一维离散傅里叶变换

#include<iostream>
#include<cmath>
#include<iomanip>
using namespace std;
#define PI 3.1415926535
class FFT {
private:
  double real[8], imag[8];
  double re[8], im[8];
  int i = 0;
public:
  FFT() {};
  void init();
  void print();
  void fft();
  void ifft();
};
void FFT::init()
{
  for (int i = 1; i < 9; i++)
    real[i-1] = double(i), imag[i-1] = 0.0;
}
void FFT::print()
{
  if (i==0)
    cout << "原始数据" << endl;
  i++;
  for (int i = 0; i < 8; i++)
    cout << real[i] << " " << imag[i] << endl;
}
void FFT::fft()
{
  double a=0, b=0;
  for (int i = 0; i < 8; i++)
  {
    a = 0; b = 0;
    for (int j = 0; j < 8; j++)
    {
      a += real[j] * cos((2 * PI*i*j) / 8);
      b += real[j] * sin((2 * PI*i*j) / 8);
    }
    re[i] = a;
    im[i] = -b;
  }
  cout << "变换后的数据" << endl;
  for (int i = 0; i < 8; i++)
  {
    cout << re[i] << " " <<setiosflags(ios::fixed)<<setprecision(10)<< im[i] << endl;
  }
}
void FFT::ifft()
{
  double a = 0, b = 0;
  for (int i = 0; i < 8; i++)
  {
    a = 0;
    b = 0;
    for (int j = 0; j < 8; j++)
    {
      a += re[j] * cos((i*j * 2 * PI) / 8) - im[j] * sin((i*j * 2 * PI) / 8);
      b += im[j] * cos((i*j * 2 * PI) / 8) + re[j] * sin((i*j * 2 * PI) / 8);
    }
    real[i] = a / 8;
    imag[i] = b / 8;
  }
}
int main()
{
  FFT a;
  a.init();
  a.print();
  a.fft();
  a.ifft();
  cout << "逆变换后的数据" << endl;
  a.print();
  return 0;
}