// fft.cpp - impelementation 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 input data
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;
}
