--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/main/signal/qp_kaiser.m	Sat Oct 29 20:25:58 2005 +0000
@@ -0,0 +1,105 @@
+## Copyright (C) 2002   AndrŽ Carezia
+##
+## 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
+
+## Usage:  qp_kaiser (nb, at, linear)
+##
+## Computes a finite impulse response (FIR) filter for use with a
+## quasi-perfect reconstruction polyphase-network filter bank. This
+## version utilizes a Kaiser window to shape the frequency response of
+## the designed filter. Tha number nb of bands and the desired
+## attenuation at in the stop-band are given as parameters.
+##
+## The Kaiser window is multiplied by the ideal impulse response
+## h(n)=a.sinc(a.n) and converted to its minimum-phase version by means
+## of a Hilbert transform.
+##
+## By using a third non-null argument, the minimum-phase calculation is
+## ommited at all.
+
+## $Id$
+##
+## Author:  AHCC <andre@carezia.eng.br>
+## Description:  Coefficients for a PPN filter bank
+
+function h = qp_kaiser (nb, at, linear)
+
+  if (nargin < 2)
+    usage ("qp_kaiser (nb, at)");
+  endif
+
+  if (nargin < 3)
+    linear = 0;
+  endif
+
+  if !(is_scalar (nb) && (nb == round(nb)) && (nb >= 0))
+    error ("qp_kaiser: nb has to be a positive integer");
+  endif
+
+  if !(is_scalar (at) && (at == real (at)))
+    error ("qp_kaiser: at has to be a real constant");
+  endif
+
+				# Bandwidth
+  bandwidth = pi/nb;
+
+				# Attenuation correction (empirically
+				# determined by M. Gerken
+				# <mgk@lcs.poli.usp.br>)
+  corr = (1.4+0.6*(at-20)/80)^(20/at);
+  at = corr * at;
+
+				# size of window (rounded to next odd
+				# integer)
+  N = (at - 8) / (2.285*bandwidth);
+  M = fix(N/2);
+  N = 2*M + 1;
+
+				# Kaiser window
+  if (at>50)
+    beta = 0.1102 * (at - 8.7);
+  elseif (at>21)
+    beta = 0.5842 * (at - 21)^0.4 + 0.07886 * (at - 21);
+  else
+    beta = 0;
+  endif
+  w = kaiser(N,beta);
+				# squared in freq. domain
+  wsquared = conv(w,w);
+
+				# multiplied by ideal lowpass filter
+  n = -(N-1):(N-1);
+  hideal = 1/nb * sinc(n/nb);
+  hcomp = wsquared .* hideal;
+
+				# extract square-root of response and
+				# compute minimum-phase version
+  Ndft = 2^15;
+  Hsqr = sqrt(abs(fft(hcomp,Ndft)));
+  if (linear)
+    h = real(ifft(Hsqr));
+    h = h(2:N);
+    h = [fliplr(h) h(1) h];
+  else
+    Hmin = Hsqr .* exp(-j*imag(hilbert(log(Hsqr))));
+    h = real(ifft(Hmin));
+    h = h(1:N);
+  endif
+				# truncate and fix amplitude scale
+				# (H(0)=1)
+  h = h / sum(h);
+
+endfunction