summaryrefslogtreecommitdiff
path: root/tests/test6/fft.c
blob: dd91d143116dd682c343e21b99456ca82b6a1fea (plain)
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
#include "fft.h"
#include <math.h>
#include <stdlib.h>

/* Everything here comes from Audacity 1.3.13
 (orignally in C++ and with more genericity and functionnality)
 Original Author : Dominic Mazzoni
 Licenced under GPL 2.0 (see LICENCE)
*/

#define MaxFastBits 16

int *gFFTBitTable[MaxFastBits]={NULL};

void InitFFT();
int NumberOfBitsNeeded(int PowerOfTwo);
inline int FastReverseBits(int i, int NumBits);
int ReverseBits(int index, int NumBits);


void FFT(int NumSamples,
		int InverseTransform,
		float *RealIn, float *ImagIn, float *RealOut, float *ImagOut)
{
	int NumBits;                 /* Number of bits needed to store indices */
	int i, j, k, n;
	int BlockSize, BlockEnd;

	double angle_numerator = 2.0 * M_PI;
	double tr, ti;                /* temp real, temp imaginary */
/*
	if (!IsPowerOfTwo(NumSamples)) {
		fprintf(stderr, "%d is not a power of two\n", NumSamples);
		exit(1);
	}
*/
	if (!gFFTBitTable[0])
		InitFFT();

	if (!InverseTransform)
		angle_numerator = -angle_numerator;

	NumBits = NumberOfBitsNeeded(NumSamples);

	/*
	 **   Do simultaneous data copy and bit-reversal ordering into outputs...
	 */
	for (i = 0; i < NumSamples; i++) {
		j = FastReverseBits(i, NumBits);
		RealOut[j] = RealIn[i];
		ImagOut[j] = (ImagIn == NULL) ? 0.0 : ImagIn[i];
	}

	/*
	 **   Do the FFT itself...
	 */

	BlockEnd = 1;
	for (BlockSize = 2; BlockSize <= NumSamples; BlockSize <<= 1) {

		double delta_angle = angle_numerator / (double) BlockSize;

		double sm2 = sin(-2 * delta_angle);
		double sm1 = sin(-delta_angle);
		double cm2 = cos(-2 * delta_angle);
		double cm1 = cos(-delta_angle);
		double w = 2 * cm1;
		double ar0, ar1, ar2, ai0, ai1, ai2;

		for (i = 0; i < NumSamples; i += BlockSize) {
			ar2 = cm2;
			ar1 = cm1;

			ai2 = sm2;
			ai1 = sm1;

			for (j = i, n = 0; n < BlockEnd; j++, n++) {
				ar0 = w * ar1 - ar2;
				ar2 = ar1;
				ar1 = ar0;

				ai0 = w * ai1 - ai2;
				ai2 = ai1;
				ai1 = ai0;

				k = j + BlockEnd;
				tr = ar0 * RealOut[k] - ai0 * ImagOut[k];
				ti = ar0 * ImagOut[k] + ai0 * RealOut[k];

				RealOut[k] = RealOut[j] - tr;
				ImagOut[k] = ImagOut[j] - ti;

				RealOut[j] += tr;
				ImagOut[j] += ti;
			}
		}
		BlockEnd = BlockSize;
	}

	/*
	 **   Need to normalize if inverse transform...
	 */

	if (InverseTransform) {
		float denom = (float) NumSamples;

		for (i = 0; i < NumSamples; i++) {
			RealOut[i] /= denom;
			ImagOut[i] /= denom;
		}
	}
}

void InitFFT() {
	int len=2;
	int b, i;
	for (b=0; b<MaxFastBits; b++) {
		gFFTBitTable[b]=malloc(len*sizeof(int));

		for (i=0; i<len; i++)
			gFFTBitTable[b][i] = ReverseBits(i, b+1);

		len <<= 1;
	}
}

int NumberOfBitsNeeded(int PowerOfTwo)
{
	int i;

/*
	if (PowerOfTwo < 2) {
		fprintf(stderr, "Error: FFT called with size %d\n", PowerOfTwo);
		exit(1);
	}
*/
	for (i = 0;; i++)
		if (PowerOfTwo & (1 << i))
			return i;
}

inline int FastReverseBits(int i, int NumBits)
{
	if (NumBits <= MaxFastBits)
		return gFFTBitTable[NumBits - 1][i];
	else
		return ReverseBits(i, NumBits);
}

int ReverseBits(int index, int NumBits)
{
   int i, rev;

   for (i = rev = 0; i < NumBits; i++) {
      rev = (rev << 1) | (index & 1);
      index >>= 1;
   }

   return rev;
}


/*
 * PowerSpectrum
 *
 * This function computes the same as RealFFT, above, but
 * adds the squares of the real and imaginary part of each
 * coefficient, extracting the power and throwing away the
 * phase.
 *
 * For speed, it does not call RealFFT, but duplicates some
 * of its code.
 */

void PowerSpectrum(float In[PSNumS], float Out[PSHalf]) {
	int i;

	float theta = M_PI / PSHalf;

	float tmpReal[PSHalf];
	float tmpImag[PSHalf];
	float RealOut[PSHalf];
	float ImagOut[PSHalf];

	for (i=0; i<PSHalf; i++) {
		tmpReal[i] = In[2*i];
		tmpImag[i] = In[2*i+1];
	}

	FFT(PSHalf, 0, tmpReal, tmpImag, RealOut, ImagOut);

	float wtemp = sin(0.5 * theta);

	float wpr = -2.0 * wtemp * wtemp;
	float wpi = -1.0 * sin(theta);
	float wr = 1.0 + wpr;
	float wi = wpi;

	int i3;

	float h1r, h1i, h2r, h2i, rt, it;
	for (i=1; i < PSHalf/2; i++) {

		i3 = PSHalf - i;

		h1r = 0.5 * (RealOut[i] + RealOut[i3]);
		h1i = 0.5 * (ImagOut[i] - ImagOut[i3]);
		h2r = 0.5 * (ImagOut[i] + ImagOut[i3]);
		h2i = -0.5 * (RealOut[i] - RealOut[i3]);

		rt = h1r + wr * h2r - wi * h2i;
		it = h1i + wr * h2i + wi * h2r;

		Out[i] = rt * rt + it * it;

		rt = h1r - wr * h2r + wi * h2i;
		it = -h1i + wr * h2i + wi * h2r;

		Out[i3] = rt * rt + it * it;

		wr = (wtemp = wr) * wpr - wi * wpi + wr;
		wi = wi * wpr + wtemp * wpi + wi;
	}

	rt = (h1r = RealOut[0]) + ImagOut[0];
	it = h1r - ImagOut[0];
	Out[0] = rt * rt + it * it;
	rt = RealOut[PSHalf / 2];
	it = ImagOut[PSHalf / 2];
	Out[PSHalf / 2] = rt * rt + it * it;
}

void DeinitFFT() {
	int i;
	if (gFFTBitTable[0]) {
		for (i=0;i<MaxFastBits;i++) {
			free(gFFTBitTable[i]);
		}
	}
}