#include
#include "fix_fft.h"
#include
/* 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) */
/*
Since we only use 3/4 of N_WAVE, we define only
this many samples, in order to conserve data space.
*/
const prog_int8_t Sinewave[N_WAVE-N_WAVE/4] PROGMEM = {
0, 3, 6, 9, 12, 15, 18, 21,
24, 28, 31, 34, 37, 40, 43, 46,
48, 51, 54, 57, 60, 63, 65, 68,
71, 73, 76, 78, 81, 83, 85, 88,
90, 92, 94, 96, 98, 100, 102, 104,
106, 108, 109, 111, 112, 114, 115, 117,
118, 119, 120, 121, 122, 123, 124, 124,
125, 126, 126, 127, 127, 127, 127, 127,
127, 127, 127, 127, 127, 127, 126, 126,
125, 124, 124, 123, 122, 121, 120, 119,
118, 117, 115, 114, 112, 111, 109, 108,
106, 104, 102, 100, 98, 96, 94, 92,
90, 88, 85, 83, 81, 78, 76, 73,
71, 68, 65, 63, 60, 57, 54, 51,
48, 46, 43, 40, 37, 34, 31, 28,
24, 21, 18, 15, 12, 9, 6, 3,
0, -3, -6, -9, -12, -15, -18, -21,
-24, -28, -31, -34, -37, -40, -43, -46,
-48, -51, -54, -57, -60, -63, -65, -68,
-71, -73, -76, -78, -81, -83, -85, -88,
-90, -92, -94, -96, -98, -100, -102, -104,
-106, -108, -109, -111, -112, -114, -115, -117,
-118, -119, -120, -121, -122, -123, -124, -124,
-125, -126, -126, -127, -127, -127, -127, -127,
/*-127, -127, -127, -127, -127, -127, -126, -126,
-125, -124, -124, -123, -122, -121, -120, -119,
-118, -117, -115, -114, -112, -111, -109, -108,
-106, -104, -102, -100, -98, -96, -94, -92,
-90, -88, -85, -83, -81, -78, -76, -73,
-71, -68, -65, -63, -60, -57, -54, -51,
-48, -46, -43, -40, -37, -34, -31, -28,
-24, -21, -18, -15, -12, -9, -6, -3, */
};
/*
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 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>= 1;
wi >>= 1;
}
for (i=m; i>= 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(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