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
|
/*
* Copyright (c) 2008 MUSIC TECHNOLOGY GROUP (MTG)
* UNIVERSITAT POMPEU FABRA
*
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or
* (at your option) any later version.
*
* This program is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*
*/
/*! \file spectrum.c
* \brief functions to convert between frequency (spectrum) and time (wavefrom) domain
*/
#include "sms.h"
/*! \brief compute a complex spectrum from a waveform
*
* \param sizeWindow size of analysis window
* \param pWaveform pointer to input waveform
* \param pWindow pointer to input window
* \param sizeMag size of output magnitude and phase spectrums
* \param pMag pointer to output magnitude spectrum
* \param pPhase pointer to output phase spectrum
* \return sizeFft, -1 on error \todo remove this return
*/
int sms_spectrum(int sizeWindow, sfloat *pWaveform, sfloat *pWindow, int sizeMag,
sfloat *pMag, sfloat *pPhase, sfloat *pFftBuffer)
{
int i, it2;
sfloat fReal, fImag;
int sizeFft = sizeMag << 1;
memset(pFftBuffer, 0, sizeFft * sizeof(sfloat));
/* apply window to waveform and center window around 0 (zero-phase windowing)*/
sms_windowCentered(sizeWindow, pWaveform, pWindow, sizeFft, pFftBuffer);
sms_fft(sizeFft, pFftBuffer);
/* convert from rectangular to polar coordinates */
for(i = 0; i < sizeMag; i++)
{
it2 = i << 1; //even numbers 0-N
fReal = pFftBuffer[it2]; /*odd numbers 1->N+1 */
fImag = pFftBuffer[it2 + 1]; /*even numbers 2->N+2 */
pMag[i] = sqrt(fReal * fReal + fImag * fImag);
pPhase[i] = atan2(-fImag, fReal); /* \todo why is fImag negated? */
/*pPhase[i] = atan2(fImag, fReal);*/
}
return sizeFft;
}
/* sms_spectrum, but without zero-phase windowing, and with phase calculated
* according by arctan(imag/real) instead of arctan2(-imag/real)
*/
int sms_spectrumW(int sizeWindow, sfloat *pWaveform, sfloat *pWindow, int sizeMag,
sfloat *pMag, sfloat *pPhase, sfloat *pFftBuffer)
{
int i, it2;
sfloat fReal, fImag;
int sizeFft = sizeMag << 1;
memset(pFftBuffer, 0, sizeFft * sizeof(sfloat));
/* apply window to waveform */
for(i = 0; i < sizeWindow; i++)
pFftBuffer[i] = pWaveform[i] * pWindow[i];
sms_fft(sizeFft, pFftBuffer);
/* convert from rectangular to polar coordinates */
for(i = 0; i < sizeMag; i++)
{
it2 = i << 1; //even numbers 0-N
fReal = pFftBuffer[it2]; /*odd numbers 1->N+1 */
fImag = pFftBuffer[it2 + 1]; /*even numbers 2->N+2 */
pMag[i] = sqrt(fReal * fReal + fImag * fImag);
pPhase[i] = atan2(fImag, fReal);
}
return sizeFft;
}
/*! \brief compute the spectrum Magnitude of a waveform
*
* This function windows the waveform with pWindow and
* performs a zero-padded FFT (if sizeMag*2 > sizeWindow).
* The spectra is then converted magnitude (RMS).
*
* \param sizeWindow size of analysis window / input wavefrom
* \param pWaveform pointer to input waveform
* \param pWindow pointer to analysis window
* \param sizeMag size of output magnitude spectrum
* \param pMag pointer to output magnitude spectrum
* \return 0 on success, -1 on error
*/
int sms_spectrumMag(int sizeWindow, sfloat *pWaveform, sfloat *pWindow,
int sizeMag, sfloat *pMag, sfloat *pFftBuffer)
{
int i,it2;
int sizeFft = sizeMag << 1;
sfloat fReal, fImag;
/* apply window to waveform, zero the rest of the array */
for(i = 0; i < sizeWindow; i++)
pFftBuffer[i] = pWaveform[i] * pWindow[i];
for(i = sizeWindow; i < sizeFft; i++)
pFftBuffer[i] = 0.;
/* compute real FFT */
sms_fft(sizeFft, pFftBuffer);
/* convert from rectangular to polar coordinates */
for(i = 0; i < sizeMag; i++)
{
it2 = i << 1;
fReal = pFftBuffer[it2];
fImag = pFftBuffer[it2+1];
pMag[i] = sqrtf(fReal * fReal + fImag * fImag);
}
return sizeFft;
}
/*! \brief function for a quick inverse spectrum, windowed
*
* Not done yet, but this will be a function that is the inverse of
* sms_spectrum above.
*
* function to perform the inverse FFT, windowing the output
* sfloat *pFMagSpectrum input magnitude spectrum
* sfloat *pFPhaseSpectrum input phase spectrum
* int sizeFft size of FFT
* sfloat *pFWaveform output waveform
* int sizeWave size of output waveform
* sfloat *pFWindow synthesis window
*/
int sms_invSpectrum(int sizeWaveform, sfloat *pWaveform, sfloat *pWindow,
int sizeMag, sfloat *pMag, sfloat *pPhase, sfloat *pFftBuffer)
{
int i;
int sizeFft = sizeMag << 1;
sms_PolarToRect(sizeMag, pFftBuffer, pMag, pPhase);
sms_ifft(sizeFft, pFftBuffer);
/* assume that the output array does not need to be cleared */
/* before, this was multiplied by .5, why? */
for(i = 0; i < sizeWaveform; i++)
//pWaveform[i] += pFftBuffer[i] * pWindow[i];
pWaveform[i] = pFftBuffer[i];
return sizeFft;
}
/*! \brief function for a quick inverse spectrum, windowed
* function to perform the inverse FFT, windowing the output
* sfloat *pFMagSpectrum input magnitude spectrum
* sfloat *pFPhaseSpectrum input phase spectrum
* int sizeFft size of FFT
* sfloat *pFWaveform output waveform
* int sizeWave size of output waveform
* sfloat *pFWindow synthesis window
*/
int sms_invQuickSpectrumW(sfloat *pFMagSpectrum, sfloat *pFPhaseSpectrum,
int sizeFft, sfloat *pFWaveform, int sizeWave,
sfloat *pFWindow, sfloat* pFftBuffer)
{
int i, it2;
int sizeMag = sizeFft >> 1;
/* convert from polar coordinates to rectangular */
for(i = 0; i < sizeMag; i++)
{
it2 = i << 1;
pFftBuffer[it2] = pFMagSpectrum[i] * cos(pFPhaseSpectrum[i]);
pFftBuffer[it2+1] = pFMagSpectrum[i] * sin(pFPhaseSpectrum[i]);
}
/* compute IFFT */
sms_ifft(sizeFft, pFftBuffer);
/* assume that the output array does not need to be cleared */
for(i = 0; i < sizeWave; i++)
pFWaveform[i] += (pFftBuffer[i] * pFWindow[i] * .5);
return sizeMag;
}
/*! \brief convert spectrum from Rectangular to Polar form
*
* \param sizeMag size of spectrum (pMag and pPhase arrays)
* \param pRect pointer output spectrum in rectangular form (2x sizeSpec)
* \param pMag pointer to sfloat array of magnitude spectrum
* \param pPhase pointer to sfloat array of phase spectrum
*/
void sms_RectToPolar(int sizeMag, sfloat *pRect, sfloat *pMag, sfloat *pPhase)
{
int i, it2;
sfloat fReal, fImag;
for(i=0; i<sizeMag; i++)
{
it2 = i << 1;
fReal = pRect[it2];
fImag = pRect[it2+1];
pMag[i] = sqrtf(fReal * fReal + fImag * fImag);
if(pPhase)
pPhase[i] = atan2f(fImag, fReal);
}
}
/*! \brief convert spectrum from Rectangular to Polar form
*
* \param sizeSpec size of spectrum (pMag and pPhase arrays)
* \param pRect pointer output spectrum in rectangular form (2x sizeSpec)
* \param pMag pointer to sfloat array of magnitude spectrum
* \param pPhase pointer to sfloat array of phase spectrum
*/
void sms_PolarToRect(int sizeSpec, sfloat *pRect, sfloat *pMag, sfloat *pPhase)
{
int i, it2;
sfloat fMag;
for(i = 0; i<sizeSpec; i++)
{
it2 = i << 1;
fMag = pMag[i];
pRect[it2] = fMag * cos (pPhase[i]);
pRect[it2+1] = fMag * sin (pPhase[i]);
}
}
/*! \brief compute magnitude spectrum of a DFT in rectangular coordinates
*
* \param sizeMag size of output Magnitude (half of input real FFT)
* \param pInRect pointer to input DFT array (real/imag sfloats)
* \param pOutMag pointer to of magnitude spectrum array
*/
void sms_spectrumRMS(int sizeMag, sfloat *pInRect, sfloat *pOutMag)
{
int i, it2;
sfloat fReal, fImag;
for(i=0; i<sizeMag; i++)
{
it2 = i << 1;
fReal = pInRect[it2];
fImag = pInRect[it2+1];
pOutMag[i] = sqrtf(fReal * fReal + fImag * fImag);
}
}
|