Contiki-NG
ifft.c
1 /*
2  * Copyright (c) 2008, Swedish Institute of Computer Science
3  * All rights reserved.
4  *
5  * Redistribution and use in source and binary forms, with or without
6  * modification, are permitted provided that the following conditions
7  * are met:
8  * 1. Redistributions of source code must retain the above copyright
9  * notice, this list of conditions and the following disclaimer.
10  * 2. Redistributions in binary form must reproduce the above copyright
11  * notice, this list of conditions and the following disclaimer in the
12  * documentation and/or other materials provided with the distribution.
13  * 3. Neither the name of the Institute nor the names of its contributors
14  * may be used to endorse or promote products derived from this software
15  * without specific prior written permission.
16  *
17  * THIS SOFTWARE IS PROVIDED BY THE INSTITUTE AND CONTRIBUTORS ``AS IS'' AND
18  * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
19  * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
20  * ARE DISCLAIMED. IN NO EVENT SHALL THE INSTITUTE OR CONTRIBUTORS BE LIABLE
21  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
22  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
23  * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
24  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
25  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
26  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
27  * SUCH DAMAGE.
28  *
29  * -----------------------------------------------------------------
30  * ifft - Integer FFT (fast fourier transform) library
31  *
32  *
33  * Author : Joakim Eriksson
34  * Created : 2008-03-27
35  * Updated : $Date: 2008/07/03 23:40:12 $
36  * $Revision: 1.3 $
37  */
38 
39 #include "contiki.h"
40 #include "lib/ifft.h"
41 
42 /*---------------------------------------------------------------------------*/
43 /* constant table of sin values in 8/7 bits resolution */
44 /* NOTE: symmetry can be used to reduce this to 1/2 or 1/4 the size */
45 #define SIN_TAB_LEN 120
46 #define RESOLUTION 7
47 
48 static const int8_t SIN_TAB[] = {
49  0,6,13,20,26,33,39,45,52,58,63,69,75,80,
50  85,90,95,99,103,107,110,114,116,119,121,
51  123,125,126,127,127,127,127,127,126,125,
52  123,121,119,116,114,110,107,103,99,95,90,
53  85,80,75,69,63,58,52,45,39,33,26,20,13,6,
54  0,-6,-13,-20,-26,-33,-39,-45,-52,-58,-63,
55  -69,-75,-80,-85,-90,-95,-99,-103,-107,-110,
56  -114,-116,-119,-121,-123,-125,-126,-127,-127,
57  -127,-127,-127,-126,-125,-123,-121,-119,-116,
58  -114,-110,-107,-103,-99,-95,-90,-85,-80,-75,
59  -69,-63,-58,-52,-45,-39,-33,-26,-20,-13,-6
60 };
61 
62 
63 static uint16_t bitrev(uint16_t j, uint16_t nu)
64 {
65  uint16_t k;
66  k = 0;
67  for (; nu > 0; nu--) {
68  k = (k << 1) + (j & 1);
69  j = j >> 1;
70  }
71  return k;
72 }
73 
74 
75 /* Non interpolating sine... which takes an angle of 0 - 999 */
76 static int16_t sinI(uint16_t angleMilli)
77 {
78  uint16_t pos;
79  pos = (uint16_t) ((SIN_TAB_LEN * (uint32_t) angleMilli) / 1000);
80  return SIN_TAB[pos % SIN_TAB_LEN];
81 }
82 
83 static int16_t cosI(uint16_t angleMilli)
84 {
85  return sinI(angleMilli + 250);
86 }
87 
88 static uint16_t ilog2(uint16_t val)
89 {
90  uint16_t log;
91  log = 0;
92  val = val >> 1; /* The 20 = 1 => log = 0 => val = 0 */
93  while (val > 0) {
94  val = val >> 1;
95  log++;
96  }
97  return log;
98 }
99 
100 
101 /* ifft(xre[], n) - integer (fixpoint) version of Fast Fourier Transform
102  An integer version of FFT that takes in-samples in an int16_t array
103  and does an fft on n samples in the array.
104  The result of the FFT is stored in the same array as the samples
105  was stored. Them imaginary part of the result is stored in xim which
106  needs to be of the same size as xre (e.g. n ints).
107 
108  Note: This fft is designed to be used with 8 bit values (e.g. not
109  16 bit values). The reason for the int16_t array is for keeping some
110  'room' for the calculations. It is also designed for doing fairly small
111  FFT:s since to large sample arrays might cause it to overflow during
112  calculations.
113 */
114 void
115 ifft(int16_t xre[], int16_t xim[], uint16_t n)
116 {
117  uint16_t nu;
118  uint16_t n2;
119  uint16_t nu1;
120  int p, k, l, i;
121  int32_t c, s, tr, ti;
122 
123  nu = ilog2(n);
124  nu1 = nu - 1;
125  n2 = n / 2;
126 
127  for (i = 0; i < n; i++)
128  xim[i] = 0;
129 
130  for (l = 1; l <= nu; l++) {
131  for (k = 0; k < n; k += n2) {
132  for (i = 1; i <= n2; i++) {
133  p = bitrev(k >> nu1, nu);
134  c = cosI((1000 * p) / n);
135  s = sinI((1000 * p) / n);
136 
137  tr = ((xre[k + n2] * c + xim[k + n2] * s) >> RESOLUTION);
138  ti = ((xim[k + n2] * c - xre[k + n2] * s) >> RESOLUTION);
139 
140  xre[k + n2] = xre[k] - tr;
141  xim[k + n2] = xim[k] - ti;
142  xre[k] += tr;
143  xim[k] += ti;
144  k++;
145  }
146  }
147  nu1--;
148  n2 = n2 / 2;
149  }
150 
151  for (k = 0; k < n; k++) {
152  p = bitrev(k, nu);
153  if (p > k) {
154  n2 = xre[k];
155  xre[k] = xre[p];
156  xre[p] = n2;
157 
158  n2 = xim[k];
159  xim[k] = xim[p];
160  xim[p] = n2;
161  }
162  }
163 
164  /* This is a fast but not 100% correct magnitude calculation */
165  /* Should be sqrt(xre[i]^2 + xim[i]^2) and normalized with div. by n */
166  for (i = 0, n2 = n / 2; i < n2; i++) {
167  xre[i] = (ABS(xre[i]) + ABS(xim[i]));
168  }
169 }