Add a useful package (from Source forge) for octave

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

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+## Copyright (C) 2002 André Carezia <acarezia@uol.com.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:  chebwin (L, at)
+##
+## Returns the filter coefficients of the L-point Dolph-Chebyshev window
+## with at dB of attenuation in the stop-band of the corresponding
+## Fourier transform.
+##
+## For the definition of the Chebyshev window, see
+##
+## * Peter Lynch, "The Dolph-Chebyshev Window: A Simple Optimal Filter",
+##   Monthly Weather Review, Vol. 125, pp. 655-660, April 1997.
+##   (http://www.maths.tcd.ie/~plynch/Publications/Dolph.pdf)
+##
+## * C. Dolph, "A current distribution for broadside arrays which
+##   optimizes the relationship between beam width and side-lobe level",
+##   Proc. IEEE, 34, pp. 335-348.
+##
+## The window is described in frequency domain by the expression:
+##
+##          Cheb(L-1, beta * cos(pi * k/L))
+##   W(k) = -------------------------------
+##                 Cheb(L-1, beta)
+##
+## with
+##
+##   beta = cosh(1/(L-1) * acosh(10^(at/20))
+##
+## and Cheb(m,x) denoting the m-th order Chebyshev polynomial calculated
+## at the point x.
+##
+## Note that the denominator in W(k) above is not computed, and after
+## the inverse Fourier transform the window is scaled by making its
+## maximum value unitary.
+##
+## See also: kaiser
+
+function w = chebwin (L, at)
+
+  if (nargin != 2)
+    print_usage;
+  elseif !(isscalar (L) && (L == round(L)) && (L > 0))
+    error ("chebwin: L has to be a positive integer");
+  elseif !(isscalar (at) && (at == real (at)))
+    error ("chebwin: at has to be a real scalar");
+  endif
+  
+  if (L == 1)
+    w = 1;
+  else
+                               # beta calculation
+    gamma = 10^(-at/20);
+    beta = cosh(1/(L-1) * acosh(1/gamma));
+                               # freq. scale
+    k = (0:L-1);
+    x = beta*cos(pi*k/L);
+                               # Chebyshev window (freq. domain)
+    p = cheb(L-1, x);
+                               # inverse Fourier transform
+    if (rem(L,2))
+      w = real(fft(p));
+      M = (L+1)/2;
+      w = w(1:M)/w(1);
+      w = [w(M:-1:2) w]';
+    else
+                               # half-sample delay (even order)
+      p = p.*exp(j*pi/L * (0:L-1));
+      w = real(fft(p));
+      M = L/2+1;
+      w = w/w(2);
+      w = [w(M:-1:2) w(2:M)]';
+    endif
+  endif 
+  
+  w = w ./ max (w (:)); 
+endfunction