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fft.cpp
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fft.cpp
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#include<iostream>
#include<math.h>
#include<stdlib.h>
#include<time.h>
using namespace std;
int INITIAL(double *x_r, double*x_i, int N) ;
void FFT(double *x_r, double *x_i, double *y_r, double *y_i,int p, int q , int r) ;
int main()
{
double *x_r, *x_i, *y_r, *y_i ;
int p, q, r, N=1 ;
cout << "Please input the p, q, r :" ;
cin >> p >> q >> r ;
for ( int i = 0 ; i<p ;i ++) N = N*2 ;
for ( int i = 0 ; i<q ;i ++) N = N*3 ;
for ( int i = 0 ; i<r ;i ++) N = N*5 ;
cout << "N = 2^" << p << " * 3^" << q << " * 5^" << r << " = " << N << endl ;
x_r = (double*) malloc( N*sizeof(double)) ;
x_i = (double*) malloc( N*sizeof(double)) ;
y_r = (double*) malloc( N*sizeof(double)) ;
y_i = (double*) malloc( N*sizeof(double)) ;
INITIAL(x_r, x_i, N) ;
FFT(x_r,x_i,y_r,y_i,p,q,r) ;
}
int INITIAL(double *x_r, double*x_i, int N)
{
for ( int i = 0 ; i< N ; i++)
{
x_r[i] = i ;
x_i[i] = 0.0 ;
}
}
void FFT(double *x_r, double *x_i, double *y_r, double *y_i, int p, int q , int r)
{
int N = 1 ;
for ( int i = 0 ; i<p ;i ++) N = N*2 ;
for ( int i = 0 ; i<q ;i ++) N = N*3 ;
for ( int i = 0 ; i<r ;i ++) N = N*5 ;
for ( int i = 0 ; i<N ; i++)
{
y_r[i] = x_r[i] ;
y_i[i] = x_i[i] ;
}
int i = 0 , j = 0, M ;
while ( i < N)
{
y_r[i] = j ;
if ( N%5 == 0 ) M = N/5 ;
else if ( N%5 != 0 && N % 3 == 0 ) M = N/3 ;
else M = N/2 ;
int k = M ;
int r = (N/M)-1 ;
while ( j >= r * k && k > 0 )
{
j -= r *k ;
if ( k%5 == 0 ) k = k/5, r = 4 ;
else if ( k%5 != 0 && k % 3 == 0 ) k = k/3, r=2 ;
else k = k/2, r=1 ;
}
j += k ;
i++ ;
}
int l = 1 ;
while (l<=r)
{
double n = pow(5,l) ;
for ( int i = 0 ; i< n/5 ; i++)
{
double phi = -2.0*M_PI*i/n ;
double theta = -2.0*M_PI/5 ;
double w_r = cos(theta);
double w_i = sin(theta);
double w2_r = cos(2*theta);
double w2_i = sin(2*theta);
double v_r = cos(phi) ;
double v_i = sin(phi) ;
double v2_r = cos(phi*2) ;
double v2_i = sin(phi*2) ;
double v3_r = cos(phi*3) ;
double v3_i = sin(phi*3) ;
double v4_r = cos(phi*4) ;
double v4_i = sin(phi*4) ;
for ( int j = i ; j < N ; j += n )
{
int j1 = j + n/5 ;
int j2 = j + 2*n/5 ;
int j3 = j + 3*n/5 ;
int j4 = j + 4*n/5 ;
double temp ;
temp = y_r[j1]*v_i + y_i[j1]*v_r ;
y_r[j1] = y_r[j1]*v_r - y_i[j1]*v_i ;
y_i[j1] = temp ;
temp = y_r[j2]*v2_i + y_i[j2]*v2_r ;
y_r[j2] = y_r[j2]*v2_r - y_i[j2]*v2_i ;
y_i[j2] = temp ;
temp = y_r[j3]*v3_i + y_i[j3]*v3_r ;
y_r[j3] = y_r[j3]*v3_r - y_i[j3]*v3_i ;
y_i[j3] = temp ;
temp = y_r[j4]*v4_i + y_i[j4]*v4_r ;
y_r[j4] = y_r[j4]*v4_r - y_i[j4]*v4_i ;
y_i[j4] = temp ;
double a11_r = y_r[j1]*w_r-w_i*y_i[j1];
double a11_i = y_i[j1]*w_r+w_i*y_r[j1];
double a21_r = y_r[j1]*w2_r-w2_i*y_i[j1] ;
double a21_i = y_i[j1]*w2_r+w2_i*y_r[j1];
double a41_r = y_r[j1]*w2_r+w2_i*y_i[j1] ;
double a41_i = y_i[j1]*w2_r-w2_i*y_r[j1];
double a31_r = y_r[j1]*w_r+w_i*y_i[j1];
double a31_i = y_i[j1]*w_r-w_i*y_r[j1];
double a42_r = y_r[j2]*w_r-w_i*y_i[j2];
double a42_i = y_i[j2]*w_r+w_i*y_r[j2];
double a12_r = y_r[j2]*w2_r-w2_i*y_i[j2] ;
double a12_i = y_i[j2]*w2_r+w2_i*y_r[j2];
double a32_r = y_r[j2]*w2_r+w2_i*y_i[j2] ;
double a32_i = y_i[j2]*w2_r-w2_i*y_r[j2];
double a22_r = y_r[j2]*w_r+w_i*y_i[j2];
double a22_i = y_i[j2]*w_r-w_i*y_r[j2];
double a23_r = y_r[j3]*w_r-w_i*y_i[j3];
double a23_i = y_i[j3]*w_r+w_i*y_r[j3];
double a33_r = y_r[j3]*w2_r-w2_i*y_i[j3] ;
double a33_i = y_i[j3]*w2_r+w2_i*y_r[j3];
double a13_r = y_r[j3]*w2_r+w2_i*y_i[j3] ;
double a13_i = y_i[j3]*w2_r-w2_i*y_r[j3];
double a43_r = y_r[j3]*w_r+w_i*y_i[j3];
double a43_i = y_i[j3]*w_r-w_i*y_r[j3];
double a34_r = y_r[j4]*w_r-w_i*y_i[j4];
double a34_i = y_i[j4]*w_r+w_i*y_r[j4];
double a44_r = y_r[j4]*w2_r-w2_i*y_i[j4] ;
double a44_i = y_i[j4]*w2_r+w2_i*y_r[j4];
double a24_r = y_r[j4]*w2_r+w2_i*y_i[j4] ;
double a24_i = y_i[j4]*w2_r-w2_i*y_r[j4];
double a14_r = y_r[j4]*w_r+w_i*y_i[j4];
double a14_i = y_i[j4]*w_r-w_i*y_r[j4];
double u_r = y_r[j1] + y_r[j2] + y_r[j3] + y_r[j4] ;
double u_i = y_i[j1] + y_i[j2] + y_i[j3] + y_i[j4] ;
y_r[j1] = y_r[j]+ a11_r + a12_r + a13_r +a14_r ;
y_i[j1] = y_i[j]+ a11_i + a12_i + a13_i +a14_i ;
y_r[j2] = y_r[j]+ a21_r + a22_r + a23_r +a24_r ;
y_i[j2] = y_i[j]+ a21_i + a22_i + a23_i +a24_i ;
y_r[j3] = y_r[j]+ a41_r + a42_r + a43_r +a44_r ;
y_i[j3] = y_i[j]+ a41_i + a42_i + a43_i +a44_i ;
y_r[j4] = y_r[j]+ a31_r + a32_r + a33_r +a34_r ;
y_i[j4] = y_i[j]+ a31_i + a32_i + a33_i +a34_i ;
y_r[j] += u_r ;
y_i[j] += u_i ;
}
}
l++ ;
}
l = 1 ;
while (l<=q)
{
double n = pow(3,l)*pow(5,r) ;
for ( int i = 0 ; i< n/3 ; i++)
{
double phi = -2.0*M_PI*i/n ;
double theta = -2.0*M_PI/3 ;
double w_r = cos(theta);
double w_i = sin(theta);
double v_r = cos(phi) ;
double v_i = sin(phi) ;
double v2_r = cos(phi*2) ;
double v2_i = sin(phi*2) ;
for ( int j = i ; j < N ; j += n )
{
int j1 = j + n/3 ;
int j2 = j + 2*n/3 ;
double temp = y_r[j1]*v_i + y_i[j1]*v_r ;
y_r[j1] = y_r[j1]*v_r - y_i[j1]*v_i ;
y_i[j1] = temp ;
temp = y_r[j2]*v2_i + y_i[j2]*v2_r ;
y_r[j2] = y_r[j2]*v2_r - y_i[j2]*v2_i ;
y_i[j2] = temp ;
double t_r = y_r[j1]*w_r-w_i*y_i[j1];
double t_i = y_i[j1]*w_r+w_i*y_r[j1];
double t2_r = y_r[j1] *w_r+w_i*y_i[j1] ;
double t2_i = y_i[j1]*w_r-w_i*y_r[j1];
double s_r = y_r[j2]*w_r+y_i[j2]*w_i;
double s_i = -y_r[j2]*w_i+y_i[j2]*w_r;
double s2_r = y_r[j2]*w_r-y_i[j2]*w_i;
double s2_i = y_r[j2]*w_i+y_i[j2]*w_r;
double u_r = y_r[j1] + y_r[j2] ;
double u_i = y_i[j1] + y_i[j2] ;
y_r[j1] = y_r[j]+t_r+s_r;
y_i[j1] = y_i[j]+t_i+s_i ;
y_r[j2] = y_r[j]+t2_r+s2_r ;
y_i[j2] = y_i[j]+t2_i+s2_i ;
y_r[j] += u_r ;
y_i[j] += u_i ;
}
}
l++ ;
}
l = 1 ;
while (l<=p)
{
double n = pow(2,l)*pow(3,q)*pow(5,r) ;
for ( int i = 0 ; i< n/2 ; i++)
{
double theta = -2.0*i*M_PI/n ;
double w_r = cos(theta);
double w_i = sin(theta);
for ( int j = i ; j < N ; j += n )
{
int k = j + n/2 ;
double t_r = y_r[k]*w_r-w_i*y_i[k];
double t_i = y_i[k]*w_r+w_i*y_r[k];
y_r[k] = y_r[j]-t_r;
y_i[k] = y_i[j]-t_i ;
y_r[j] += t_r ;
y_i[j] += t_i ;
}
}
l++ ;
}
for ( int i = 0 ; i < N ; i++) cout << y_r[i] << " i * " << y_i[i] << endl ;
}