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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 cepstrum.c
- * \brief routines for different Fast Fourier Transform Algorithms
- *
- */
-
-#include "sms.h"
-#include <gsl/gsl_matrix.h>
-#include <gsl/gsl_linalg.h>
-#include <gsl/gsl_blas.h>
-
-#define COEF ( 8 * powf(PI, 2))
-#define CHOLESKY 1
-
-typedef struct
-{
- int nPoints;
- int nCoeff;
- gsl_matrix *pM;
- gsl_matrix *pMt;
- gsl_matrix *pR;
- gsl_matrix *pMtMR;
- gsl_vector *pXk;
- gsl_vector *pMtXk;
- gsl_vector *pC;
- gsl_permutation *pPerm;
-} CepstrumMatrices;
-
-void FreeDCepstrum(CepstrumMatrices *m)
-{
- gsl_matrix_free(m->pM);
- gsl_matrix_free(m->pMt);
- gsl_matrix_free(m->pR);
- gsl_matrix_free(m->pMtMR);
- gsl_vector_free(m->pXk);
- gsl_vector_free(m->pMtXk);
- gsl_vector_free(m->pC);
- gsl_permutation_free (m->pPerm);
-
-}
-
-void AllocateDCepstrum(int nPoints, int nCoeff, CepstrumMatrices *m)
-{
- if(m->nPoints != 0 || m->nCoeff != 0)
- FreeDCepstrum(m);
- m->nPoints = nPoints;
- m->nCoeff = nCoeff;
- m->pM = gsl_matrix_alloc(nPoints, nCoeff);
- m->pMt = gsl_matrix_alloc(nCoeff, nPoints);
- m->pR = gsl_matrix_calloc(nCoeff, nCoeff);
- m->pMtMR = gsl_matrix_alloc(nCoeff, nCoeff);
- m->pXk = gsl_vector_alloc(nPoints);
- m->pMtXk = gsl_vector_alloc(nCoeff);
- m->pC = gsl_vector_alloc(nCoeff);
- m->pPerm = gsl_permutation_alloc (nCoeff);
-}
-
-/*! \brief Discrete Cepstrum Transform
- *
- * method for computing cepstrum aenalysis from a discrete
- * set of partial peaks (frequency and amplitude)
- *
- * This implementation is owed to the help of Jordi Janer (thanks!) from the MTG,
- * along with the following paper:
- * "Regularization Techniques for Discrete Cepstrum Estimation"
- * Olivier Cappe and Eric Moulines, IEEE Signal Processing Letters, Vol. 3
- * No.4, April 1996
- *
- * \todo add anchor point add at frequency = 0 with the same magnitude as the first
- * peak in pMag. This does not change the size of the cepstrum, only helps to smoothen it
- * at the very beginning.
- *
- * \param sizeCepstrum order+1 of the discrete cepstrum
- * \param pCepstrum pointer to output array of cepstrum coefficients
- * \param sizeFreq number of partials peaks (the size of pFreq should be the same as pMag
- * \param pFreq pointer to partial peak frequencies (hertz)
- * \param pMag pointer to partial peak magnitudes (linear)
- * \param fLambda regularization factor
- * \param iMaxFreq maximum frequency of cepstrum
- */
-void sms_dCepstrum( int sizeCepstrum, sfloat *pCepstrum, int sizeFreq, sfloat *pFreq, sfloat *pMag,
- sfloat fLambda, int iMaxFreq)
-{
- int i, k;
- sfloat factor;
- sfloat fNorm = PI / (sfloat)iMaxFreq; /* value to normalize frequencies to 0:0.5 */
- //static sizeCepstrumStatic
- static CepstrumMatrices m;
- //printf("nPoints: %d, nCoeff: %d \n", m.nPoints, m.nCoeff);
- if(m.nPoints != sizeCepstrum || m.nCoeff != sizeFreq)
- AllocateDCepstrum(sizeFreq, sizeCepstrum, &m);
- int s; /* signum: "(-1)^n, where n is the number of interchanges in the permutation." */
- /* compute matrix M (eq. 4)*/
- for (i=0; i<sizeFreq; i++)
- {
- gsl_matrix_set (m.pM, i, 0, 1.); // first colum is all 1
- for (k=1; k <sizeCepstrum; k++)
- gsl_matrix_set (m.pM, i, k , 2.*sms_sine(PI_2 + fNorm * k * pFreq[i]) );
- }
-
- /* compute transpose of M */
- gsl_matrix_transpose_memcpy (m.pMt, m.pM);
-
- /* compute R diagonal matrix (for eq. 7)*/
- factor = COEF * (fLambda / (1.-fLambda)); /* \todo why is this divided like this again? */
- for (k=0; k<sizeCepstrum; k++)
- gsl_matrix_set(m.pR, k, k, factor * powf((sfloat) k,2.));
-
- /* MtM = Mt * M, later will add R */
- gsl_blas_dgemm (CblasNoTrans, CblasNoTrans, 1., m.pMt, m.pM, 0.0, m.pMtMR);
- /* add R to make MtMR */
- gsl_matrix_add (m.pMtMR, m.pR);
-
- /* set pMag in X and multiply with Mt to get pMtXk */
- for(k = 0; k <sizeFreq; k++)
- gsl_vector_set(m.pXk, k, log(pMag[k]));
- gsl_blas_dgemv (CblasNoTrans, 1., m.pMt, m.pXk, 0., m.pMtXk);
-
- /* solve x (the cepstrum) in Ax = b, where A=MtMR and b=pMtXk */
-
- /* ==== the Cholesky Decomposition way ==== */
- /* MtM is 'symmetric and positive definite?' */
- //gsl_linalg_cholesky_decomp (m.pMtMR);
- //gsl_linalg_cholesky_solve (m.pMtMR, m.pMtXk, m.pC);
-
- /* ==== the LU decomposition way ==== */
- gsl_linalg_LU_decomp (m.pMtMR, m.pPerm, &s);
- gsl_linalg_LU_solve (m.pMtMR, m.pPerm, m.pMtXk, m.pC);
-
-
- /* copy pC to pCepstrum */
- for(i = 0; i < sizeCepstrum; i++)
- pCepstrum[i] = gsl_vector_get (m.pC, i);
-}
-
-/*! \brief Spectrum Envelope from Cepstrum
- *
- * from a set of cepstrum coefficients, compute the spectrum envelope
- *
- * \param sizeCepstrum order + 1 of the cepstrum
- * \param pCepstrum pointer to array of cepstrum coefficients
- * \param sizeEnv size of spectrum envelope (max frequency in bins) \todo does this have to be a pow2
- * \param pEnv pointer to output spectrum envelope (real part only)
- */
-void sms_dCepstrumEnvelope(int sizeCepstrum, sfloat *pCepstrum, int sizeEnv, sfloat *pEnv)
-{
-
- static sfloat *pFftBuffer;
- static int sizeFftArray = 0;
- int sizeFft = sizeEnv << 1;
- int i;
- if(sizeFftArray != sizeFft)
- {
- if(sizeFftArray != 0) free(pFftBuffer);
- sizeFftArray = sms_power2(sizeFft);
- if(sizeFftArray != sizeFft)
- {
- sms_error("bad fft size, incremented to power of 2");
- }
- if ((pFftBuffer = (sfloat *) malloc(sizeFftArray * sizeof(sfloat))) == NULL)
- {
- sms_error("could not allocate memory for fft array");
- return;
- }
- }
- memset(pFftBuffer, 0, sizeFftArray * sizeof(sfloat));
-
- pFftBuffer[0] = pCepstrum[0] * 0.5;
- for (i = 1; i < sizeCepstrum-1; i++)
- pFftBuffer[i] = pCepstrum[i];
-
-
- sms_fft(sizeFftArray, pFftBuffer);
-
- for (i = 0; i < sizeEnv; i++)
- pEnv[i] = powf(EXP, 2. * pFftBuffer[i*2]);
-}
-
-/*! \brief main function for computing spectral envelope from sinusoidal peaks
- *
- * Magnitudes should already be in linear for this function.
- * If pSmsData->iEnvelope == SMS_ENV_CEP, will return cepstrum coefficeints
- * If pSmsData->iEnvelope == SMS_ENV_FBINS, will return linear magnitude spectrum
- *
- * \param pSmsData pointer to SMS_Data structure with all the arrays necessary
- * \param pSpecEnvParams pointer to a structure of parameters for spectral enveloping
- */
-void sms_spectralEnvelope( SMS_Data *pSmsData, SMS_SEnvParams *pSpecEnvParams)
-{
- int i, k;
- int sizeCepstrum = pSpecEnvParams->iOrder+1;
- //int nPeaks = 0;
- static sfloat pFreqBuff[1000], pMagBuff[1000];
-
- /* \todo see if this memset is even necessary, once working */
- //memset(pSmsData->pSpecEnv, 0, pSpecEnvParams->nCoeff * sizeof(sfloat));
-
- /* try to store cepstrum coefficients in pSmsData->nEnvCoeff always.
- if cepstrum is what is wanted, memset the rest. otherwise, hand this array 2x to dCepstrumEnvelope */
- if(pSpecEnvParams->iOrder + 1> pSmsData->nEnvCoeff)
- {
- sms_error("cepstrum order is larger than the size of the spectral envelope");
- return;
- }
-
- /* find out how many tracks were actually found... many are zero
- \todo is this necessary? */
- for(i = 0, k=0; i < pSmsData->nTracks; i++)
- {
- if(pSmsData->pFSinFreq[i] > 0.00001)
- {
- if(pSpecEnvParams->iAnchor != 0)
- {
- if(k == 0) /* add anchor at beginning */
-
- {
- pFreqBuff[k] = 0.0;
- pMagBuff[k] = pSmsData->pFSinAmp[i];
- k++;
- }
- }
- pFreqBuff[k] = pSmsData->pFSinFreq[i];
- pMagBuff[k] = pSmsData->pFSinAmp[i];
- k++;
- }
- }
- /* \todo see if adding an anchor at the max freq helps */
-
-
- if(k < 1) // how few can this be? try out a few in python
- return;
- sms_dCepstrum(sizeCepstrum, pSmsData->pSpecEnv, k, pFreqBuff, pMagBuff,
- pSpecEnvParams->fLambda, pSpecEnvParams->iMaxFreq);
-
- if(pSpecEnvParams->iType == SMS_ENV_FBINS)
- {
- sms_dCepstrumEnvelope(sizeCepstrum, pSmsData->pSpecEnv,
- pSpecEnvParams->nCoeff, pSmsData->pSpecEnv);
- }
-}