--- /dev/null
+## Copyright (C) 2000 Paul Kienzle <pkienzle@users.sf.net>
+##
+## 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: b = fir2(n, f, m [, grid_n [, ramp_n]] [, window])
+##
+## Produce an FIR filter of order n with arbitrary frequency response,
+## returning the n+1 filter coefficients in b.
+##
+## n: order of the filter (1 less than the length of the filter)
+## f: frequency at band edges
+## f is a vector of nondecreasing elements in [0,1]
+## the first element must be 0 and the last element must be 1
+## if elements are identical, it indicates a jump in freq. response
+## m: magnitude at band edges
+## m is a vector of length(f)
+## grid_n: length of ideal frequency response function
+## defaults to 512, should be a power of 2 bigger than n
+## ramp_n: transition width for jumps in filter response
+## defaults to grid_n/20; a wider ramp gives wider transitions
+## but has better stopband characteristics.
+## window: smoothing window
+## defaults to hamming(n+1) row vector
+## returned filter is the same shape as the smoothing window
+##
+## To apply the filter, use the return vector b:
+## y=filter(b,1,x);
+## Note that plot(f,m) shows target response.
+##
+## Example:
+## f=[0, 0.3, 0.3, 0.6, 0.6, 1]; m=[0, 0, 1, 1/2, 0, 0];
+## [h, w] = freqz(fir2(100,f,m));
+## plot(f,m,';target response;',w/pi,abs(h),';filter response;');
+
+function b = fir2(n, f, m, grid_n, ramp_n, window)
+
+ if nargin < 3 || nargin > 6
+ print_usage;
+ endif
+
+ ## verify frequency and magnitude vectors are reasonable
+ t = length(f);
+ if t<2 || f(1)!=0 || f(t)!=1 || any(diff(f)<0)
+ usage("frequency must be nondecreasing starting from 0 and ending at 1");
+ endif
+ if t != length(m)
+ usage("frequency and magnitude vectors must be the same length");
+ endif
+
+ ## find the grid spacing and ramp width
+ if (nargin>4 && length(grid_n)>1) || \
+ (nargin>5 && (length(grid_n)>1 || length(ramp_n)>1))
+ usage("grid_n and ramp_n must be integers");
+ endif
+ if nargin < 4, grid_n=512; endif
+ if nargin < 5, ramp_n=grid_n/20; endif
+
+ ## find the window parameter, or default to hamming
+ w=[];
+ if length(grid_n)>1, w=grid_n; grid_n=512; endif
+ if length(ramp_n)>1, w=ramp_n; ramp_n=grid_n/20; endif
+ if nargin < 6, window=w; endif
+ if isempty(window), window=hamming(n+1); endif
+ if !isreal(window) || ischar(window), window=feval(window, n+1); endif
+ if length(window) != n+1, usage("window must be of length n+1"); endif
+
+ ## make sure grid is big enough for the window
+ if 2*grid_n < n+1, grid_n = 2^nextpow2(n+1); endif
+
+ ## Apply ramps to discontinuities
+ if (ramp_n > 0)
+ ## remember original frequency points prior to applying ramps
+ basef = f(:); basem = m(:);
+
+ ## separate identical frequencies, but keep the midpoint
+ idx = find (diff(f) == 0);
+ f(idx) = f(idx) - ramp_n/grid_n/2;
+ f(idx+1) = f(idx+1) + ramp_n/grid_n/2;
+ f = [f(:);basef(idx)]';
+
+ ## make sure the grid points stay monotonic in [0,1]
+ f(f<0) = 0;
+ f(f>1) = 1;
+ f = unique([f(:);basef(idx)(:)]');
+
+ ## preserve window shape even though f may have changed
+ m = interp1(basef, basem, f);
+
+ # axis([-.1 1.1 -.1 1.1])
+ # plot(f,m,'-xb;ramped;',basef,basem,'-or;original;'); pause;
+ endif
+
+ ## interpolate between grid points
+ grid = interp1(f,m,linspace(0,1,grid_n+1)');
+ # hold on; plot(linspace(0,1,grid_n+1),grid,'-+g;grid;'); hold off; pause;
+
+ ## Transform frequency response into time response and
+ ## center the response about n/2, truncating the excess
+ if (rem(n,2) == 0)
+ b = ifft([grid ; grid(grid_n:-1:2)]);
+ mid = (n+1)/2;
+ b = real ([ b([end-floor(mid)+1:end]) ; b(1:ceil(mid)) ]);
+ else
+ ## Add zeros to interpolate by 2, then pick the odd values below.
+ b = ifft([grid ; zeros(grid_n*2,1) ;grid(grid_n:-1:2)]);
+ b = 2 * real([ b([end-n+1:2:end]) ; b(2:2:(n+1))]);
+ endif
+ ## Multiplication in the time domain is convolution in frequency,
+ ## so multiply by our window now to smooth the frequency response.
+ if rows(window) > 1
+ b = b .* window;
+ else
+ b = b' .* window;
+ endif
+endfunction
+
+%!demo
+%! f=[0, 0.3, 0.3, 0.6, 0.6, 1]; m=[0, 0, 1, 1/2, 0, 0];
+%! [h, w] = freqz(fir2(100,f,m));
+%! subplot(121);
+%! plot(f,m,';target response;',w/pi,abs(h),';filter response;');
+%! subplot(122);
+%! plot(f,20*log10(m+1e-5),';target response (dB);',...
+%! w/pi,20*log10(abs(h)),';filter response (dB);');
+
+%!demo
+%! f=[0, 0.3, 0.3, 0.6, 0.6, 1]; m=[0, 0, 1, 1/2, 0, 0];
+%! plot(f,20*log10(m+1e-5),';target response;');
+%! hold on;
+%! [h, w] = freqz(fir2(50,f,m,512,0));
+%! plot(w/pi,20*log10(abs(h)),';filter response (ramp=0);');
+%! [h, w] = freqz(fir2(50,f,m,512,25.6));
+%! plot(w/pi,20*log10(abs(h)),';filter response (ramp=pi/20 rad);');
+%! [h, w] = freqz(fir2(50,f,m,512,51.2));
+%! plot(w/pi,20*log10(abs(h)),';filter response (ramp=pi/10 rad);');
+%! hold off;
+
+%!demo
+%! % Classical Jakes spectrum
+%! % X represents the normalized frequency from 0
+%! % to the maximum Doppler frequency
+%! asymptote = 2/3;
+%! X = linspace(0,asymptote-0.0001,200);
+%! Y = (1 - (X./asymptote).^2).^(-1/4);
+%!
+%! % The target frequency response is 0 after the asymptote
+%! X = [X, asymptote, 1];
+%! Y = [Y, 0, 0];
+%!
+%! title('Theoretical/Synthesized CLASS spectrum');
+%! xlabel('Normalized frequency (Fs=2)');
+%! ylabel('Magnitude');
+%!
+%! plot(X,Y,'b;Target spectrum;');
+%! hold on;
+%! [H,F]=freqz(fir2(20, X, Y));
+%! plot(F/pi,abs(H),'c;Synthesized spectrum (n=20);');
+%! [H,F]=freqz(fir2(50, X, Y));
+%! plot(F/pi,abs(H),'r;Synthesized spectrum (n=50);');
+%! [H,F]=freqz(fir2(200, X, Y));
+%! plot(F/pi,abs(H),'g;Synthesized spectrum (n=200);');
+%! hold off;
+%! xlabel(''); ylabel(''); title('');
git://git.creatis.insa-lyon.fr / CreaPhase.git / blobdiff