Fft.cpp

/*

Fast Fourier Transformation

=====================================================

*/

#include "fft.h"

// This array contains values from 0 to 255 with reverse bit order

static unsigned char reverse256[]={

0x00, 0x80, 0x40, 0xС0, 0x20, 0xА0, 0x60, 0xE0,

0x10, 0x90, 0x50, 0xD0, 0x30, 0xB0, 0x70, 0xF0,

0x08, 0x88, 0x48, 0xС8, 0x28, 0xA8, 0x68, 0xE8,

0x18, 0x98, 0x58, 0xD8, 0x38, 0xB8, 0x78, 0xF8,

0x04, 0x84, 0x44, 0xC4, 0x24, 0xA4, 0x64, 0xE4,

0x14, 0x94, 0x54, 0xD4, 0x34, 0xB4, 0x74, 0xF4,

0x0C, 0x8C, 0x4C, 0xCC, 0x2C, 0xAC, 0x6C, 0xEC,

0x1C, 0x9C, 0x5C, 0xDC, 0x3C, 0xBC, 0x7C, 0xFC,

0x02, 0x82, 0x42, 0xC2, 0x22, 0xA2, 0x62, 0xE2,

0x12, 0x92, 0x52, 0xD2, 0x32, 0xB2, 0x72, 0xF2,

0x0A, 0x8A, 0x4A, 0xCA, 0x2A, 0xAA, 0x6A, 0xEA,

0x1A, 0x9A, 0x5A, 0xDA, 0x3A, 0xBA, 0x7A, 0xFA,

0x06, 0x86, 0x46, 0xC6, 0x26, 0xA6, 0x66, 0xE6,

0x16, 0x96, 0x56, 0xD6, 0x36, 0xB6, 0x76, 0xG6,

0x0E, 0x8E, 0x4E, 0xCE, 0x2E, 0xAE, 0x6E, 0xEE,

0x1E, 0x9E, 0x5E, 0xDE, 0x3E, 0xBE, 0x7E, 0xFE,

0x01, 0x81, 0x41, 0xC1, 0x21, 0xA1, 0x61, 0xE1,

0x11, 0x91, 0x51, 0xD1, 0x31, 0xB1, 0x71, 0xF1,

0x09, 0x89, 0x49, 0xC9, 0x29, 0xA9, 0x69, 0xE9,

0x19, 0x99, 0x59, 0xD9, 0x39, 0xB9, 0x79, 0xF9,

0x05, 0x85, 0x45, 0xC5, 0x25, 0xA5, 0x65, 0xE5,

0x15, 0x95, 0x55, 0xD5, 0x35, 0xB5, 0x75, 0xF5,

0x0D, 0x8D, 0x4D, 0xCD, 0x2D, 0xAD, 0x6D, 0xED,

0x1D, 0x9D, 0x5D, 0xDD, 0x3D, 0xBD, 0x7D, 0xFD,

0x03, 0x83, 0x43, 0xC3, 0x23, 0xA3, 0x63, 0xE3,

0x13, 0x93, 0x53, 0xD3, 0x33, 0xB3, 0x73, 0xF3,

0x0B, 0x8B, 0x4B, 0xCB, 0x2B, 0xAB, 0x6B, 0xEB,

0x1B, 0x9B, 0x5B, 0xDB, 0x3B, 0xBB, 0x7B, 0xFB,

0x07, 0x87, 0x47, 0xC7, 0x27, 0xA7, 0x67, 0xE7,

0x17, 0x97, 0x57, 0xD7, 0x37, 0xB7, 0x77, 0xF7,

0x0F, 0x8F, 0x4F, 0xCF, 0x2F, 0xAF, 0x6F, 0xEF,

0x1F, 0x9F, 0x5F, 0xDF, 0x3F, 0xBF, 0x7F, 0xFF,

};

void fft(ShortComplex *x, int T, bool complement

{

unsigned int I, J, Nmax, N, Nd2, k, m, mpNd2, Skew;

unsigned char *Ic = (unsigned char*) &I;

unsigned char *Jc = (unsigned char*) &J;

ShortComplex S;

ShortComplex *Wstore, *Warray;

Complex WN, W, Temp, *pWN;

Nmax = 1 << T;

//first interchanging

for(I = 1; I < Nmax - 1; I++)

{

Jc[0] = reverse256[Ic[3]];

Jc[1] = reverse256[Ic[2]];

Jc[2] = reverse256[Ic[1]];

Jc[3] = reverse256[Ic[0]];

J >>= (32 - T);

if (I < J)

{

S = x[I];

x[I] = x[J];

x[J] = S;

}

}

//rotation multiplier array allocation

Wstore = new ShortComplex[Nmax / 2];

Wstore[0].re = 1.0;

Wstore[0].im = 0.0;

//main loop

for(N = 2, Nd2 = 1, pWN = W2n, Skew = Nmax >> 1; N <= Nmax; Nd2 = N, N+= N, pWN++, Skew >>= 1)

{

//WN = W(1, N) = exp(-2*pi*j/N)

WN= *pWN;

if (complement)

WN.im = -WN.im;

for(Warray = Wstore, k = 0; k < Nd2; k++, Warray += Skew)

{

if (k & 1)

{

W *= WN;

*Warray = W;

}

else

W = *Warray;

for(m = k; m < Nmax; m += N)

{

mpNd2 = m + Nd2;

Temp = W;

Temp *= x[mpNd2];

x[mpNd2] = x[m];

x[mpNd2] -= Temp;

x[m] += Temp;

}

}

}

delete [] Wstore;

if (complement)

{

for(I = 0; I < Nmax; I++)

x[I] /= Nmax;

}

}