#include "TH1D.h"
#include "TVirtualFFT.h"
#include "TF1.h"
#include "TCanvas.h"

void FFT_Back(){

   //prepare the canvas for drawing
   TCanvas *myc = new TCanvas("myc", "Fast Fourier Transform", 800, 600);
   myc->SetFillColor(45);
   TPad *c1_1 = new TPad("c1_1", "c1_1",0.01,0.51,0.49,0.99);
   TPad *c1_2 = new TPad("c1_2", "c1_2",0.51,0.51,0.99,0.99);
   TPad *c1_3 = new TPad("c1_3", "c1_3",0.01,0.01,0.49,0.49);
   TPad *c1_4 = new TPad("c1_4", "c1_4",0.51,0.01,0.99,0.49);
   c1_1->Draw();
   c1_2->Draw();
   c1_3->Draw();
   c1_4->Draw();
   c1_1->SetFillColor(30);
   c1_1->SetFrameFillColor(42);
   c1_2->SetFillColor(30);
   c1_2->SetFrameFillColor(42);
   c1_3->SetFillColor(30);
   c1_3->SetFrameFillColor(42);
   c1_4->SetFillColor(30);
   c1_4->SetFrameFillColor(42);
   c1_1->cd();

   //A function to sample
   TF1 *fsin = new TF1("fsin", "sin(x)", 0, 2*TMath::Pi());
   fsin->Draw();


   Int_t n=1000;
   TH1D *hsin = new TH1D("hsin", "hsin", n+1, 0, 2*TMath::Pi());
   Double_t x;



   //Fill the histogram with function values
   for (Int_t i=0; i<=n; i++){
      x = (Double_t(i)/n)*(2*TMath::Pi());
      hsin->SetBinContent(i+1, fsin->Eval(x));
   }
   hsin->Draw("same");
   fsin->GetXaxis()->SetLabelSize(0.05);
   fsin->GetYaxis()->SetLabelSize(0.05);
    
   c1_2->cd();
   double re, im;
   TH1 *hm =0;
   hm = hsin->FFT(hm, "MAG");
   hm->Draw();

   c1_3->cd();
   TH1 *hp = 0;
   hp = hsin->FFT(hp, "PH");
   hp->Draw();

   c1_4->cd();
   TVirtualFFT *fft = TVirtualFFT::GetCurrentTransform();
   fft->GetPointsComplex(re,im);

   TVirtualFFT *fft_back = TVirtualFFT::FFT(1, &n, "C2R M K");
   fft_back->SetPointsComplex(re,im);
   fft_back->Transform();
   TH1 *hb = 0;
   hb = TH1::TransformHisto(fft_back,hb,"MAG");
   hb->Draw();

}