Fast Fourier transform — FFT — source code

//   fft.cpp - implementation of class
//   of fast Fourier transform - FFT
//
//   The code is property of LIBROW
//   You can use it on your own
//   When utilizing credit LIBROW site

//   Include declaration file
#include "fft.h"
//   Include math library
#include <math.h>

//   FORWARD FOURIER TRANSFORM
//     Input  - input data
//     Output - transform result
//     N      - length of both input data and result
bool CFFT::Forward(const complex *const Input, complex *const Output,
   const unsigned int N)
{
   //   Check input parameters
   if (!Input || !Output || N < 1 || N & (N - 1))
      return false;
   //   Initialize data
   Rearrange(Input, Output, N);
   //   Call FFT implementation
   Perform(Output, N);
   //   Succeeded
   return true;
}

//   FORWARD FOURIER TRANSFORM, INPLACE VERSION
//     Data - both input data and output
//     N    - length of both input data and result
bool CFFT::Forward(complex *const Data, const unsigned int N)
{
   //   Check input parameters
   if (!Data || N < 1 || N & (N - 1))
      return false;
   //   Rearrange
   Rearrange(Data, N);
   //   Call FFT implementation
   Perform(Data, N);
   //   Succeeded
   return true;
}

//   INVERSE FOURIER TRANSFORM
//     Input  - input data
//     Output - transform result
//     N      - length of both input data and result
//     Scale  - if to scale result
bool CFFT::Inverse(const complex *const Input, complex *const Output,
   const unsigned int N, const bool Scale /* = true */)
{
   //   Check input parameters
   if (!Input || !Output || N < 1 || N & (N - 1))
      return false;
   //   Initialize data
   Rearrange(Input, Output, N);
   //   Call FFT implementation
   Perform(Output, N, true);
   //   Scale if necessary
   if (Scale)
      CFFT::Scale(Output, N);
   //   Succeeded
   return true;
}

//   INVERSE FOURIER TRANSFORM, INPLACE VERSION
//     Data  - both input data and output
//     N     - length of both input data and result
//     Scale - if to scale result
bool CFFT::Inverse(complex *const Data, const unsigned int N,
   const bool Scale /* = true */)
{
   //   Check input parameters
   if (!Data || N < 1 || N & (N - 1))
      return false;
   //   Rearrange
   Rearrange(Data, N);
   //   Call FFT implementation
   Perform(Data, N, true);
   //   Scale if necessary
   if (Scale)
      CFFT::Scale(Data, N);
   //   Succeeded
   return true;
}

//   Rearrange function
void CFFT::Rearrange(const complex *const Input, complex *const Output,
   const unsigned int N)
{
   //   Data entry position
   unsigned int Target = 0;
   //   Process all positions of input signal
   for (unsigned int Position = 0; Position < N; ++Position)
   {
      //  Set data entry
      Output[Target] = Input[Position];
      //   Bit mask
      unsigned int Mask = N;
      //   While bit is set
      while (Target & (Mask >>= 1))
         //   Drop bit
         Target &= ~Mask;
      //   The current bit is 0 - set it
      Target |= Mask;
   }
}

//   Inplace version of rearrange function
void CFFT::Rearrange(complex *const Data, const unsigned int N)
{
   //   Swap position
   unsigned int Target = 0;
   //   Process all positions of input signal
   for (unsigned int Position = 0; Position < N; ++Position)
   {
      //   Only for not yet swapped entries
      if (Target > Position)
      {
         //   Swap entries
         const complex Temp(Data[Target]);
         Data[Target] = Data[Position];
         Data[Position] = Temp;
      }
      //   Bit mask
      unsigned int Mask = N;
      //   While bit is set
      while (Target & (Mask >>= 1))
         //   Drop bit
         Target &= ~Mask;
      //   The current bit is 0 - set it
      Target |= Mask;
   }
}

//   FFT implementation
void CFFT::Perform(complex *const Data, const unsigned int N,
   const bool Inverse /* = false */)
{
   const double pi = Inverse ? 3.14159265358979323846 : -3.14159265358979323846;
   //   Iteration through dyads, quadruples, octads and so on...
   for (unsigned int Step = 1; Step < N; Step <<= 1)
   {
      //   Jump to the next entry of the same transform factor
      const unsigned int Jump = Step << 1;
      //   Angle increment
      const double delta = pi / double(Step);
      //   Auxiliary sin(delta / 2)
      const double Sine = sin(delta * .5);
      //   Multiplier for trigonometric recurrence
      const complex Multiplier(-2. * Sine * Sine, sin(delta));
      //   Start value for transform factor, fi = 0
      complex Factor(1.);
      //   Iteration through groups of different transform factor
      for (unsigned int Group = 0; Group < Step; ++Group)
      {
         //   Iteration within group 
         for (unsigned int Pair = Group; Pair < N; Pair += Jump)
         {
            //   Match position
            const unsigned int Match = Pair + Step;
            //   Second term of two-point transform
            const complex Product(Factor * Data[Match]);
            //   Transform for fi + pi
            Data[Match] = Data[Pair] - Product;
            //   Transform for fi
            Data[Pair] += Product;
         }
         //   Successive transform factor via trigonometric recurrence
         Factor = Multiplier * Factor + Factor;
      }
   }
}

//   Scaling of inverse FFT result
void CFFT::Scale(complex *const Data, const unsigned int N)
{
   const double Factor = 1. / double(N);
   //   Scale all data entries
   for (unsigned int Position = 0; Position < N; ++Position)
      Data[Position] *= Factor;
}