## Copyright (C) 2002 André 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
## 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
# )
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