## Copyright (C) 1999 Paul Kienzle
##
## 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., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA

## usage: [x, t] = impz(b [, a, n, fs])
##
## Generate impulse-response characteristics of the filter. The filter
## coefficients correspond to the the z-plane rational function with
## numerator b and denominator a.  If a is not specified, it defaults to
## 1. If n is not specified, or specified as [], it will be chosen such
## that the signal has a chance to die down to -120dB, or to not explode
## beyond 120dB, or to show five periods if there is no significant
## damping. If no return arguments are requested, plot the results.
##
## See also: freqz, zplane

## 1999 pkienzle@kienzle.powernet.co.uk
##      - if nargout=0, produce plot and don't set return values

## TODO: Call equivalent function from control toolbox since it is
## TODO:    probably more sophisticated than this one, and since it
## TODO:    is silly to maintain two different versions of essentially
## TODO:    the same thing.
function [x_r, t_r] = impz(b, a, n, fs)

  if nargin == 0 || nargin > 4
    usage("impz(b [, a, n, fs])");
  end
  if nargin < 2, a = [1]; end
  if nargin < 3, n = []; end
  if nargin < 4, fs = 1; end

  if isempty(n) && length(a) > 1
    precision = 1e-6;
    r = roots(a);
    maxpole = max(abs(r));
    if (maxpole > 1+precision)     # unstable -- cutoff at 120 dB
      n = floor(6/log10(maxpole));
    elseif (maxpole < 1-precision) # stable -- cutoff at -120 dB
      n = floor(-6/log10(maxpole));
    else                        # periodic -- cutoff after 5 cycles
      n = 30;
      
				# find longest period less than infinity
				# cutoff after 5 cycles (w=10*pi)
      rperiodic = r(find(abs(r)>=1-precision & abs(arg(r))>0));
      if !isempty(rperiodic)
	n_periodic = ceil(10*pi./min(abs(arg(rperiodic))));
	if (n_periodic > n)
	  n = n_periodic;
	end
      end
      
				# find most damped pole
				# cutoff at -60 dB
      rdamped = r(find(abs(r)<1-precision));
      if !isempty(rdamped)
	n_damped = floor(-3/log10(max(abs(rdamped))));
	if (n_damped > n)
	  n = n_damped;
	end
      end
    end
    n = n + length(b);
  elseif isempty(n)
    n = length(b);
  end

  if length(a) == 1
    x = fftfilt(b/a, [1, zeros(1,n-1)]);
  else
    x = filter(b, a, [1, zeros(1,n-1)]);
  end
  t = [0:n-1]/fs;

  if nargout >= 1 x_r = x; end;
  if nargout >= 2 t_r = t; end;
  if nargout == 0
    unwind_protect
      title "Impulse Response";
      if (fs > 1000)
      	t = t * 1000;
      	xlabel("Time (msec)");
      else
      	xlabel("Time (sec)");
      end
      plot(t, x, "^r;;");
    unwind_protect_cleanup
      title ("")
      xlabel ("")
    end_unwind_protect
  end

endfunction