Implementing IFFT - c

Question

Trying to implement IFFT. If i set the input to this:
{0, 1, 0, 0, 0, 0, 0, 1}
it should transform it to a cosine with the lowest wave number. Instead i get this weird pattern:
bin 0: 2.000000 I 0.000000
bin 1: 0.000000 I 1.414214
bin 2: 0.000000 I 0.000000
bin 3: 0.000000 I 1.414214
bin 4: -2.000000 I 0.000000
bin 5: 0.000000 I -1.414214
bin 6: 0.000000 I 0.000000
bin 7: -0.000000 I -1.414214
I just took the FFT code and conjugated twiddle factors. Im told this should work fine. (besides the scaling factor) I don't understand what is wrong.
main.c
#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include "utils.h"
COMPLEX_FLOAT * coefficients;
void calculate_coefficients(int N)
{
COMPLEX_FLOAT * co = (COMPLEX_FLOAT *)malloc(N/2 * sizeof(COMPLEX_FLOAT));
coefficients = co;
for(int i = 0; i < N/2; i++)
{
co[i] = cf_exp(-2.0f*PI*((float)i)/((float)N));
}
}
COMPLEX_FLOAT* ifftr(COMPLEX_FLOAT* input, int N, int multiplier, int offset)
{
COMPLEX_FLOAT *output;
COMPLEX_FLOAT *E, *O;
output = (COMPLEX_FLOAT *)malloc(N * sizeof(COMPLEX_FLOAT));
if(N == 1)
{
output[0] = input[offset];
}
else
{
E = fftr(input, N/2, multiplier*2, offset);
O = fftr(input, N/2, multiplier*2, multiplier + offset);
for(int i = 0; i < N/2; i++)
{
int index = i * multiplier;
COMPLEX_FLOAT tmp = cmul(conjugate(coefficients[index]),O[i]);
output[i] = cadd(E[i], tmp);
output[i + N/2] = csub(E[i], tmp);
}
free(E);
free(O);
}
return output;
}
void ifft(COMPLEX_FLOAT* input, COMPLEX_FLOAT* output, int N)
{
COMPLEX_FLOAT * out;
calculate_coefficients(N);
out = ifftr(input,N,1,0);
for(int i = 0; i < N; i++)
{
output[i] = out[i];
}
free(out);
free(coefficients);
return;
}
int main()
{
int size = 8;
COMPLEX_FLOAT dummy[size];
COMPLEX_FLOAT frq[size];
for(int i = 0; i < size; i++)
{
frq[i].imag = 0;
if(i == 2)
{
frq[i].real = 1;
}
else if(size - i == 1)
{
frq[i].real = 1;
}
else
{
frq[i].real = 0;
}
}
ifft(frq, dummy, size);
for(int i = 0; i < size; i++)
{
printf("bin %d: %f\t I %f\n", i, dummy[i].real, dummy[i].imag);
}
return 0;
}
utils.c
#include "utils.h"
#include "math.h"
COMPLEX_FLOAT cadd(COMPLEX_FLOAT a, COMPLEX_FLOAT b)
{
COMPLEX_FLOAT out;
out.real = a.real + b.real;
out.imag = a.imag + b.imag;
return out;
}
COMPLEX_FLOAT csub(COMPLEX_FLOAT a, COMPLEX_FLOAT b)
{
COMPLEX_FLOAT out;
out.real = a.real - b.real;
out.imag = a.imag - b.imag;
return out;
}
COMPLEX_FLOAT cmul(COMPLEX_FLOAT a, COMPLEX_FLOAT b)
{
COMPLEX_FLOAT out;
out.real = a.real * b.real - a.imag * b.imag;
out.imag = a.real * b.imag + b.real * a.imag;
return out;
}
COMPLEX_FLOAT cf_exp(float a)
{
COMPLEX_FLOAT out;
out.real = (float)cos(a);
out.imag = (float)sin(a);
return out;
}
COMPLEX_FLOAT conjugate(COMPLEX_FLOAT a)
{
COMPLEX_FLOAT out;
out.real = a.real;
out.imag = -a.imag;
return out;
}
COMPLEX_FLOAT real_num(float n)
{
COMPLEX_FLOAT out;
out.real = n;
out.imag = 0;
return out;
}

Answer 1

I was calling the wrong recursive function fftr instead of ifftr
COMPLEX_FLOAT* ifftr(COMPLEX_FLOAT* input, int N, int multiplier, int offset)
{
COMPLEX_FLOAT *output;
COMPLEX_FLOAT *E, *O;
output = (COMPLEX_FLOAT *)malloc(N * sizeof(COMPLEX_FLOAT));
if(N == 1)
{
output[0] = input[offset];
}
else
{
E = ifftr(input, N/2, multiplier*2, offset);
O = ifftr(input, N/2, multiplier*2, multiplier + offset);
for(int i = 0; i < N/2; i++)
{
int index = i * multiplier;
COMPLEX_FLOAT tmp = cmul(conjugate(coefficients[index]),O[i]);
output[i] = cadd(E[i], tmp);
output[i + N/2] = csub(E[i], tmp);
}
free(E);
free(O);
}
return output;
}