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/* fft.c - Fixed-point Fast Fourier Transform */
/*
fix_fft() perform FFT or inverse FFT
fix_mpy() perform fixed-point multiplication.
Sinewave[1024] sinewave normalized to 32767 (= 1.0).
All data are fixed-point short integers, in which
-32768 to +32768 represent -1.0 to +1.0. 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 one in the lower half is reported as 0dB.
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 the 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.
Source Code taken by http://www.jjj.de/crs4: integer_fft.c
Last Modified by Sebastian Haas at Oct. 2014.
*/
#include "fft.h"
#include <xtensa/tie/fft_inst.h>
/*
* fix_fft() - perform fast Fourier transform.
*
* if n>0 FFT is done, if n<0 inverse FFT is done
* fr[n],fi[n] are real,imaginary arrays, INPUT AND RESULT.
* size of data = 2^m
* set inverse to 0=dft, 1=idft
*/
int fix_fft(fixed fr[], fixed fi[], int m, int inverse)
{
int mr,nn,i,j,l,k,istep, n, scale, shift;
fixed qr,qi; //even input
fixed tr,ti; //odd input
fixed wr,wi; //twiddle factor
//number of input data
n = 1<<m;
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; //step width of current butterfly
for(m=0; m<l; ++m)
{
j = m << k;
/* 0 <= j < N_WAVE/2 */
wr = Sinewave[j+N_WAVE/4];
wi = -Sinewave[j];
if(inverse) wi = -wi;
if(shift)
{
wr >>= 1;
wi >>= 1;
}
for(i=m; i<n; i+=istep)
{
j = i + l;
FFT_reg reg;
fixed *reg_s = ((fixed*) &reg);
reg_s[3] = fr[i];
reg_s[2] = fr[j];
reg_s[1] = fi[i];
reg_s[0] = fi[j];
FFT_calc(reg, wr, wi, shift);
fr[i] = reg_s[3];
fr[j] = reg_s[2];
fi[i] = reg_s[1];
fi[j] = reg_s[0];
}
}
--k;
l = istep;
}
return scale;
}
/*
fix_mpy() - fixed-point multiplication
*/
fixed fix_mpy(fixed a, fixed b)
{
FIX_MPY(a,a,b);
return a;
}
fixed Sinewave[1024] = {
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,
-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,
};