c@349: /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */
c@349: 
c@349: /*
c@349:     QM DSP library
c@349:     Centre for Digital Music, Queen Mary, University of London.
c@349:  
c@349:     This program is free software; you can redistribute it and/or
c@349:     modify it under the terms of the GNU General Public License as
c@349:     published by the Free Software Foundation; either version 2 of the
c@349:     License, or (at your option) any later version.  See the file
c@349:     COPYING included with this distribution for more information.
c@349: */
c@349: 
c@349: #include "KaiserWindow.h"
c@349: 
c@349: #include "maths/MathUtilities.h"
c@349: 
c@349: KaiserWindow::Parameters
c@349: KaiserWindow::parametersForTransitionWidth(double attenuation,
cannam@483:                                            double transition)
c@349: {
c@349:     Parameters p;
c@349:     p.length = 1 + (attenuation > 21.0 ?
cannam@483:                     ceil((attenuation - 7.95) / (2.285 * transition)) :
cannam@483:                     ceil(5.79 / transition));
c@349:     p.beta = (attenuation > 50.0 ? 
cannam@483:               0.1102 * (attenuation - 8.7) :
cannam@483:               attenuation > 21.0 ? 
cannam@483:               0.5842 * pow(attenuation - 21.0, 0.4) + 0.07886 * (attenuation - 21.0) :
cannam@483:               0);
c@349:     return p;
c@349: }
c@349: 
c@349: static double besselTerm(double x, int i)
c@349: {
c@349:     if (i == 0) {
cannam@483:         return 1;
c@349:     } else {
cannam@483:         double f = MathUtilities::factorial(i);
cannam@483:         return pow(x/2, i*2) / (f*f);
c@349:     }
c@349: }
c@349: 
c@349: static double bessel0(double x)
c@349: {
c@349:     double b = 0.0;
c@349:     for (int i = 0; i < 20; ++i) {
cannam@483:         b += besselTerm(x, i);
c@349:     }
c@349:     return b;
c@349: }
c@349: 
c@349: void
c@349: KaiserWindow::init()
c@349: {
c@349:     double denominator = bessel0(m_beta);
c@352:     bool even = (m_length % 2 == 0);
c@352:     for (int i = 0; i < (even ? m_length/2 : (m_length+1)/2); ++i) {
cannam@483:         double k = double(2*i) / double(m_length-1) - 1.0;
cannam@483:         m_window.push_back(bessel0(m_beta * sqrt(1.0 - k*k)) / denominator);
c@349:     }
c@352:     for (int i = 0; i < (even ? m_length/2 : (m_length-1)/2); ++i) {
c@352:         m_window.push_back(m_window[int(m_length/2) - i - 1]);
c@352:     }
c@349: }