# Incorrect result from fix_fft on Adruino Due

Hi,
I’m trying to play with the FFT function after sampling the data from ADC. The adc seems to sample the correct result but the fix_fft doesn’t seems to give a correct real/imag number. I’m wondering if anyone has idea what goes wrong in the fit_fft file?
There are some discussions here and looks like Magician was saying something wrong with this c code. Anyone know what he’s talking baout?
I’m also open to advices to any other FFT library that’s easy to use.
Thanks! Any help is appreciated.
Here is the head and cpp files.

fix_fft.h

``````#ifndef FIXFFT_H
#define FIXFFT_H

#if defined(ARDUINO) && ARDUINO >= 100
#include "Arduino.h"
#else
#include "WProgram.h"
#endif

/*
fix_fft() - perform forward/inverse fast Fourier transform.
fr[n],fi[n] are real and imaginary arrays, both INPUT AND
RESULT (in-place FFT), with 0 <= n < 2**m; set inverse to
0 for forward transform (FFT), or 1 for iFFT.
*/
int fix_fft(char fr[], char fi[], int m, int inverse);

/*
fix_fftr() - forward/inverse FFT on array of real numbers.
Real FFT/iFFT using half-size complex FFT by distributing
even/odd samples into real/imaginary arrays respectively.
In order to save data space (i.e. to avoid two arrays, one
for real, one for imaginary samples), we proceed in the
following two steps: a) samples are rearranged in the real
array so that all even samples are in places 0-(N/2-1) and
all imaginary samples in places (N/2)-(N-1), and b) fix_fft
is called with fr and fi pointing to index 0 and index N/2
respectively in the original array. The above guarantees
that fix_fft "sees" consecutive real samples as alternating
real and imaginary samples in the complex array.
*/
int fix_fftr(char f[], int m, int inverse);

#endif
``````

fix_fft.cpp

``````#include <avr/pgmspace.h>
#include "fix_fft.h"
#if defined(ARDUINO) && ARDUINO >= 100
#include "Arduino.h"
#else
#include "WProgram.h"
#endif

/* fix_fft.c - Fixed-point in-place Fast Fourier Transform  */
/*
All data are fixed-point short integers, in which -32768
to +32768 represent -1.0 to +1.0 respectively. Integer
arithmetic is used for speed, instead of the more natural
floating-point.

For the forward FFT (time -> freq), fixed scaling is
performed to prevent arithmetic overflow, and to map a 0dB
sine/cosine wave (i.e. amplitude = 32767) to two -6dB freq
coefficients. The return value is always 0.

For the inverse FFT (freq -> time), fixed scaling cannot be
done, as two 0dB coefficients would sum to a peak amplitude
of 64K, overflowing the 32k range of the fixed-point integers.
Thus, the fix_fft() routine performs variable scaling, and
returns a value which is the number of bits LEFT by which
the output must be shifted to get the actual amplitude
(i.e. if fix_fft() returns 3, each value of fr[] and fi[]
must be multiplied by 8 (2**3) for proper scaling.
Clearly, this cannot be done within fixed-point short
integers. In practice, if the result is to be used as a
filter, the scale_shift can usually be ignored, as the
result will be approximately correctly normalized as is.

Written by:  Tom Roberts  11/8/89
Made portable:  Malcolm Slaney 12/15/94 malcolm@interval.com
Enhanced:  Dimitrios P. Bouras  14 Jun 2006 dbouras@ieee.org
Modified for 8bit values David Keller  10.10.2010
*/

#define N_WAVE      256    /* full length of Sinewave[] */
#define LOG2_N_WAVE 8      /* log2(N_WAVE) */

/*
FIX_MPY() - fixed-point multiplication & scaling.
Substitute inline assembly for hardware-specific
optimization suited to a particluar DSP processor.
Scaling ensures that result remains 16-bit.
*/
inline char FIX_MPY(char a, char b)
{

//Serial.println(a);
//Serial.println(b);

/* shift right one less bit (i.e. 15-1) */
int c = ((int)a * (int)b) >> 6;
/* last bit shifted out = rounding-bit */
b = c & 0x01;
/* last shift + rounding bit */
a = (c >> 1) + b;

/*
Serial.println(Sinewave[3]);
Serial.println(c);
Serial.println(a);
while(1);*/

return a;
}

/*
fix_fft() - perform forward/inverse fast Fourier transform.
fr[n],fi[n] are real and imaginary arrays, both INPUT AND
RESULT (in-place FFT), with 0 <= n < 2**m; set inverse to
0 for forward transform (FFT), or 1 for iFFT.
*/
int fix_fft(char fr[], char fi[], int m, int inverse)
{
int mr, nn, i, j, l, k, istep, n, scale, shift;
char qr, qi, tr, ti, wr, wi;

n = 1 << m;

/* max FFT size = N_WAVE */
if (n > N_WAVE)
return -1;

mr = 0;
nn = n - 1;
scale = 0;

/* decimation in time - re-order data */
for (m=1; m<=nn; ++m) {
l = n;
do {
l >>= 1;
} while (mr+l > nn);
mr = (mr & (l-1)) + l;

if (mr <= m)
continue;
tr = fr[m];
fr[m] = fr[mr];
fr[mr] = tr;
ti = fi[m];
fi[m] = fi[mr];
fi[mr] = ti;
}

l = 1;
k = LOG2_N_WAVE-1;
while (l < n) {
if (inverse) {
/* variable scaling, depending upon data */
shift = 0;
for (i=0; i<n; ++i) {
j = fr[i];
if (j < 0)
j = -j;
m = fi[i];
if (m < 0)
m = -m;
if (j > 16383 || m > 16383) {
shift = 1;
break;
}
}
if (shift)
++scale;
} else {
/*
fixed scaling, for proper normalization --
there will be log2(n) passes, so this results
in an overall factor of 1/n, distributed to
maximize arithmetic accuracy.
*/
shift = 1;
}
/*
it may not be obvious, but the shift will be
performed on each data point exactly once,
during this pass.
*/
istep = l << 1;
for (m=0; m<l; ++m) {
j = m << k;
/* 0 <= j < N_WAVE/2 */

/*Serial.println("asdfasdf");
Serial.println(wr);
Serial.println(j+N_WAVE/4);
Serial.println(Sinewave[256]);

Serial.println("");*/

if (inverse)
wi = -wi;
if (shift) {
wr >>= 1;
wi >>= 1;
}
for (i=m; i<n; i+=istep) {
j = i + l;
tr = FIX_MPY(wr,fr[j]) - FIX_MPY(wi,fi[j]);
ti = FIX_MPY(wr,fi[j]) + FIX_MPY(wi,fr[j]);
qr = fr[i];
qi = fi[i];
if (shift) {
qr >>= 1;
qi >>= 1;
}
fr[j] = qr - tr;
fi[j] = qi - ti;
fr[i] = qr + tr;
fi[i] = qi + ti;
}
}
--k;
l = istep;
}
return scale;
}

int fix_fftr(char f[], int m, int inverse)
{
int i, N = 1<<(m-1), scale = 0;
char tt, *fr=f, *fi=&f[N];

if (inverse)
scale = fix_fft(fi, fr, m-1, inverse);
for (i=1; i<N; i+=2) {
tt = f[N+i-1];
f[N+i-1] = f[i];
f[i] = tt;
}
if (! inverse)
scale = fix_fft(fi, fr, m-1, inverse);
return scale;
}
``````

My main program is this:

``````#include <fix_fft.h>
#define Samplepoints 128
#define TIAInput A0

char im_in[Samplepoints];
char real_in[Samplepoints];
int val_in=0;
int mag_in[Samplepoints];
int phase_in[Samplepoints];

void loop() {
analogWriteResolution(12);
for (int i=0;i<Samplepoints;i++) {
}

for (int i=0;i<Samplepoints;i++) {
im_in[i]=0;
}

fix_fft(real_in,im_in,7,0);

for (int i=0;i<Samplepoints/2;i++) {
//Serial.println("Magnitude:");
Serial.println(i);
Serial.println((int)real_in[i]);
Serial.println((int)im_in[i]);
delay(1000);
}

}
``````