-
Notifications
You must be signed in to change notification settings - Fork 51
/
fix_fft.c
372 lines (337 loc) · 19.1 KB
/
fix_fft.c
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
/* fix_fft.c - Fixed-point in-place DIT Fast Fourier Transform */
/*
All data are fixed-point uint16_t 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 uint16_t
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
*/
/*
This implementation uses a lookup table for bit reverse sorting,
which adds 2kbyte to the memory footprint.
The iFFT range detector has been optimized.
The bitshifting of signed integers is undefined, so these have been
replaced by divisions. The compiler will optimize it.
The size is fixed at 1024.
*/
#include "pico/stdlib.h"
#include "pico/multicore.h"
#include "pico/platform.h"
#include "fix_fft.h"
/** Fixed point Sine lookup table, [-1, 1] == [-32768, 32767] **/
int16_t Sine[3*FFT_SIZE/4] =
{
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
};
static int16_t bitrev[FFT_SIZE] =
{
0x000, 0x200, 0x100, 0x300, 0x080, 0x280, 0x180, 0x380, 0x040, 0x240, 0x140, 0x340, 0x0c0, 0x2c0, 0x1c0, 0x3c0,
0x020, 0x220, 0x120, 0x320, 0x0a0, 0x2a0, 0x1a0, 0x3a0, 0x060, 0x260, 0x160, 0x360, 0x0e0, 0x2e0, 0x1e0, 0x3e0,
0x010, 0x210, 0x110, 0x310, 0x090, 0x290, 0x190, 0x390, 0x050, 0x250, 0x150, 0x350, 0x0d0, 0x2d0, 0x1d0, 0x3d0,
0x030, 0x230, 0x130, 0x330, 0x0b0, 0x2b0, 0x1b0, 0x3b0, 0x070, 0x270, 0x170, 0x370, 0x0f0, 0x2f0, 0x1f0, 0x3f0,
0x008, 0x208, 0x108, 0x308, 0x088, 0x288, 0x188, 0x388, 0x048, 0x248, 0x148, 0x348, 0x0c8, 0x2c8, 0x1c8, 0x3c8,
0x028, 0x228, 0x128, 0x328, 0x0a8, 0x2a8, 0x1a8, 0x3a8, 0x068, 0x268, 0x168, 0x368, 0x0e8, 0x2e8, 0x1e8, 0x3e8,
0x018, 0x218, 0x118, 0x318, 0x098, 0x298, 0x198, 0x398, 0x058, 0x258, 0x158, 0x358, 0x0d8, 0x2d8, 0x1d8, 0x3d8,
0x038, 0x238, 0x138, 0x338, 0x0b8, 0x2b8, 0x1b8, 0x3b8, 0x078, 0x278, 0x178, 0x378, 0x0f8, 0x2f8, 0x1f8, 0x3f8,
0x004, 0x204, 0x104, 0x304, 0x084, 0x284, 0x184, 0x384, 0x044, 0x244, 0x144, 0x344, 0x0c4, 0x2c4, 0x1c4, 0x3c4,
0x024, 0x224, 0x124, 0x324, 0x0a4, 0x2a4, 0x1a4, 0x3a4, 0x064, 0x264, 0x164, 0x364, 0x0e4, 0x2e4, 0x1e4, 0x3e4,
0x014, 0x214, 0x114, 0x314, 0x094, 0x294, 0x194, 0x394, 0x054, 0x254, 0x154, 0x354, 0x0d4, 0x2d4, 0x1d4, 0x3d4,
0x034, 0x234, 0x134, 0x334, 0x0b4, 0x2b4, 0x1b4, 0x3b4, 0x074, 0x274, 0x174, 0x374, 0x0f4, 0x2f4, 0x1f4, 0x3f4,
0x00c, 0x20c, 0x10c, 0x30c, 0x08c, 0x28c, 0x18c, 0x38c, 0x04c, 0x24c, 0x14c, 0x34c, 0x0cc, 0x2cc, 0x1cc, 0x3cc,
0x02c, 0x22c, 0x12c, 0x32c, 0x0ac, 0x2ac, 0x1ac, 0x3ac, 0x06c, 0x26c, 0x16c, 0x36c, 0x0ec, 0x2ec, 0x1ec, 0x3ec,
0x01c, 0x21c, 0x11c, 0x31c, 0x09c, 0x29c, 0x19c, 0x39c, 0x05c, 0x25c, 0x15c, 0x35c, 0x0dc, 0x2dc, 0x1dc, 0x3dc,
0x03c, 0x23c, 0x13c, 0x33c, 0x0bc, 0x2bc, 0x1bc, 0x3bc, 0x07c, 0x27c, 0x17c, 0x37c, 0x0fc, 0x2fc, 0x1fc, 0x3fc,
0x002, 0x202, 0x102, 0x302, 0x082, 0x282, 0x182, 0x382, 0x042, 0x242, 0x142, 0x342, 0x0c2, 0x2c2, 0x1c2, 0x3c2,
0x022, 0x222, 0x122, 0x322, 0x0a2, 0x2a2, 0x1a2, 0x3a2, 0x062, 0x262, 0x162, 0x362, 0x0e2, 0x2e2, 0x1e2, 0x3e2,
0x012, 0x212, 0x112, 0x312, 0x092, 0x292, 0x192, 0x392, 0x052, 0x252, 0x152, 0x352, 0x0d2, 0x2d2, 0x1d2, 0x3d2,
0x032, 0x232, 0x132, 0x332, 0x0b2, 0x2b2, 0x1b2, 0x3b2, 0x072, 0x272, 0x172, 0x372, 0x0f2, 0x2f2, 0x1f2, 0x3f2,
0x00a, 0x20a, 0x10a, 0x30a, 0x08a, 0x28a, 0x18a, 0x38a, 0x04a, 0x24a, 0x14a, 0x34a, 0x0ca, 0x2ca, 0x1ca, 0x3ca,
0x02a, 0x22a, 0x12a, 0x32a, 0x0aa, 0x2aa, 0x1aa, 0x3aa, 0x06a, 0x26a, 0x16a, 0x36a, 0x0ea, 0x2ea, 0x1ea, 0x3ea,
0x01a, 0x21a, 0x11a, 0x31a, 0x09a, 0x29a, 0x19a, 0x39a, 0x05a, 0x25a, 0x15a, 0x35a, 0x0da, 0x2da, 0x1da, 0x3da,
0x03a, 0x23a, 0x13a, 0x33a, 0x0ba, 0x2ba, 0x1ba, 0x3ba, 0x07a, 0x27a, 0x17a, 0x37a, 0x0fa, 0x2fa, 0x1fa, 0x3fa,
0x006, 0x206, 0x106, 0x306, 0x086, 0x286, 0x186, 0x386, 0x046, 0x246, 0x146, 0x346, 0x0c6, 0x2c6, 0x1c6, 0x3c6,
0x026, 0x226, 0x126, 0x326, 0x0a6, 0x2a6, 0x1a6, 0x3a6, 0x066, 0x266, 0x166, 0x366, 0x0e6, 0x2e6, 0x1e6, 0x3e6,
0x016, 0x216, 0x116, 0x316, 0x096, 0x296, 0x196, 0x396, 0x056, 0x256, 0x156, 0x356, 0x0d6, 0x2d6, 0x1d6, 0x3d6,
0x036, 0x236, 0x136, 0x336, 0x0b6, 0x2b6, 0x1b6, 0x3b6, 0x076, 0x276, 0x176, 0x376, 0x0f6, 0x2f6, 0x1f6, 0x3f6,
0x00e, 0x20e, 0x10e, 0x30e, 0x08e, 0x28e, 0x18e, 0x38e, 0x04e, 0x24e, 0x14e, 0x34e, 0x0ce, 0x2ce, 0x1ce, 0x3ce,
0x02e, 0x22e, 0x12e, 0x32e, 0x0ae, 0x2ae, 0x1ae, 0x3ae, 0x06e, 0x26e, 0x16e, 0x36e, 0x0ee, 0x2ee, 0x1ee, 0x3ee,
0x01e, 0x21e, 0x11e, 0x31e, 0x09e, 0x29e, 0x19e, 0x39e, 0x05e, 0x25e, 0x15e, 0x35e, 0x0de, 0x2de, 0x1de, 0x3de,
0x03e, 0x23e, 0x13e, 0x33e, 0x0be, 0x2be, 0x1be, 0x3be, 0x07e, 0x27e, 0x17e, 0x37e, 0x0fe, 0x2fe, 0x1fe, 0x3fe,
0x001, 0x201, 0x101, 0x301, 0x081, 0x281, 0x181, 0x381, 0x041, 0x241, 0x141, 0x341, 0x0c1, 0x2c1, 0x1c1, 0x3c1,
0x021, 0x221, 0x121, 0x321, 0x0a1, 0x2a1, 0x1a1, 0x3a1, 0x061, 0x261, 0x161, 0x361, 0x0e1, 0x2e1, 0x1e1, 0x3e1,
0x011, 0x211, 0x111, 0x311, 0x091, 0x291, 0x191, 0x391, 0x051, 0x251, 0x151, 0x351, 0x0d1, 0x2d1, 0x1d1, 0x3d1,
0x031, 0x231, 0x131, 0x331, 0x0b1, 0x2b1, 0x1b1, 0x3b1, 0x071, 0x271, 0x171, 0x371, 0x0f1, 0x2f1, 0x1f1, 0x3f1,
0x009, 0x209, 0x109, 0x309, 0x089, 0x289, 0x189, 0x389, 0x049, 0x249, 0x149, 0x349, 0x0c9, 0x2c9, 0x1c9, 0x3c9,
0x029, 0x229, 0x129, 0x329, 0x0a9, 0x2a9, 0x1a9, 0x3a9, 0x069, 0x269, 0x169, 0x369, 0x0e9, 0x2e9, 0x1e9, 0x3e9,
0x019, 0x219, 0x119, 0x319, 0x099, 0x299, 0x199, 0x399, 0x059, 0x259, 0x159, 0x359, 0x0d9, 0x2d9, 0x1d9, 0x3d9,
0x039, 0x239, 0x139, 0x339, 0x0b9, 0x2b9, 0x1b9, 0x3b9, 0x079, 0x279, 0x179, 0x379, 0x0f9, 0x2f9, 0x1f9, 0x3f9,
0x005, 0x205, 0x105, 0x305, 0x085, 0x285, 0x185, 0x385, 0x045, 0x245, 0x145, 0x345, 0x0c5, 0x2c5, 0x1c5, 0x3c5,
0x025, 0x225, 0x125, 0x325, 0x0a5, 0x2a5, 0x1a5, 0x3a5, 0x065, 0x265, 0x165, 0x365, 0x0e5, 0x2e5, 0x1e5, 0x3e5,
0x015, 0x215, 0x115, 0x315, 0x095, 0x295, 0x195, 0x395, 0x055, 0x255, 0x155, 0x355, 0x0d5, 0x2d5, 0x1d5, 0x3d5,
0x035, 0x235, 0x135, 0x335, 0x0b5, 0x2b5, 0x1b5, 0x3b5, 0x075, 0x275, 0x175, 0x375, 0x0f5, 0x2f5, 0x1f5, 0x3f5,
0x00d, 0x20d, 0x10d, 0x30d, 0x08d, 0x28d, 0x18d, 0x38d, 0x04d, 0x24d, 0x14d, 0x34d, 0x0cd, 0x2cd, 0x1cd, 0x3cd,
0x02d, 0x22d, 0x12d, 0x32d, 0x0ad, 0x2ad, 0x1ad, 0x3ad, 0x06d, 0x26d, 0x16d, 0x36d, 0x0ed, 0x2ed, 0x1ed, 0x3ed,
0x01d, 0x21d, 0x11d, 0x31d, 0x09d, 0x29d, 0x19d, 0x39d, 0x05d, 0x25d, 0x15d, 0x35d, 0x0dd, 0x2dd, 0x1dd, 0x3dd,
0x03d, 0x23d, 0x13d, 0x33d, 0x0bd, 0x2bd, 0x1bd, 0x3bd, 0x07d, 0x27d, 0x17d, 0x37d, 0x0fd, 0x2fd, 0x1fd, 0x3fd,
0x003, 0x203, 0x103, 0x303, 0x083, 0x283, 0x183, 0x383, 0x043, 0x243, 0x143, 0x343, 0x0c3, 0x2c3, 0x1c3, 0x3c3,
0x023, 0x223, 0x123, 0x323, 0x0a3, 0x2a3, 0x1a3, 0x3a3, 0x063, 0x263, 0x163, 0x363, 0x0e3, 0x2e3, 0x1e3, 0x3e3,
0x013, 0x213, 0x113, 0x313, 0x093, 0x293, 0x193, 0x393, 0x053, 0x253, 0x153, 0x353, 0x0d3, 0x2d3, 0x1d3, 0x3d3,
0x033, 0x233, 0x133, 0x333, 0x0b3, 0x2b3, 0x1b3, 0x3b3, 0x073, 0x273, 0x173, 0x373, 0x0f3, 0x2f3, 0x1f3, 0x3f3,
0x00b, 0x20b, 0x10b, 0x30b, 0x08b, 0x28b, 0x18b, 0x38b, 0x04b, 0x24b, 0x14b, 0x34b, 0x0cb, 0x2cb, 0x1cb, 0x3cb,
0x02b, 0x22b, 0x12b, 0x32b, 0x0ab, 0x2ab, 0x1ab, 0x3ab, 0x06b, 0x26b, 0x16b, 0x36b, 0x0eb, 0x2eb, 0x1eb, 0x3eb,
0x01b, 0x21b, 0x11b, 0x31b, 0x09b, 0x29b, 0x19b, 0x39b, 0x05b, 0x25b, 0x15b, 0x35b, 0x0db, 0x2db, 0x1db, 0x3db,
0x03b, 0x23b, 0x13b, 0x33b, 0x0bb, 0x2bb, 0x1bb, 0x3bb, 0x07b, 0x27b, 0x17b, 0x37b, 0x0fb, 0x2fb, 0x1fb, 0x3fb,
0x007, 0x207, 0x107, 0x307, 0x087, 0x287, 0x187, 0x387, 0x047, 0x247, 0x147, 0x347, 0x0c7, 0x2c7, 0x1c7, 0x3c7,
0x027, 0x227, 0x127, 0x327, 0x0a7, 0x2a7, 0x1a7, 0x3a7, 0x067, 0x267, 0x167, 0x367, 0x0e7, 0x2e7, 0x1e7, 0x3e7,
0x017, 0x217, 0x117, 0x317, 0x097, 0x297, 0x197, 0x397, 0x057, 0x257, 0x157, 0x357, 0x0d7, 0x2d7, 0x1d7, 0x3d7,
0x037, 0x237, 0x137, 0x337, 0x0b7, 0x2b7, 0x1b7, 0x3b7, 0x077, 0x277, 0x177, 0x377, 0x0f7, 0x2f7, 0x1f7, 0x3f7,
0x00f, 0x20f, 0x10f, 0x30f, 0x08f, 0x28f, 0x18f, 0x38f, 0x04f, 0x24f, 0x14f, 0x34f, 0x0cf, 0x2cf, 0x1cf, 0x3cf,
0x02f, 0x22f, 0x12f, 0x32f, 0x0af, 0x2af, 0x1af, 0x3af, 0x06f, 0x26f, 0x16f, 0x36f, 0x0ef, 0x2ef, 0x1ef, 0x3ef,
0x01f, 0x21f, 0x11f, 0x31f, 0x09f, 0x29f, 0x19f, 0x39f, 0x05f, 0x25f, 0x15f, 0x35f, 0x0df, 0x2df, 0x1df, 0x3df,
0x03f, 0x23f, 0x13f, 0x33f, 0x0bf, 0x2bf, 0x1bf, 0x3bf, 0x07f, 0x27f, 0x17f, 0x37f, 0x0ff, 0x2ff, 0x1ff, 0x3ff
};
/** FIX_MPY() **/
/*
* Assume Q(0,15) notation, 1 sign, 0 int, 15 frac bits
*/
int16_t __not_in_flash_func(FIX_MPY)(int16_t a, int16_t b) // Fixed-point mpy and scaling
{
int32_t c;
c = (int32_t)a * (int32_t)b; // multiply
c = c + 0x4000; // and round up
c = c >> 15; // Shift right fractional bits
return((int16_t)c); // Return scaled product
}
/** FIX_FFT() **/
/*
* fr[] i samples [1024]
* fi[] q samples [1024]
* inverse true: iFFT
* Note: i-FFT could also be calculated by exchanging the arrays for FFT (fxtbook.pdf 21.7)
*/
int __not_in_flash_func(fix_fft)(int16_t *fr, int16_t *fi, bool inverse)
{
uint16_t i, j, m, k, step, scale;
bool shift;
int16_t qr, qi, tr, ti, wr, wi;
int16_t *bp;
/* Decimation in time: re-order samples */
bp=&bitrev[0];
for (i=0; i<FFT_SIZE; i++)
{
if (*bp > i)
{
tr = fr[i]; fr[i] = fr[*bp]; fr[*bp] = tr;
ti = fi[i]; fi[i] = fi[*bp]; fi[*bp] = ti;
}
bp++;
}
scale = 0;
step = 1; // Counting up: 1, 2, 4, 8, ...
/* FFT Stages */
for (k=FFT_ORDER; k>0; k--) // #cycles: FFT_ORDER
{
/* Scaling
* Variable scaling, depends on current data
* --> it seems quite CPU intensive to go through complete array
* FFT_ORDER times, could this be optimized?
* If always scaling:
* --> the main loop has log_2(FFT_SIZE) cycles,
* resulting in an overall factor of 1/FFT_SIZE,
* distributed over cycles to maximize accuracy.
*/
shift = false; // No shift, unless...
for (i=0; i<FFT_SIZE; ++i) // Range test all samples
{
if ((fr[i] > 0x3fff) || (fr[i] < -0x4000) || (fi[i] > 0x3fff) || (fi[i] < -0x4000))
{
shift = true;
scale++;
break; // Bail out at first detect
}
}
/* Inner loops resolving the butterflies for each stage*/
for (m=0; m<step; m++) // #cycles: step
{
// Determine wiggle factors
j = m << (k-1); // 0 <= j < FFT_SIZE/2
wr = Sine[j+FFT_SIZE/4]; // Real part, i.e. Cosine
wi = inverse ? Sine[j] : -Sine[j]; // Imaginary part
if (shift) { wr = wr/2; wi = wi/2; } // Scale factors by 1/2
for (i=m; i<FFT_SIZE; i+=(step*2)) // #cycles: FFT_SIZE/step
{
j = i + step; // re-assign j !
tr = FIX_MPY(wr,fr[j]) - FIX_MPY(wi,fi[j]); // Complex multiply
ti = FIX_MPY(wr,fi[j]) + FIX_MPY(wi,fr[j]);
qr = shift ? fr[i]/2 : fr[i];
qi = shift ? fi[i]/2 : fi[i];
fr[i] = qr + tr;
fi[i] = qi + ti;
fr[j] = qr - tr;
fi[j] = qi - ti;
} // #total: FFT_ORDER * step * FFT_SIZE/step
}
step = step<<1;
}
return scale;
}
#ifdef BLAH
// int16_t contains signed fixed point representation Q(1,14)
// 1 sign bit, 1 int bit and 14 frac bits
// precomputed value K represents 0.5
#define Q 14
#define K (1 << (Q - 1))
// a + b
int16_t q_add(int16_t a, int16_t b)
{
int32_t tmp;
tmp = (int32_t)a + (int32_t)b;
if (tmp > 0x7FFF) // Clip result
tmp = 0x7FFF;
else if (tmp < -0x8000)
tmp = -0x8000;
return (int16_t)tmp;
}
// a - b
int16_t q_sub(int16_t a, int16_t b)
{
return a - b;
}
// a * b
int16_t q_mul(int16_t a, int16_t b)
{
int32_t tmp;
tmp = (int32_t)a * (int32_t)b;
tmp += K; // Rounding; mid values are rounded up
tmp = tmp >> Q; // Correct by dividing by base
if (tmp > 0x7FFF) // Clip result
tmp = 0x7FFF;
else if (tmp < -0x8000)
tmp = -0x8000;
return (int16_t)tmp;
}
// a / b
int16_t q_div(int16_t a, int16_t b)
{
int32_t tmp;
tmp = (int32_t)a << Q; // Pre multiply with base
if ((tmp >= 0 && b >= 0) || (tmp < 0 && b < 0)) // Rounding; mid values are rounded up
tmp += (b >> 2);
else // or down...
tmp -= (b >> 2);
return (int16_t)(tmp / b);
}
#endif