Chris@366: /* -*- c-basic-offset: 4 indent-tabs-mode: nil -*-  vi:set ts=8 sts=4 sw=4: */
Chris@366: /*
Chris@366:     Constant-Q library
Chris@366:     Copyright (c) 2013-2014 Queen Mary, University of London
Chris@366: 
Chris@366:     Permission is hereby granted, free of charge, to any person
Chris@366:     obtaining a copy of this software and associated documentation
Chris@366:     files (the "Software"), to deal in the Software without
Chris@366:     restriction, including without limitation the rights to use, copy,
Chris@366:     modify, merge, publish, distribute, sublicense, and/or sell copies
Chris@366:     of the Software, and to permit persons to whom the Software is
Chris@366:     furnished to do so, subject to the following conditions:
Chris@366: 
Chris@366:     The above copyright notice and this permission notice shall be
Chris@366:     included in all copies or substantial portions of the Software.
Chris@366: 
Chris@366:     THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
Chris@366:     EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
Chris@366:     MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
Chris@366:     NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
Chris@366:     CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF
Chris@366:     CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION
Chris@366:     WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
Chris@366: 
Chris@366:     Except as contained in this notice, the names of the Centre for
Chris@366:     Digital Music; Queen Mary, University of London; and Chris Cannam
Chris@366:     shall not be used in advertising or otherwise to promote the sale,
Chris@366:     use or other dealings in this Software without prior written
Chris@366:     authorization.
Chris@366: */
Chris@366: 
Chris@366: #include "KaiserWindow.h"
Chris@366: 
Chris@366: #include "MathUtilities.h"
Chris@366: 
Chris@366: KaiserWindow::Parameters
Chris@366: KaiserWindow::parametersForTransitionWidth(double attenuation,
Chris@366: 					   double transition)
Chris@366: {
Chris@366:     Parameters p;
Chris@366:     p.length = 1 + (attenuation > 21.0 ?
Chris@366: 		    ceil((attenuation - 7.95) / (2.285 * transition)) :
Chris@366: 		    ceil(5.79 / transition));
Chris@366:     p.beta = (attenuation > 50.0 ? 
Chris@366: 	      0.1102 * (attenuation - 8.7) :
Chris@366: 	      attenuation > 21.0 ? 
Chris@366: 	      0.5842 * pow(attenuation - 21.0, 0.4) + 0.07886 * (attenuation - 21.0) :
Chris@366: 	      0);
Chris@366:     return p;
Chris@366: }
Chris@366: 
Chris@366: static double besselTerm(double x, int i)
Chris@366: {
Chris@366:     if (i == 0) {
Chris@366: 	return 1;
Chris@366:     } else {
Chris@366: 	double f = MathUtilities::factorial(i);
Chris@366: 	return pow(x/2, i*2) / (f*f);
Chris@366:     }
Chris@366: }
Chris@366: 
Chris@366: static double bessel0(double x)
Chris@366: {
Chris@366:     double b = 0.0;
Chris@366:     for (int i = 0; i < 20; ++i) {
Chris@366: 	b += besselTerm(x, i);
Chris@366:     }
Chris@366:     return b;
Chris@366: }
Chris@366: 
Chris@366: void
Chris@366: KaiserWindow::init()
Chris@366: {
Chris@366:     double denominator = bessel0(m_beta);
Chris@366:     bool even = (m_length % 2 == 0);
Chris@366:     for (int i = 0; i < (even ? m_length/2 : (m_length+1)/2); ++i) {
Chris@366: 	double k = double(2*i) / double(m_length-1) - 1.0;
Chris@366: 	m_window.push_back(bessel0(m_beta * sqrt(1.0 - k*k)) / denominator);
Chris@366:     }
Chris@366:     for (int i = 0; i < (even ? m_length/2 : (m_length-1)/2); ++i) {
Chris@366:         m_window.push_back(m_window[int(m_length/2) - i - 1]);
Chris@366:     }
Chris@366: }