/* * 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 windows.c * \brief functions for creating various windows * * Use sms_getWindow() for selecting which window will be made */ #include "sms.h" /* \brief scale a window by its integral (numeric quadrature) * * In order to get a normalized magnitude spectrum (ex. Fourier analysis * of a sinusoid with linear magnitude 1 gives one peak of magnitude 1 in * the frequency domain), the spectrum windowing function should be * normalized by its area under the curve. * * \param sizeWindow the size of the window * \param pWindow pointer to an array that will hold the window */ void sms_scaleWindow ( int sizeWindow, sfloat *pWindow) { int i; sfloat fSum = 0; sfloat fScale; for(i = 0; i < sizeWindow; i++) fSum += pWindow[i]; /* fSum = fSum / 2; */ /* for(i = 0; i < sizeWindow; i++) */ /* pWindow[i] /= fSum; */ fScale = 2. / fSum; for(i = 0; i < sizeWindow; i++) pWindow[i] *= fScale; } /*! \brief window to be used in the IFFT synthesis * * contains both an inverse Blackman-Harris and triangular window. * * \todo read X. Rodet, Ph. Depalle, "Spectral Envelopes and Inverse FFT * Synthesis." Proc. 93rd AES Convention, October 1992 * \param sizeWindow the size of the window * \param pFWindow pointer to an array that will hold the window */ void IFFTwindow (int sizeWindow, sfloat *pFWindow) { int i; sfloat a0 = .35875, a1 = .48829, a2 = .14128, a3 = .01168; double fConst = TWO_PI / sizeWindow, fIncr = 2.0 /sizeWindow, fVal = 0; /* compute inverse of Blackman-Harris 92dB window */ for(i = 0; i < sizeWindow; i++) { pFWindow[i] = 1 / (a0 - a1 * cos(fConst * i) + a2 * cos(fConst * 2 * i) - a3 * cos(fConst * 3 * i)); } /* scale function by a triangular */ for (i = 0; i < sizeWindow / 2; i++) { pFWindow[i] = fVal * pFWindow[i] / 2.787457; fVal += fIncr; } for (i = sizeWindow / 2; i < sizeWindow; i++) { pFWindow[i] = fVal * pFWindow[i] / 2.787457; fVal -= fIncr; } } /*! \brief BlackmanHarris window with 62dB rolloff * * \todo where did these come from? * \param sizeWindow the size of the window * \param pFWindow pointer to an array that will hold the window */ void BlackmanHarris62 (int sizeWindow, sfloat *pFWindow) { int i; double fSum = 0; /* for 3 term -62.05 */ sfloat a0 = .44959, a1 = .49364, a2 = .05677; double fConst = TWO_PI / sizeWindow; /* compute window */ for(i = 0; i < sizeWindow; i++) { fSum += pFWindow[i] = a0 - a1 * cos(fConst * i) + a2 * cos(fConst * 2 * i); } /* I do not know why I now need this factor of two */ /* fSum = fSum / 2; */ /* /\* scale function *\/ */ /* for (i = 0; i < sizeWindow; i++) */ /* pFWindow[i] = pFWindow[i] / fSum; */ } /*! \brief BlackmanHarris window with 70dB rolloff * * \param sizeWindow the size of the window * \param pFWindow pointer to an array that will hold the window */ void BlackmanHarris70 (int sizeWindow, sfloat *pFWindow) { int i; double fSum = 0; /* for 3 term -70.83 */ sfloat a0 = .42323, a1 = .49755, a2 = .07922; double fConst = TWO_PI / sizeWindow; /* compute window */ for(i = 0; i < sizeWindow; i++) { fSum += pFWindow[i] = a0 - a1 * cos(fConst * i) + a2 * cos(fConst * 2 * i); } /* fSum = fSum / 2; */ /* /\* scale function *\/ */ /* for (i = 0; i < sizeWindow; i++) */ /* { */ /* pFWindow[i] = pFWindow[i] / fSum; */ /* } */ } /*! \brief BlackmanHarris window with 74dB rolloff * * \param sizeWindow the size of the window * \param pFWindow pointer to an array that will hold the window */ void BlackmanHarris74 (int sizeWindow, sfloat *pFWindow) { int i; double fSum = 0; /* for -74dB from the Nuttall paper */ sfloat a0 = .40217, a1 = .49703, a2 = .09892, a3 = .00188; double fConst = TWO_PI / sizeWindow; /* compute window */ for(i = 0; i < sizeWindow; i++) { fSum += pFWindow[i] = a0 - a1 * cos(fConst * i) + a2 * cos(fConst * 2 * i) + a3 * cos(fConst * 3 * i); } /* I do not know why I now need this factor of two */ /* fSum = fSum / 2; */ /* /\* scale function *\/ */ /* for (i = 0; i < sizeWindow; i++) */ /* pFWindow[i] = pFWindow[i] / fSum; */ } /*! \brief BlackmanHarris window with 92dB rolloff * * \param sizeWindow the size of the window * \param pFWindow pointer to an array that will hold the window */ void BlackmanHarris92 (int sizeWindow, sfloat *pFWindow) { int i; double fSum = 0; /* for -92dB */ sfloat a0 = .35875, a1 = .48829, a2 = .14128, a3 = .01168; double fConst = TWO_PI / sizeWindow; /* compute window */ for(i = 0; i < sizeWindow; i++) { fSum += pFWindow[i] = a0 - a1 * cos(fConst * i) + a2 * cos(fConst * 2 * i) + a3 * cos(fConst * 3 * i); } /* I do not know why I now need this factor of two */ /* fSum = fSum / 2; */ /* /\* scale function *\/ */ /* for (i = 0; i < sizeWindow; i++) */ /* pFWindow[i] = pFWindow[i] / fSum; */ } /*! \brief default BlackmanHarris window (70dB rolloff) * * \param sizeWindow the size of the window * \param pFWindow pointer to an array that will hold the window */ void BlackmanHarris (int sizeWindow, sfloat *pFWindow) { BlackmanHarris70 (sizeWindow, pFWindow); } /*! \brief Hamming window * * * * \param sizeWindow window size * \param pWindow window array */ void Hamming (int sizeWindow, sfloat *pWindow) { int i; sfloat fSum = 0; for(i = 0; i < sizeWindow; i++) { fSum += pWindow[i] = 0.53836 - 0.46164*cos(TWO_PI*i/(sizeWindow-1)); } //ScaleWindow(sizeWindow, pWindow); /* fSum = fSum / 2; */ /* for(i = 0; i < sizeWindow; i++) */ /* pFWindow[i] /= fSum; */ } /*! \brief Hanning window * * \param sizeWindow window size * \param pWindow window array */ void Hanning (int sizeWindow, sfloat *pWindow) { int i; for(i = 0; i < sizeWindow; i++) pWindow[i] = (sin(PI*i/(sizeWindow-1)))*(sin(PI*i/(sizeWindow-1))); } /*! \brief main function for getting various windows * * \todo note on window scales * * \see SMS_WINDOWS for the different window types available * \param sizeWindow window size * \param pFWindow window array * \param iWindowType the desired window type defined by #SMS_WINDOWS */ void sms_getWindow (int sizeWindow, sfloat *pFWindow, int iWindowType) { switch (iWindowType) { case SMS_WIN_BH_62: BlackmanHarris62 (sizeWindow, pFWindow); break; case SMS_WIN_BH_70: BlackmanHarris70 (sizeWindow, pFWindow); break; case SMS_WIN_BH_74: BlackmanHarris74 (sizeWindow, pFWindow); break; case SMS_WIN_BH_92: BlackmanHarris92 (sizeWindow, pFWindow); break; case SMS_WIN_HAMMING: Hamming (sizeWindow, pFWindow); break; case SMS_WIN_HANNING: Hanning (sizeWindow, pFWindow); break; case SMS_WIN_IFFT: IFFTwindow (sizeWindow, pFWindow); break; default: BlackmanHarris (sizeWindow, pFWindow); } } /*! \brief apply a window and center around sample 0 * * function to center a waveform around sample 0, also known * as 'zero-phase windowing'. Half the samples are at the beginning, * half at the end, with the remaining samples (sizeFft-sizeWindow) * in the middle (zero-padding for an interpolated spectrum). * * \todo do I need to garuntee that sizeWindow is odd-lengthed? * * \param sizeWindow size of waveform/waveform * \param pWaveform pointer to waveform * \param pWindow pointer to window * \param sizeFft size of FFT * \param pFftBuffer pointer to FFT buffer */ void sms_windowCentered (int sizeWindow, sfloat *pWaveform, sfloat *pWindow, int sizeFft, sfloat *pFftBuffer) { int i, iOffset, iMiddleWindow; iMiddleWindow = (sizeWindow+1) >> 1; iOffset = sizeFft - (iMiddleWindow - 1); for (i=0; i