opt_register((char *)&val,typ,c,str)
#define optrunset(r) {int r(); opt_run_set( r );}
#endif /* _OPT_H */

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<!--#set var="TITLE" value="ECGSYN for Windows"-->
<!--#include virtual="/head.shtml"-->
<p>
There are two versions of the <code>ecgsyn.exe</code> executable in this directory. Using the
<a href="../src/">ECGSYN source files</a>, the first version was compiled with <code>Cygwin64 2.6.0 gcc 5.4.0</code>,
and the second version with <code>MinGW-w64 gcc 4.9.2</code>, both under Windows 10.</p>
<p>
To run the Cygwin executable, you will need to have the Cygwin DLLs installed in your PATH in
order to run this program successfully. The simplest and most reliable
way to do this is to install the <a href="http://www.cygwin.com/" target="other">Cygwin development toolkit</a>.
To run the MinGW executable, you should install <a href="https://sourceforge.net/projects/mingw-w64/" target="other">MinGW-w64</a>.
</p>

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<head><title>Index of /static/published-projects/ecgsyn/1.0.0/C/windows/</title></head>
<body>
<h1>Index of /static/published-projects/ecgsyn/1.0.0/C/windows/</h1><hr><pre><a href="../">../</a>
<a href="HEADER.shtml">HEADER.shtml</a> 12-Apr-2019 17:35 821
<a href="HEADER.shtml~">HEADER.shtml~</a> 12-Apr-2019 17:35 647
<a href="cygwin_ecgsyn.zip">cygwin_ecgsyn.zip</a> 12-Apr-2019 17:35 35146
<a href="mingw_ecgsyn.zip">mingw_ecgsyn.zip</a> 12-Apr-2019 17:35 34966
</pre><hr></body>
</html>

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<!--#set var="TITLE" value="ECGSYN implemented in Java"-->
<!--#include virtual="/head.shtml"-->
<p>
This directory contains Mauricio Villarroel's implementation of
<a href="../">ECGSYN</a> as a Java applet.
<p>
To run the applet in your web browser, click
<a href="ecgsyn-java.html">here</a>.
<p>
The individual Java files can be downloaded by following the links
below, or you may download all of them, together with the C and Matlab
implementations of ECGSYN, as a single gzip-compressed tar archive, <a
href="../ecgsyn.tar.gz"><tt>ecgsyn.tar.gz</tt></a>. (See <a
href="/faq.shtml#tar-gz">How can I unpack a .tar.gz archive?</a> if
you need help doing this.)
<hr>

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<HTML>
<HEAD>
<TITLE>ECGSYN Java Application</TITLE>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"></HEAD>
<BODY bgcolor="#003366" text="#FFFFCC" link="#FFFF33" vlink="#FFCC00" leftmargin="0" topmargin="0" marginwidth="0" marginheight="0">
<table width="925" border="0" align="center" cellpadding="0" cellspacing="5">
<tr>
<td height="50" colspan="2">&nbsp;
<H3>
<HR WIDTH="100%">
</H3>
<H3 align="center"><font color="#FF9900">JAVA Application for <br>
ECGSYN: A Dynamical Model for Generating
Synthetic Electrocardiogram Signals
</font></H3>
<H3>
<HR WIDTH="100%">
</H3>
</td>
</tr>
<tr>
<td width="300" align="left" valign="top"><p><strong>ECGSYN</strong>:</p>
<p><strong>&copy;</strong> ECGSYN Copyright by Patrick E. McSharry and Gari
D. Clifford. <br>
&copy; Java code copyright by Mauricio Villarroel.<br>
<br>
For the Mathematical Model, see:</p>
<table width="100%" border="1" cellspacing="0" cellpadding="5">
<tr>
<td align="left" valign="top">IEEE Transactions On Biomedical Engineering,
50(3), 289-294, March 2003</td>
</tr>
</table>
<p> Contact: </p>
<ul>
<li><a href="mailto:patrick@mcsharry.net">Patrck McSharry</a></li>
<li><a href="mailto:gari@mit.edu">Gari Clifford</a></li>
<li><a href="mailto:mauricio.villarroel@estudiantes.ucb.edu.bo">Mauricio Villarroel</a></li>
</ul>
<p>Please read the <a href="ecgLicense.txt">Software License</a>.
</p></td>
<td align="center" valign="middle">ECG Ouput Sample image:<br><p><img src="ecgplot.PNG" alt="ECGSYN-Java Output Sample image" width="580" height="330" border="1"></p>
<p>Source code: <a href="ecgApplet.tar.gz">ecgApplet.tar.gz</a></p></td>
</tr>
<tr>
<td height="50">&nbsp;</td>
<td height="50" align="center" valign="middle">&nbsp;</td>
</tr>
<tr>
<td colspan="2" align="center" valign="top"><strong><font size="4">You can
test the ECGSYN Java Application:</font></strong></td>
</tr>
<tr>
<td colspan="2" align="center" valign="top"><applet name= "ecgApplet" code="ecgApplet.class" width=915 height=570>
</applet></td>
</tr>
</table>
<H3>&nbsp; </H3>
<P>&nbsp; </P>
<HR WIDTH="100%"><FONT SIZE=-1><I>ECGSYN Java Application<br>
Last updated on October 27, 2003</I></FONT>
<p align="justify">Return to ECGSYN <a href="http://www.maths.ox.ac.uk/~mcsharry/ecgsyn">Home page</a>.</p>
</BODY>
</HTML>

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/************************************************************************/
/* */
/* ECGSYN Java Application */
/* */
/* Copyright (C) 2003 Mauricio Villarroel */
/* (mauricio DOT villarroel AT estudiantes DOT ucb DOT edu DOT bo) */
/* */
/* ecgApplet.java and all its components are free software; you can */
/* redistribute them and/or modify it under the terms of the */
/* GNU General Public License as published by the Free Software */
/* Foundation; either version 2 of the License, or (at your option) */
/* any later version. */
/* */
/* This file is distributed in the hope that it will be useful, but */
/* WITHOUT ANY WARRANTY; without even the implied warranty of */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. */
/* See the GNU General Public License for more details. */
/* */
/************************************************************************/
/* */
/* This file was created for the ECGSYN Application. */
/* */
/* ECGSYN: A program for generating a realistic synthetic */
/* Electrocardiogram Signals. */
/* Copyright (c) 2003 by Patrick McSharry & Gari Clifford. */
/* All rights reserved. */
/* */
/* See IEEE Transactions On Biomedical Engineering, */
/* 50(3), 289-294, March 2003. */
/* Contact: */
/* P. McSharry (patrick AT mcsharry DOT net) */
/* G. Clifford (gari AT mit DOT edu) */
/* */
/************************************************************************/
/* */
/* Further updates to this software will be published on: */
/* http://www.physionet.org/ */
/* */
/************************************************************************/

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<HTML>
<HEAD>
<TITLE>ECGSYN Java Application</TITLE>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1"></HEAD>
<BODY bgcolor="#003366" text="#FFFFCC" link="#FFFF33" vlink="#FFCC00" leftmargin="0" topmargin="0" marginwidth="0" marginheight="0">
<table width="925" border="0" align="center" cellpadding="0" cellspacing="5">
<tr>
<td height="50" colspan="2">&nbsp;
<H3>
<HR WIDTH="100%">
</H3>
<H3 align="center"><font color="#FF9900">JAVA Application for <br>
ECGSYN: A Dynamical Model for Generating
Synthetic Electrocardiogram Signals
</font></H3>
<H3>
<HR WIDTH="100%">
</H3>
</td>
</tr>
<tr>
<td width="300" align="left" valign="top"><p><strong>ECGSYN</strong>:</p>
<p><strong>&copy;</strong> ECGSYN Copyright by Patrick E. McSharry and Gari
D. Clifford. <br>
&copy; Java code copyright by Mauricio Villarroel.<br>
<br>
For the Mathematical Model, see:</p>
<table width="100%" border="1" cellspacing="0" cellpadding="5">
<tr>
<td align="left" valign="top">IEEE Transactions On Biomedical Engineering,
50(3), 289-294, March 2003</td>
</tr>
</table>
<p> Contact: </p>
<ul>
<li><a href="mailto:patrick@mcsharry.net">Patrck McSharry</a></li>
<li><a href="mailto:gari@mit.edu">Gari Clifford</a></li>
<li><a href="mailto:mauricio.villarroel@estudiantes.ucb.edu.bo">Mauricio Villarroel</a></li>
</ul>
<p>Please read the <a href="ecgLicense.txt">Software License</a>.
</p></td>
<td align="center" valign="middle">ECG Ouput Sample image:<br><p><img src="ecgplot.PNG" alt="ECGSYN-Java Output Sample image" width="580" height="330" border="1"></p>
<p>Source code: <a href="../ecgsyn.tar.gz">ecgsyn.tar.gz</a></p></td>
</tr>
<tr>
<td height="50">&nbsp;</td>
<td height="50" align="center" valign="middle">&nbsp;</td>
</tr>
<tr>
<td colspan="2" align="center" valign="top"><strong><font size="4">You can
test the ECGSYN Java Application:</font></strong></td>
</tr>
<tr>
<td colspan="2" align="center" valign="top"><applet name= "ecgApplet" code="ecgApplet.class" width=915 height=570>
</applet></td>
</tr>
</table>
<H3>&nbsp; </H3>
<P>&nbsp; </P>
<HR WIDTH="100%"><FONT SIZE=-1><I>ECGSYN Java Application<br>
Last updated on October 27, 2003</I></FONT>
<p align="justify">Return to ECGSYN <a href="../">Home page</a>.</p>
</BODY>
</HTML>

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<html>
<head><title>Index of /static/published-projects/ecgsyn/1.0.0/Java/</title></head>
<body>
<h1>Index of /static/published-projects/ecgsyn/1.0.0/Java/</h1><hr><pre><a href="../">../</a>
<a href="FormatNumber.class">FormatNumber.class</a> 12-Apr-2019 17:35 1020
<a href="HEADER.shtml">HEADER.shtml</a> 12-Apr-2019 17:35 673
<a href="ecgApplet%241.class">ecgApplet$1.class</a> 12-Apr-2019 17:35 989
<a href="ecgApplet%2410.class">ecgApplet$10.class</a> 12-Apr-2019 17:35 671
<a href="ecgApplet%2411.class">ecgApplet$11.class</a> 12-Apr-2019 17:35 671
<a href="ecgApplet%2412.class">ecgApplet$12.class</a> 12-Apr-2019 17:35 671
<a href="ecgApplet%2413.class">ecgApplet$13.class</a> 12-Apr-2019 17:35 671
<a href="ecgApplet%2414.class">ecgApplet$14.class</a> 12-Apr-2019 17:35 671
<a href="ecgApplet%2415.class">ecgApplet$15.class</a> 12-Apr-2019 17:35 671
<a href="ecgApplet%2416.class">ecgApplet$16.class</a> 12-Apr-2019 17:35 672
<a href="ecgApplet%2417.class">ecgApplet$17.class</a> 12-Apr-2019 17:35 672
<a href="ecgApplet%2418.class">ecgApplet$18.class</a> 12-Apr-2019 17:35 672
<a href="ecgApplet%242.class">ecgApplet$2.class</a> 12-Apr-2019 17:35 669
<a href="ecgApplet%243.class">ecgApplet$3.class</a> 12-Apr-2019 17:35 669
<a href="ecgApplet%244.class">ecgApplet$4.class</a> 12-Apr-2019 17:35 669
<a href="ecgApplet%245.class">ecgApplet$5.class</a> 12-Apr-2019 17:35 941
<a href="ecgApplet%246.class">ecgApplet$6.class</a> 12-Apr-2019 17:35 941
<a href="ecgApplet%247.class">ecgApplet$7.class</a> 12-Apr-2019 17:35 941
<a href="ecgApplet%248.class">ecgApplet$8.class</a> 12-Apr-2019 17:35 1108
<a href="ecgApplet%249.class">ecgApplet$9.class</a> 12-Apr-2019 17:35 669
<a href="ecgApplet%24ECGAnimate.class">ecgApplet$ECGAnimate.class</a> 12-Apr-2019 17:35 2716
<a href="ecgApplet%24doubleVerifier.class">ecgApplet$doubleVerifier.class</a> 12-Apr-2019 17:35 1485
<a href="ecgApplet%24ecgCalc.class">ecgApplet$ecgCalc.class</a> 12-Apr-2019 17:35 13305
<a href="ecgApplet%24ecgPanel.class">ecgApplet$ecgPanel.class</a> 12-Apr-2019 17:35 2618
<a href="ecgApplet%24integerVerifier.class">ecgApplet$integerVerifier.class</a> 12-Apr-2019 17:35 1489
<a href="ecgApplet%24sfVerifier.class">ecgApplet$sfVerifier.class</a> 12-Apr-2019 17:35 1825
<a href="ecgApplet%24sfecgVerifier.class">ecgApplet$sfecgVerifier.class</a> 12-Apr-2019 17:35 1615
<a href="ecgApplet.class">ecgApplet.class</a> 12-Apr-2019 17:35 40664
<a href="ecgApplet.form">ecgApplet.form</a> 12-Apr-2019 17:35 79509
<a href="ecgApplet.html">ecgApplet.html</a> 12-Apr-2019 17:35 2583
<a href="ecgApplet.java">ecgApplet.java</a> 12-Apr-2019 17:35 109386
<a href="ecgLicense.txt">ecgLicense.txt</a> 12-Apr-2019 17:35 2964
<a href="ecgplot.PNG">ecgplot.PNG</a> 12-Apr-2019 17:35 10273
<a href="ecgsyn-java.html">ecgsyn-java.html</a> 12-Apr-2019 17:35 2541
</pre><hr></body>
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<!--#set var="TITLE" value="ECGSYN for Matlab/Octave"-->
<!--#include virtual="/head.shtml"-->
<p>
This directory contains <a href="../">ECGSYN</a> implemented in Matlab
m-code.
<hr>

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function dxdt = derivsecgsyn(t,x,flag,rr,sfint,ti,ai,bi)
% dxdt = derivsecgsyn(t,x,flag,rr,sampfreq,ti,ai,bi)
% ODE file for generating the synthetic ECG
% This file provides dxdt = F(t,x) taking input paramters:
% rr: rr process
% sfint: Internal sampling frequency [Hertz]
% Order of extrema: [P Q R S T]
% ti = angles of extrema [radians]
% ai = z-position of extrema
% bi = Gaussian width of peaks
% Copyright (c) 2003 by Patrick McSharry & Gari Clifford, All Rights Reserved
% See IEEE Transactions On Biomedical Engineering, 50(3), 289-294, March 2003.
% Contact P. McSharry (patrick AT mcsharry DOT net) or
% G.D. Clifford (gari AT mit DOT edu)
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
%
% ecgsyn.m and its dependents are freely availble from Physionet -
% http://www.physionet.org/ - please report any bugs to the authors above.
xi = cos(ti);
yi = sin(ti);
ta = atan2(x(2),x(1));
r0 = 1;
a0 = 1.0 - sqrt(x(1)^2 + x(2)^2)/r0;
ip = 1+floor(t*sfint);
w0 = 2*pi/rr(ip);
fresp = 0.25;
zbase = 0.005*sin(2*pi*fresp*t);
dx1dt = a0*x(1) - w0*x(2);
dx2dt = a0*x(2) + w0*x(1);
dti = rem(ta - ti, 2*pi);
dx3dt = - sum(ai.*dti.*exp(-0.5*(dti./bi).^2)) - 1.0*(x(3) - zbase);
dxdt = [dx1dt; dx2dt; dx3dt];

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function [s, ipeaks] = ecgsyn(sfecg,N,Anoise,hrmean,hrstd,lfhfratio,sfint,ti,ai,bi)
% [s, ipeaks] = ecgsyn(sfecg,N,Anoise,hrmean,hrstd,lfhfratio,sfint,ti,ai,bi)
% Produces synthetic ECG with the following outputs:
% s: ECG (mV)
% ipeaks: labels for PQRST peaks: P(1), Q(2), R(3), S(4), T(5)
% A zero lablel is output otherwise ... use R=find(ipeaks==3);
% to find the R peaks s(R), etc.
%
% Operation uses the following parameters (default values in []s):
% sfecg: ECG sampling frequency [256 Hertz]
% N: approximate number of heart beats [256]
% Anoise: Additive uniformly distributed measurement noise [0 mV]
% hrmean: Mean heart rate [60 beats per minute]
% hrstd: Standard deviation of heart rate [1 beat per minute]
% lfhfratio: LF/HF ratio [0.5]
% sfint: Internal sampling frequency [256 Hertz]
% Order of extrema: [P Q R S T]
% ti = angles of extrema [-70 -15 0 15 100] degrees
% ai = z-position of extrema [1.2 -5 30 -7.5 0.75]
% bi = Gaussian width of peaks [0.25 0.1 0.1 0.1 0.4]
% Copyright (c) 2003 by Patrick McSharry & Gari Clifford, All Rights Reserved
% See IEEE Transactions On Biomedical Engineering, 50(3), 289-294, March 2003.
% Contact P. McSharry (patrick@mcsharry.net) or G. Clifford (gari@mit.edu)
% This program is free software; you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation; either version 2 of the License, or
% (at your option) any later version.
%
% This program is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% You should have received a copy of the GNU General Public License
% along with this program; if not, write to the Free Software
% Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
%
% ecgsyn.m and its dependents are freely availble from Physionet -
% http://www.physionet.org/ - please report any bugs to the authors above.
% set parameter default values
if nargin < 1
sfecg = 256;
end
if nargin < 2
N = 256;
end
if nargin < 3
Anoise = 0;
end
if nargin < 4
hrmean = 60;
end
if nargin < 5
hrstd = 1;
end
if nargin < 6
lfhfratio = 0.5;
end
if nargin < 7
sfint = 512;
end
if nargin <8
% P Q R S T
ti = [-70 -15 0 15 100];
end
% convert to radians
ti = ti*pi/180;
if nargin <9 % z position of attractor
% P Q R S T
ai = [1.2 -5 30 -7.5 0.75];
end
if nargin <10 % Gaussian width of each attractor
% P Q R S T
bi = [0.25 0.1 0.1 0.1 0.4];
end
% adjust extrema parameters for mean heart rate
hrfact = sqrt(hrmean/60);
hrfact2 = sqrt(hrfact);
bi = hrfact*bi;
ti = [hrfact2 hrfact 1 hrfact hrfact2].*ti;
% check that sfint is an integer multiple of sfecg
q = round(sfint/sfecg);
qd = sfint/sfecg;
if q ~= qd
error(['Internal sampling frequency (sfint) must be an integer multiple ' ...
'of the ECG sampling frequency (sfecg). Your current choices are: ' ...
'sfecg = ' int2str(sfecg) ' and sfint = ' int2str(sfint) '.']);
end
% define frequency parameters for rr process
% flo and fhi correspond to the Mayer waves and respiratory rate respectively
flo = 0.1;
fhi = 0.25;
flostd = 0.01;
fhistd = 0.01;
fid = 1;
fprintf(fid,'ECG sampled at %d Hz\n',sfecg);
fprintf(fid,'Approximate number of heart beats: %d\n',N);
fprintf(fid,'Measurement noise amplitude: %d \n',Anoise);
fprintf(fid,'Heart rate mean: %d bpm\n',hrmean);
fprintf(fid,'Heart rate std: %d bpm\n',hrstd);
fprintf(fid,'LF/HF ratio: %g\n',lfhfratio);
fprintf(fid,'Internal sampling frequency: %g\n',sfint);
fprintf(fid,' P Q R S T\n');
fprintf(fid,'ti = [%g %g %g %g %g] radians\n',ti(1),ti(2),ti(3),ti(4),ti(5));
fprintf(fid,'ai = [%g %g %g %g %g]\n',ai(1),ai(2),ai(3),ai(4),ai(5));
fprintf(fid,'bi = [%g %g %g %g %g]\n',bi(1),bi(2),bi(3),bi(4),bi(5));
% calculate time scales for rr and total output
sampfreqrr = 1;
trr = 1/sampfreqrr;
tstep = 1/sfecg;
rrmean = (60/hrmean);
Nrr = 2^(ceil(log2(N*rrmean/trr)));
% compute rr process
rr0 = rrprocess(flo,fhi,flostd,fhistd,lfhfratio,hrmean,hrstd,sampfreqrr,Nrr);
% upsample rr time series from 1 Hz to sfint Hz
rr = interp(rr0,sfint);
% make the rrn time series
dt = 1/sfint;
rrn = zeros(length(rr),1);
tecg=0;
i = 1;
while i <= length(rr)
tecg = tecg+rr(i);
ip = round(tecg/dt);
rrn(i:ip) = rr(i);
i = ip+1;
end
Nt = ip;
% integrate system using fourth order Runge-Kutta
fprintf(fid,'Integrating dynamical system\n');
x0 = [1,0,0.04];
Tspan = [0:dt:(Nt-1)*dt];
[T,X0] = ode45('derivsecgsyn',Tspan,x0,[],rrn,sfint,ti,ai,bi);
% downsample to required sfecg
X = X0(1:q:end,:);
% extract R-peaks times
ipeaks = detectpeaks(X, ti, sfecg);
% Scale signal to lie between -0.4 and 1.2 mV
z = X(:,3);
zmin = min(z);
zmax = max(z);
zrange = zmax - zmin;
z = (z - zmin)*(1.6)/zrange -0.4;
% include additive uniformly distributed measurement noise
eta = 2*rand(length(z),1)-1;
s = z + Anoise*eta;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function rr = rrprocess(flo, fhi, flostd, fhistd, lfhfratio, hrmean, hrstd, sfrr, n)
w1 = 2*pi*flo;
w2 = 2*pi*fhi;
c1 = 2*pi*flostd;
c2 = 2*pi*fhistd;
sig2 = 1;
sig1 = lfhfratio;
rrmean = 60/hrmean;
rrstd = 60*hrstd/(hrmean*hrmean);
df = sfrr/n;
w = [0:n-1]'*2*pi*df;
dw1 = w-w1;
dw2 = w-w2;
Hw1 = sig1*exp(-0.5*(dw1/c1).^2)/sqrt(2*pi*c1^2);
Hw2 = sig2*exp(-0.5*(dw2/c2).^2)/sqrt(2*pi*c2^2);
Hw = Hw1 + Hw2;
Hw0 = [Hw(1:n/2); Hw(n/2:-1:1)];
Sw = (sfrr/2)*sqrt(Hw0);
ph0 = 2*pi*rand(n/2-1,1);
ph = [ 0; ph0; 0; -flipud(ph0) ];
SwC = Sw .* exp(j*ph);
x = (1/n)*real(ifft(SwC));
xstd = std(x);
ratio = rrstd/xstd;
rr = rrmean + x*ratio;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function ind = detectpeaks(X, thetap, sfecg)
N = length(X);
irpeaks = zeros(N,1);
theta = atan2(X(:,2),X(:,1));
ind0 = zeros(N,1);
for i=1:N-1
a = ( (theta(i) <= thetap) & (thetap <= theta(i+1)) );
j = find(a==1);
if ~isempty(j)
d1 = thetap(j) - theta(i);
d2 = theta(i+1) - thetap(j);
if d1 < d2
ind0(i) = j;
else
ind0(i+1) = j;
end
end
end
d = ceil(sfecg/64);
d = max([2 d])
ind = zeros(N,1);
z = X(:,3);
zmin = min(z);
zmax = max(z);
zext = [zmin zmax zmin zmax zmin];
sext = [1 -1 1 -1 1];
for i=1:5
clear ind1 Z k vmax imax iext;
ind1 = find(ind0==i);
n = length(ind1);
Z = ones(n,2*d+1)*zext(i)*sext(i);
for j=-d:d
k = find( (1 <= ind1+j) & (ind1+j <= N) );
Z(k,d+j+1) = z(ind1(k)+j)*sext(i);
end
[vmax, ivmax] = max(Z,[],2);
iext = ind1 + ivmax-d-1;
ind(iext) = i;
end

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<html>
<head><title>Index of /static/published-projects/ecgsyn/1.0.0/Matlab/</title></head>
<body>
<h1>Index of /static/published-projects/ecgsyn/1.0.0/Matlab/</h1><hr><pre><a href="../">../</a>
<a href="HEADER.shtml">HEADER.shtml</a> 12-Apr-2019 17:35 186
<a href="derivsecgsyn.m">derivsecgsyn.m</a> 12-Apr-2019 17:35 1911
<a href="ecgsyn.m">ecgsyn.m</a> 12-Apr-2019 17:35 6795
</pre><hr></body>
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<html>
<head><title>Index of /static/published-projects/ecgsyn/1.0.0/</title></head>
<body>
<h1>Index of /static/published-projects/ecgsyn/1.0.0/</h1><hr><pre><a href="../">../</a>
<a href="C/">C/</a> 12-Apr-2019 17:35 -
<a href="Java/">Java/</a> 12-Apr-2019 17:35 -
<a href="Matlab/">Matlab/</a> 12-Apr-2019 17:35 -
<a href="paper/">paper/</a> 12-Apr-2019 17:35 -
<a href="sample-output/">sample-output/</a> 12-Apr-2019 17:35 -
<a href="ecgsyn.tar.gz">ecgsyn.tar.gz</a> 12-Apr-2019 17:35 165286
</pre><hr></body>
</html>

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/* Century Schoolbook font is very similar to Computer Modern Math: cmmi */
.MATH { font-family: "Century Schoolbook", serif; }
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BIG.XHUGE { font-size : xx-large }
/* heading styles */
H1 { }
H2 { }
H3 { }
H4 { }
H5 { }
/* mathematics styles */
DIV.displaymath { } /* math displays */
TD.eqno { } /* equation-number cells */
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2 Final//EN">
<!--Converted with jLaTeX2HTML 2002 (1.62) JA patch-1.4
patched version by: Kenshi Muto, Debian Project.
LaTeX2HTML 2002 (1.62),
original version by: Nikos Drakos, CBLU, University of Leeds
* revised and updated by: Marcus Hennecke, Ross Moore, Herb Swan
* with significant contributions from:
Jens Lippmann, Marek Rouchal, Martin Wilck and others -->
<HTML>
<HEAD>
<TITLE>Footnotes</TITLE>
<META NAME="description" CONTENT="Footnotes">
<META NAME="keywords" CONTENT="ecgpqrst">
<META NAME="resource-type" CONTENT="document">
<META NAME="distribution" CONTENT="global">
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
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<META HTTP-EQUIV="Content-Style-Type" CONTENT="text/css">
<LINK REL="STYLESHEET" HREF="ecgpqrst.css">
<LINK REL="previous" HREF="node8.html">
<LINK REL="up" HREF="index.shtml">
</HEAD>
<BODY >
<DL>
<DT><A NAME="foot31">...<IMG
WIDTH="21" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img6.png"
ALT="$^{2,3}$"></A><A
HREF="index.shtml#tex2html1"><SUP><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
SRC="file:/usr/share/latex2html/icons/footnote.png"></SUP></A></DT>
<DD><IMG
WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img5.png"
ALT="$^1$">Department of Engineering Science,
University of Oxford, Oxford OX1 3PJ.
<PRE>.
</PRE>
</DD>
<DT><A NAME="foot32">...</A><A
HREF="index.shtml#tex2html2"><SUP><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
SRC="file:/usr/share/latex2html/icons/footnote.png"></SUP></A></DT>
<DD><IMG
WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img7.png"
ALT="$^2$">Mathematical Institute, University of Oxford, Oxford OX1 3LB.
<PRE>.
</PRE>
</DD>
<DT><A NAME="foot33">...</A><A
HREF="index.shtml#tex2html3"><SUP><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
SRC="file:/usr/share/latex2html/icons/footnote.png"></SUP></A></DT>
<DD><IMG
WIDTH="11" HEIGHT="17" ALIGN="BOTTOM" BORDER="0"
SRC="img8.png"
ALT="$^3$">Centre for the Analysis of Time Series, London School
of Economics, London WC2A 2AE.
<PRE>.
</PRE>
</DD>
<DT><A NAME="foot34">...</A><A
HREF="index.shtml#tex2html4"><SUP><IMG ALIGN="BOTTOM" BORDER="1" ALT="[*]"
SRC="file:/usr/share/latex2html/icons/footnote.png"></SUP></A></DT>
<DD>E-mail: mcsharry@robots.ox.ac.uk
<PRE>.
</PRE>
</DD>
</DL>
</BODY>
</HTML>

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