Add a useful package (from Source forge) for octave

[CreaPhase.git] / octave_packages / signal-1.1.3 / qp_kaiser.m

diff --git a/octave_packages/signal-1.1.3/qp_kaiser.m b/octave_packages/signal-1.1.3/qp_kaiser.m
new file mode 100644 (file)
index 0000000..c1b4c2e
--- /dev/null
+++ b/octave_packages/signal-1.1.3/qp_kaiser.m
@@ -0,0 +1,90 @@
+## Copyright (C) 2002 André Carezia <andre@carezia.eng.br>
+##
+## 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 3 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, see <http://www.gnu.org/licenses/>.
+
+## 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.
+
+function h = qp_kaiser (nb, at, linear = 0)
+
+  if (nargin < 2)
+    print_usage;
+  elseif !(isscalar (nb) && (nb == round(nb)) && (nb >= 0))
+    error ("qp_kaiser: nb has to be a positive integer");
+  elseif !(isscalar (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