In various web pages and projects across the web lives a mysterious file that does a FFT in C. There are several different versions modified by various people to do various things. I have no idea where it came form.
All I know is that this particular version by yours truly runs on Arduino and 8-bit AVR chips in general.
#include <avr/pgmspace.h>
#include <Arduino.h>
/* 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
AVR: Pepijn de Vos 8 March 2015
*/
#define N_WAVE 1024 /* full length of Sinewave[] */
#define LOG2_N_WAVE 10 /* log2(N_WAVE) */
/*
Henceforth "short" implies 16-bit word. If this is not
the case in your architecture, please replace "short"
with a type definition which *is* a 16-bit word.
*/
/*
Since we only use 3/4 of N_WAVE, we define only
this many samples, in order to conserve data space.
*/
const short Sinewave[N_WAVE-N_WAVE/4] PROGMEM = {
0, 201, 402, 603, 804, 1005, 1206, 1406,
1607, 1808, 2009, 2209, 2410, 2610, 2811, 3011,
3211, 3411, 3611, 3811, 4011, 4210, 4409, 4608,
4807, 5006, 5205, 5403, 5601, 5799, 5997, 6195,
6392, 6589, 6786, 6982, 7179, 7375, 7571, 7766,
7961, 8156, 8351, 8545, 8739, 8932, 9126, 9319,
9511, 9703, 9895, 10087, 10278, 10469, 10659, 10849,
11038, 11227, 11416, 11604, 11792, 11980, 12166, 12353,
12539, 12724, 12909, 13094, 13278, 13462, 13645, 13827,
14009, 14191, 14372, 14552, 14732, 14911, 15090, 15268,
15446, 15623, 15799, 15975, 16150, 16325, 16499, 16672,
16845, 17017, 17189, 17360, 17530, 17699, 17868, 18036,
18204, 18371, 18537, 18702, 18867, 19031, 19194, 19357,
19519, 19680, 19840, 20000, 20159, 20317, 20474, 20631,
20787, 20942, 21096, 21249, 21402, 21554, 21705, 21855,
22004, 22153, 22301, 22448, 22594, 22739, 22883, 23027,
23169, 23311, 23452, 23592, 23731, 23869, 24006, 24143,
24278, 24413, 24546, 24679, 24811, 24942, 25072, 25201,
25329, 25456, 25582, 25707, 25831, 25954, 26077, 26198,
26318, 26437, 26556, 26673, 26789, 26905, 27019, 27132,
27244, 27355, 27466, 27575, 27683, 27790, 27896, 28001,
28105, 28208, 28309, 28410, 28510, 28608, 28706, 28802,
28897, 28992, 29085, 29177, 29268, 29358, 29446, 29534,
29621, 29706, 29790, 29873, 29955, 30036, 30116, 30195,
30272, 30349, 30424, 30498, 30571, 30643, 30713, 30783,
30851, 30918, 30984, 31049, 31113, 31175, 31236, 31297,
31356, 31413, 31470, 31525, 31580, 31633, 31684, 31735,
31785, 31833, 31880, 31926, 31970, 32014, 32056, 32097,
32137, 32176, 32213, 32249, 32284, 32318, 32350, 32382,
32412, 32441, 32468, 32495, 32520, 32544, 32567, 32588,
32609, 32628, 32646, 32662, 32678, 32692, 32705, 32717,
32727, 32736, 32744, 32751, 32757, 32761, 32764, 32766,
32767, 32766, 32764, 32761, 32757, 32751, 32744, 32736,
32727, 32717, 32705, 32692, 32678, 32662, 32646, 32628,
32609, 32588, 32567, 32544, 32520, 32495, 32468, 32441,
32412, 32382, 32350, 32318, 32284, 32249, 32213, 32176,
32137, 32097, 32056, 32014, 31970, 31926, 31880, 31833,
31785, 31735, 31684, 31633, 31580, 31525, 31470, 31413,
31356, 31297, 31236, 31175, 31113, 31049, 30984, 30918,
30851, 30783, 30713, 30643, 30571, 30498, 30424, 30349,
30272, 30195, 30116, 30036, 29955, 29873, 29790, 29706,
29621, 29534, 29446, 29358, 29268, 29177, 29085, 28992,
28897, 28802, 28706, 28608, 28510, 28410, 28309, 28208,
28105, 28001, 27896, 27790, 27683, 27575, 27466, 27355,
27244, 27132, 27019, 26905, 26789, 26673, 26556, 26437,
26318, 26198, 26077, 25954, 25831, 25707, 25582, 25456,
25329, 25201, 25072, 24942, 24811, 24679, 24546, 24413,
24278, 24143, 24006, 23869, 23731, 23592, 23452, 23311,
23169, 23027, 22883, 22739, 22594, 22448, 22301, 22153,
22004, 21855, 21705, 21554, 21402, 21249, 21096, 20942,
20787, 20631, 20474, 20317, 20159, 20000, 19840, 19680,
19519, 19357, 19194, 19031, 18867, 18702, 18537, 18371,
18204, 18036, 17868, 17699, 17530, 17360, 17189, 17017,
16845, 16672, 16499, 16325, 16150, 15975, 15799, 15623,
15446, 15268, 15090, 14911, 14732, 14552, 14372, 14191,
14009, 13827, 13645, 13462, 13278, 13094, 12909, 12724,
12539, 12353, 12166, 11980, 11792, 11604, 11416, 11227,
11038, 10849, 10659, 10469, 10278, 10087, 9895, 9703,
9511, 9319, 9126, 8932, 8739, 8545, 8351, 8156,
7961, 7766, 7571, 7375, 7179, 6982, 6786, 6589,
6392, 6195, 5997, 5799, 5601, 5403, 5205, 5006,
4807, 4608, 4409, 4210, 4011, 3811, 3611, 3411,
3211, 3011, 2811, 2610, 2410, 2209, 2009, 1808,
1607, 1406, 1206, 1005, 804, 603, 402, 201,
0, -201, -402, -603, -804, -1005, -1206, -1406,
-1607, -1808, -2009, -2209, -2410, -2610, -2811, -3011,
-3211, -3411, -3611, -3811, -4011, -4210, -4409, -4608,
-4807, -5006, -5205, -5403, -5601, -5799, -5997, -6195,
-6392, -6589, -6786, -6982, -7179, -7375, -7571, -7766,
-7961, -8156, -8351, -8545, -8739, -8932, -9126, -9319,
-9511, -9703, -9895, -10087, -10278, -10469, -10659, -10849,
-11038, -11227, -11416, -11604, -11792, -11980, -12166, -12353,
-12539, -12724, -12909, -13094, -13278, -13462, -13645, -13827,
-14009, -14191, -14372, -14552, -14732, -14911, -15090, -15268,
-15446, -15623, -15799, -15975, -16150, -16325, -16499, -16672,
-16845, -17017, -17189, -17360, -17530, -17699, -17868, -18036,
-18204, -18371, -18537, -18702, -18867, -19031, -19194, -19357,
-19519, -19680, -19840, -20000, -20159, -20317, -20474, -20631,
-20787, -20942, -21096, -21249, -21402, -21554, -21705, -21855,
-22004, -22153, -22301, -22448, -22594, -22739, -22883, -23027,
-23169, -23311, -23452, -23592, -23731, -23869, -24006, -24143,
-24278, -24413, -24546, -24679, -24811, -24942, -25072, -25201,
-25329, -25456, -25582, -25707, -25831, -25954, -26077, -26198,
-26318, -26437, -26556, -26673, -26789, -26905, -27019, -27132,
-27244, -27355, -27466, -27575, -27683, -27790, -27896, -28001,
-28105, -28208, -28309, -28410, -28510, -28608, -28706, -28802,
-28897, -28992, -29085, -29177, -29268, -29358, -29446, -29534,
-29621, -29706, -29790, -29873, -29955, -30036, -30116, -30195,
-30272, -30349, -30424, -30498, -30571, -30643, -30713, -30783,
-30851, -30918, -30984, -31049, -31113, -31175, -31236, -31297,
-31356, -31413, -31470, -31525, -31580, -31633, -31684, -31735,
-31785, -31833, -31880, -31926, -31970, -32014, -32056, -32097,
-32137, -32176, -32213, -32249, -32284, -32318, -32350, -32382,
-32412, -32441, -32468, -32495, -32520, -32544, -32567, -32588,
-32609, -32628, -32646, -32662, -32678, -32692, -32705, -32717,
-32727, -32736, -32744, -32751, -32757, -32761, -32764, -32766,
};
/*
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.
*/
short fix_mpy(short a, short b)
{
/* shift right one less bit (i.e. 15-1) */
long c = ((long)a * (long)b) >> 14;
/* last bit shifted out = rounding-bit */
b = c & 0x01;
/* last shift + rounding bit */
a = (c >> 1) + b;
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(short fr[], short fi[], short m, short inverse)
{
long mr, nn, i, j, l, k, istep, n, scale, shift;
short 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 */
wr = pgm_read_dword(&(Sinewave[j+N_WAVE/4]));
wi = -pgm_read_dword(&(Sinewave[j]));
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;
}
/*
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(short f[], long m, short inverse)
{
long i, N = 1<<(m-1), scale = 0;
short 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;
}The licensing and versioning on this thing apparently works as follows: Add your name and date to the list of authors and post it in your corner of the web. That’s all.
