diff --git a/examples/CMakeLists.txt b/examples/CMakeLists.txt
index edfba88..42515f4 100644
--- a/examples/CMakeLists.txt
+++ b/examples/CMakeLists.txt
@@ -1,5 +1,11 @@
 include_directories (${CMAKE_SOURCE_DIR}/src)
 
+find_package(Qt5 COMPONENTS
+                 Widgets
+                 PrintSupport
+                 REQUIRED
+)
+
 file(
 	GLOB 
 	usage_examples
@@ -9,7 +15,7 @@ file(
 foreach(f ${usage_examples})
   get_filename_component(exampleName ${f} NAME_WE) 
   add_executable(${exampleName} ${f}) 
-	target_link_libraries(${exampleName} ${OpenCV_LIBS})
+	target_link_libraries(${exampleName} ${OpenCV_LIBS} fftw3 plotcpp qcustomplot Qt5::Widgets Qt5::PrintSupport)
   install(PROGRAMS ${CMAKE_CURRENT_BINARY_DIR}/${exampleName}
     DESTINATION bin
     RENAME ${CMAKE_PROJECT_NAME}-${exampleName})
diff --git a/examples/test-fft.cpp b/examples/test-fft.cpp
new file mode 100644
index 0000000..17db501
--- /dev/null
+++ b/examples/test-fft.cpp
@@ -0,0 +1,51 @@
+#include <fftw3.h>
+#include <cmath>
+#include <libplotcpp/plotcpp.hpp>
+
+double pi() {
+	return 3.1415;
+}
+
+std::vector<double> tfd2vect(fftw_complex* tfd, int N) {
+	std::vector<double> res;
+	auto it = tfd;
+	for (int i = 0; i != N; ++i) {
+		fftw_complex c = {*it[0], *it[1]};
+		res.push_back(sqrt(c[0]*c[0] + c[1]*c[1]));
+		it++;
+	}
+
+	return res;
+}
+
+int main(int argc, char** argv) {
+	QApplication app(argc, argv);
+	fftw_complex *in, *out;
+	fftw_plan p;
+
+	int N = 500;
+	in = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);
+	out = (fftw_complex*) fftw_malloc(sizeof(fftw_complex) * N);
+	p = fftw_plan_dft_1d(N, in, out, FFTW_FORWARD, FFTW_MEASURE);
+
+	std::vector<double> xx;
+	for (int i = 0; i != N; ++i) {
+		xx.push_back(i);
+	}
+
+	for (int i = 0; i != N; ++i) {
+		in[i][0] = sin(2*pi()*50*i/N);
+	}
+
+	fftw_execute(p); /* repeat as needed */
+
+	std::vector<double> res = tfd2vect(out, N);
+	PlotCpp g;
+	g.plot(xx, res);
+	g.draw();
+
+
+	fftw_destroy_plan(p);
+	fftw_free(in); fftw_free(out);
+	return app.exec();
+}
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index de84d7b..ce8f025 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -1,8 +1,11 @@
 # file(GLOB headers   *.hpp)
 # file(GLOB lib_files *.cpp)
 
-add_executable(traitement traitement.cpp)
-target_link_libraries(traitement ${OpenCV_LIBS})
+# add_executable(traitement traitement.cpp)
+# target_link_libraries(traitement ${OpenCV_LIBS} fftw3)
+
+add_executable(test-fft test-fft.cpp)
+target_link_libraries(test-fft)
 
 # target_include_directories(blk PUBLIC ${CMAKE_CURRENT_SOURCE_DIR})
 # target_compile_options    (blk PUBLIC -std=c++11                 )
diff --git a/src/math.hpp b/src/math.hpp
new file mode 100644
index 0000000..ef2c90a
--- /dev/null
+++ b/src/math.hpp
@@ -0,0 +1,111 @@
+#pragma once
+
+#include <vector>
+#include <complex>
+#include <opencv2/opencv.hpp>
+#include <iterator>
+#include <cmath>
+
+namespace math {
+
+  using complex = std::complex<float>;
+  using signal = std::vector<double>;
+  using csignal = std::vector<complex>;
+  using contour = std::vector<cv::Point>;
+  constexpr double pi() {return std::atan(1)*4;}
+
+  //TODO implémenter la fft
+  csignal fft(const signal& input) {
+    //TODO: s'assurer que le signal est bien formé (i.e. bonne taille)
+    return fft_rec(input);
+  };
+
+  csignal fft_rec(const signal& input) {
+    int size = input.size();
+
+    if (size == 1) {
+      return input;
+    } else {
+      signal odd;
+      signal even;
+      std::back_insert_iterator<signal> odd_back_it(odd);
+      std::back_insert_iterator<signal> even_back_it(even);
+      bool insert_in_even = false;
+
+      for (auto it = input.begin(); it != input.end(); ++it) {
+        if (insert_in_even) {
+          *even_back_it++ = *it;
+          insert_in_even = false;
+        } else {
+          *odd_back_it++ = *it;
+          insert_in_even = true;
+        }
+      }
+
+      signal odd_fft = fft_rec(odd);
+      signal even_fft = fft_rec(even);
+      signal res;
+      res.reserve(size);
+
+      for (int k = 0; k<size/2; ++k) {
+        complex t = std::exp(complex(0, -2*pi()*k/size))*odd[k];
+        res[k] = even[k] + t;
+        res[size/2+k] = even[k] - t;
+      }
+      return res;
+    }
+  }
+
+  complex mean(const signal& sig) {
+    complex res = 0;
+    for (auto x: sig) {
+      res += x;
+    }
+    return complex(res.real()/sig.size(), res.imag()/sig.size());
+  };
+
+  signal cont2sig(const contour& cont) {
+    signal sig;
+    auto sig_it = sig.begin();
+    auto cont_it = cont.begin();
+
+    for (auto cont_it = cont.begin(); cont_it != cont.end(); ++cont_it) {
+      *sig_it = complex((*cont_it).x, (*cont_it).y);
+      sig_it++;
+    }
+    return sig;
+  };
+
+  contour coef2cont(const signal& tfd, complex mean, int size, int cmax) {
+    contour cont;
+    auto tf_it = tfd.begin();
+    auto cont_it = cont.begin();
+
+    for (auto tf_it = tfd.begin(); tf_it != tfd.end(); ++tf_it) {
+      //TODO retrouver la formule
+      //*cont_it = mean; 
+    }
+    return cont;
+  };
+
+  int max_cont(const std::vector<contour>& contours) {
+    int max = 0;
+    int id = 0;
+    for (int i=0; i<contours.size(); ++i) {
+      if (contours[i].size() > max) {
+        max = contours[i].size();
+        id = i;
+      }  
+    }
+    return id;
+  };
+
+  contour simplify_contour(const contour& cont, int cmax) {
+    contour res;
+    signal z = cont2sig(cont);
+    complex zm = mean(z);
+    signal tfd = fft(z);
+    res = coef2cont(tfd, zm, 0, cmax);
+    return res;
+  };
+}
diff --git a/src/test-fft.cpp b/src/test-fft.cpp
new file mode 100644
index 0000000..cd382a0
--- /dev/null
+++ b/src/test-fft.cpp
@@ -0,0 +1,13 @@
+#include <math.hpp>
+#include <cmath>
+
+int main(int argc, char** argv) {
+  math::signal s;
+
+  for (int i=0; i<100; ++i) {
+    s.push_back(std::sin(2*math::pi()*50*i/100));
+  }
+  math::fft(s);
+
+  return 0;
+}
diff --git a/src/traitement.cpp b/src/traitement.cpp
index 76f7079..80ece67 100644
--- a/src/traitement.cpp
+++ b/src/traitement.cpp
@@ -1,4 +1,7 @@
 #include "opencv2/opencv.hpp"
+#include <math.h>
+#include <algorithm>
+#include "math.hpp"
 
 int filter(const cv::Mat& img, cv::Mat output, int seuil) {
 	bool detect = false;
@@ -25,12 +28,15 @@ int filter(const cv::Mat& img, cv::Mat output, int seuil) {
 }
 
 int main(int argc, char** argv) {
-	int seuil=80;
+	int seuil=0;
 
 	if (argc > 1) {
 		seuil = atol(argv[1]);
 	}
 
+	int cmax = 10;
+	int N = 5000;
+
 	char detect;
 	cv::VideoCapture cap(0); 
 	if(!cap.isOpened())  
@@ -39,10 +45,10 @@ int main(int argc, char** argv) {
 	cv::namedWindow("Detection",1);
 	cv::namedWindow("Contours",1);
 	while(true) {
-		int X,Y,DIM,index;
+		int X, Y, DIM, index;
 		unsigned int numc;
-		uchar R,G,B;
-		std::vector<std::vector<cv::Point> > contours;
+		uchar R, G, B;
+		std::vector<std::vector<cv::Point>> contours;
 		std::vector<cv::Vec4i> hierarchy;
 		cv::Mat frame;
 		cap >> frame;
@@ -60,15 +66,14 @@ int main(int argc, char** argv) {
 		cv::imshow("Detection", binaire);
 		cv::findContours(binaire, contours, hierarchy, CV_RETR_EXTERNAL, CV_CHAIN_APPROX_NONE);
 		cv::Mat Dessin = cv::Mat::zeros(X,Y, CV_8UC1);
-		unsigned int max = 0;
-		int id = 0;
-		for(numc = 0; numc<contours.size(); numc++) {
-			if (contours[numc].size() > max) {
-				max = contours[numc].size();
-				id = numc;
-			}
-		}
+
+    int id = math::max_cont(contours);
+		std::cout << contours[id].size() << std::endl;
+
+		std::vector<cv::Point> new_cont = math::simplify_contour(contours[id], cmax);
+
 		cv::drawContours(Dessin, contours, id, 255);
+		cv::drawContours(Dessin, new_cont, id, 255);
 		cv::imshow("Contours", Dessin);
 		if(cv::waitKey(30) == 27) {
 			break;