octave-signal 1.3.2-5 / usr / share / octave / packages / signal-1.3.2 / fir2.m

## 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/>.

## -*- texinfo -*-
## @deftypefn  {Function File} {@var{b} =} fir2 (@var{n}, @var{f}, @var{m})
## @deftypefnx {Function File} {@var{b} =} fir2 (@var{n}, @var{f}, @var{m}, @var{grid_n})
## @deftypefnx {Function File} {@var{b} =} fir2 (@var{n}, @var{f}, @var{m}, @var{grid_n}, @var{ramp_n})
## @deftypefnx {Function File} {@var{b} =} fir2 (@var{n}, @var{f}, @var{m}, @var{grid_n}, @var{ramp_n}, @var{window})
##
## Produce an order @var{n} FIR filter with arbitrary frequency response
## @var{m} over frequency bands @var{f}, returning the @var{n}+1 filter
## coefficients in @var{b}.  The vector @var{f} specifies the frequency band
## edges of the filter response and @var{m} specifies the magnitude response
## at each frequency.
##
## The vector @var{f} must be nondecreasing over the range [0,1], and the
## first and last elements must be 0 and 1, respectively.  A discontinuous
## jump in the frequency response can be specified by duplicating a band edge
## in @var{f} with different values in @var{m}.
##
## The resolution over which the frequency response is evaluated can be
## controlled with the @var{grid_n} argument.  The default is 512 or the
## next larger power of 2 greater than the filter length.
##
## The band transition width for discontinuities can be controlled with the
## @var{ramp_n} argument.  The default is @var{grid_n}/25.  Larger values
## will result in wider band transitions but better stopband rejection.
##
## An optional shaping @var{window} can be given as a vector with length
## @var{n}+1.  If not specified, a Hamming window of length @var{n}+1 is used.
##
## To apply the filter, use the return vector @var{b} with the @code{filter}
## function, for example @code{y = filter (b, 1, x)}.
##
## Example:
## @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;");
## @end example
## @seealso{filter, fir1}
## @end deftypefn

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)
    error ("fir2: frequency must be nondecreasing starting from 0 and ending at 1");
  elseif t != length(m)
    error ("fir2: frequency and magnitude vectors must be the same length");
  ## find the grid spacing and ramp width
  elseif (nargin>4 && length(grid_n)>1) || ...
         (nargin>5 && (length(grid_n)>1 || length(ramp_n)>1))
    error ("fir2: grid_n and ramp_n must be integers");
  endif
  if nargin < 4, grid_n=[]; endif
  if nargin < 5, ramp_n=[]; endif

  ## find the window parameter, or default to hamming
  w=[];
  if length(grid_n)>1, w=grid_n; grid_n=[]; endif
  if length(ramp_n)>1, w=ramp_n; ramp_n=[]; 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, error ("fir2: window must be of length n+1"); endif

  ## Default grid size is 512... unless n+1 >= 1024
  if isempty (grid_n)
    if n+1 < 1024
      grid_n = 512;
    else
      grid_n = n+1;
    endif
  endif

  ## ML behavior appears to always round the grid size up to a power of 2
  grid_n = 2 ^ nextpow2 (grid_n);

  ## Error out if the grid size is not big enough for the window
  if 2*grid_n < n+1
    error ("fir2: grid size must be greater than half the filter order");
  endif

  if isempty (ramp_n), ramp_n = fix (grid_n / 25); 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.
  ## Also, for matlab compatibility, we return return values in 1 row
  b = b(:)' .* window(:)';

endfunction

%% Test that the grid size is rounded up to the next power of 2
%!xtest
%! f = [0 0.6 0.6 1]; m = [1 1 0 0];
%! b9  = fir2 (30, f, m, 9);
%! b16 = fir2 (30, f, m, 16);
%! b17 = fir2 (30, f, m, 17);
%! b32 = fir2 (30, f, m, 32);
%! assert ( isequal (b9,  b16))
%! assert ( isequal (b17, b32))
%! assert (~isequal (b16, b17))

%% Test expected magnitudes of passbands, stopbands, and cutoff frequencies
%!test
%! f = [0, 0.7, 0.7, 1]; m = [0, 0, 1, 1];
%! b = fir2 (50, f, m);
%! h = abs (freqz (b, 1, [0, 0.7, 1], 2));
%! assert (h(1) <= 3e-3)
%! assert (h(2) <= 1/sqrt (2))
%! assert (h(3), 1, 2e-3)

%!test
%! f = [0, 0.25, 0.25, 0.75, 0.75, 1]; m = [0, 0, 1, 1, 0, 0];
%! b = fir2 (50, f, m);
%! h = abs (freqz (b, 1, [0, 0.25, 0.5, 0.75, 1], 2));
%! assert (h(1) <= 3e-3)
%! assert (h(2) <= 1/sqrt (2))
%! assert (h(3), 1, 2e-3)
%! assert (h(4) <= 1/sqrt (2))
%! assert (h(5) <= 3e-3)

%!test
%! f = [0, 0.45, 0.45, 0.55, 0.55, 1]; m = [1, 1, 0, 0, 1, 1];
%! b = fir2 (50, f, m);
%! h = abs (freqz (b, 1, [0, 0.45, 0.5, 0.55, 1], 2));
%! assert (h(1), 1, 2e-3)
%! assert (h(2) <= 1/sqrt (2))
%! assert (h(3) <= 1e-1)
%! assert (h(4) <= 1/sqrt (2))
%! assert (h(5), 1, 2e-3)

%!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];
%!
%! 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;
%! title('Theoretical/Synthesized CLASS spectrum');
%! xlabel('Normalized frequency (Fs=2)');
%! ylabel('Magnitude');