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//
// main.c
// NaiveFFT
//
// Created by Jacky Jack on 10/08/2021.
//
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <string.h>
#include <math.h>
#include <complex.h>
//data array
#define DATA_SIZE (8)
double data_i[DATA_SIZE] = {1.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f};
double data_q[DATA_SIZE] = {0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f,0.0f};
//calc the fft
void fft_if(double *x_i, double *x_q, int n, int inv) {
int i=0,j=0,k=0,m=0, irem=0, sign;
double tq,ti;
printf("FFT\n");
k=n/2;
for (j=1,i=1;i<n; i++) {
if (i<j) {
//swap values
ti = x_i[j];
tq = x_q[j];
x_i[j] = x_i[i];
x_q[j] = x_q[i];
x_i[i] = ti;
x_q[i] = tq;
printf("i=%d j=%d\n",i,j);
//find middle point
k = n/2;
while (k<j) {
j = j-k;
k=k/2;
}
} else {
printf("i=%d j=%d\n",i,j);
k = n/2;
while (k<j) {
j = j - k;
k = k/2;
}
}
j = j+k;
}
for (i=0;i<DATA_SIZE;i++) {
printf("%.2f ",x_i[i]);
}
printf("\n");
for (i=0;i<DATA_SIZE;i++) {
printf("%.2f ",x_q[i]);
}
printf("\n");
//calculate number of stages:
//m=log2(n)
m=0;
irem = n;
while(irem>1) {
irem = irem/2;
m = m+1;
}
//FFT or IFFT
if (inv==1) {
sign = 1;
} else {
sign = -1;
}
// transform
for (i=0; i<m; i++) {
int le=pow(2,i);
int le1=le/2;
double ui=1.0;
double uq=0.0;
double wi = cos(M_PI/le1);
double wq = sign*sin(M_PI/le1);
for (j=1; j<le1;j++) {
i=j;
while (i<n) {
int ip = i+le1;
ti = x_i[ip]*ui - x_q[ip]*uq;
tq = x_q[ip]*ui + x_i[ip]*uq;
x_i[ip] = x_i[i] - ti;
x_q[ip] = x_q[i] - tq;
x_i[i] = x_i[i] + ti;
x_q[i] = x_q[i] + tq;
i = i+le;
}
double temp = ui*wi - uq*wq;
uq = uq*wi + ui*wq;
ui = temp;
}
}
//if inverse
if (inv==1) {
for (i=0;i<n;i++) {
x_i[i] = x_i[i]/n;
x_q[i] = x_q[i]/n;
}
}
}
//dft works fine
void dft(double *x_i, double *x_q, int n, int inv) {
double Wn,Wk;
//static array
//double Xi[DATA_SIZE],Xq[DATA_SIZE];
//dynamic array
double *Xi, *Xq;
double c,s;
int i,j;
Xi = malloc(n*sizeof(double));
Xq = malloc(n*sizeof(double));
Wn = 2*M_PI/n;
if (inv==1) {
Wn=-Wn;
}
for (i=0;i<n;i++) {
Xi[i] = 0.0f;
Xq[i] = 0.0f;
Wk = i*Wn;
for (j=0;j<n;j++) {
c = cos(j*Wk);
s = sin(j*Wk);
//i - real, q - imaginary
Xi[i] = Xi[i] + x_i[j]*c + x_q[j]*s;
Xq[i] = Xq[i] - x_i[j]*s + x_q[j]*c;
}
if (inv==1) {
Xi[i] = Xi[i]/n;
Xq[i] = Xq[i]/n;
}
}
for (i=0;i<n;i++) {
x_i[i] = Xi[i];
x_q[i] = Xq[i];
}
}
int main(int argc, const char * argv[]) {
int i;
// insert code here...
printf("Hello FFT World!\n");
for (i=0;i<DATA_SIZE;i++) {
printf("%.2f ",data_i[i]);
}
printf("\n");
for (i=0;i<DATA_SIZE;i++) {
printf("%.2f ",data_q[i]);
}
printf("\n");
fft_if(data_i, data_q, DATA_SIZE, 0);
//dft(data_i, data_q, DATA_SIZE,0);
for (i=0;i<DATA_SIZE;i++) {
printf("%.2f ",data_i[i]);
}
printf("\n");
for (i=0;i<DATA_SIZE;i++) {
printf("%.2f ",data_q[i]);
}
printf("\n");
return 0;
}
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