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Diffstat (limited to 'sms/cepstrum.c')
| -rw-r--r-- | sms/cepstrum.c | 259 |
1 files changed, 259 insertions, 0 deletions
diff --git a/sms/cepstrum.c b/sms/cepstrum.c new file mode 100644 index 0000000..430f1c3 --- /dev/null +++ b/sms/cepstrum.c @@ -0,0 +1,259 @@ +/* + * 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 / (float)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(float))) == 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); + } +} |