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/*
* 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;
int err = 0;
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? */
}
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] = pWindow[i] * pWaveform[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 the output array has been taken care off */
/* 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 sizeMag = sizeFft >> 1, i, it2;
sfloat fPower;
/* convert from polar coordinates to rectangular */
for (i = 0; i<sizeMag; i++)
{
it2 = i << 1;
fPower = pFMagSpectrum[i];
pFftBuffer[it2] = fPower * cos (pFPhaseSpectrum[i]);
pFftBuffer[it2+1] = fPower * sin (pFPhaseSpectrum[i]);
}
/* compute IFFT */
sms_ifft(sizeFft, pFftBuffer);
/* assume the output array has been taken care off */
/* \todo is a seperate pFftBuffer necessary here?
it seems like multiplying the window into the waveform
would be fine, without pFftBuffer */
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);
}
}
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