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Sourcecode: octave-matcompat version File versions

kaiserord.m

## Copyright (C) 2000 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., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

## usage: [n, Wn, beta, ftype] = kaiserord(f, m, dev [, fs])
##
## Returns the parameters needed for fir1 to produce a filter of the
## desired specification from a kaiser window:
##       n: order of the filter (length of filter minus 1)
##       Wn: band edges for use in fir1
##       beta: parameter for kaiser window of length n+1
##       ftype: choose between pass and stop bands
##       b = fir1(n,Wn,kaiser(n+1,beta),ftype,'noscale');
##
## f: frequency bands, given as pairs, with the first half of the
##    first pair assumed to start at 0 and the last half of the last
##    pair assumed to end at 1.  It is important to separate the
##    band edges, since narrow transition regions require large order
##    filters.
## m: magnitude within each band.  Should be non-zero for pass band
##    and zero for stop band.  All passbands must have the same
##    magnitude, or you will get the error that pass and stop bands
##    must be strictly alternating.
## dev: deviation within each band.  Since all bands in the resulting
##    filter have the same deviation, only the minimum deviation is
##    used.  In this version, a single scalar will work just as well.
## fs: sampling rate.  Used to convert the frequency specification into
##    the [0, 1], where 1 corresponds to the Nyquist frequency, fs/2.
##
## The Kaiser window parameters n and beta are computed from the
## relation between ripple (A=-20*log10(dev)) and transition width 
## (dw in radians) discovered empirically by Kaiser:
##
##           / 0.1102(A-8.7)                        A > 50
##    beta = | 0.5842(A-21)^0.4 + 0.07886(A-21)     21 <= A <= 50
##           \ 0.0                                  A < 21
##
##    n = (A-8)/(2.285 dw)
##
## Example
##    [n, w, beta, ftype] = kaiserord([1000,1200], [1,0], [0.05,0.05], 11025);
##    freqz(fir1(n,w,kaiser(n+1,beta),ftype,'noscale'),1,[],11025);

## TODO: order is underestimated for the final test case: 2 stop bands.
## TODO:     octave> ftest("kaiserord") # shows test cases

function [n, w, beta, ftype] = kaiserord(f, m, dev, fs)

  if (nargin<2 || nargin>4)
    usage("[n, w, beta, ftype] = kaiserord(f, m, dev [, fs])");
  endif

  ## default sampling rate parameter
  if nargin<4, fs=2; endif

  ## parameter checking
  if length(f)!=2*length(m)-2 
    error("kaiserord must have one magnitude for each frequency band");
  endif
  if any(m(1:length(m)-2)!=m(3:length(m)))
    error("kaiserord pass and stop bands must be strictly alternating");
  endif
  if length(dev)!=length(m) && length(dev)!=1
    error("kaiserord must have one deviation for each frequency band");
  endif
  dev = min(dev);
  if dev <= 0, error("kaiserord must have dev>0"); endif

  ## use midpoints of the transition region for band edges
  w = (f(1:2:length(f))+f(2:2:length(f)))/fs;

  ## determine ftype
  if length(w) == 1
    if m(1)>m(2), ftype='low'; else ftype='high'; endif
  elseif length(w) == 2
    if m(1)>m(2), ftype='stop'; else ftype='pass'; endif
  else
    if m(1)>m(2), ftype='DC-1'; else ftype='DC-0'; endif
  endif

  ## compute beta from dev
  A = -20*log10(dev);
  if (A > 50)
    beta = 0.1102*(A-8.7);
  elseif (A >= 21)
    beta = 0.5842*(A-21)^0.4 + 0.07886*(A-21);
  else
    beta = 0.0;
  endif

  ## compute n from beta and dev
  dw = 2*pi*min(f(2:2:length(f))-f(1:2:length(f)))/fs;
  n = max(1,ceil((A-8)/(2.285*dw)));

  ## if last band is high, make sure the order of the filter is even.
  if ((m(1)>m(2)) == (rem(length(w),2)==0)) && rem(n,2)==1, n = n+1; endif
endfunction

%!demo
%! Fs = 11025;
%! for i=1:4
%!   if i==1,
%!     subplot(221); bands=; mag=; dev=;
%!   elseif i==2
%!     subplot(222); bands=; mag=; dev=;
%!   elseif i==3
%!     subplot(223); bands=; mag=; dev=0.1;
%!   elseif i==4
%!     subplot(224); bands=100*; 
%!     mag=; dev=0.05;
%!   endif
%!   [n, w, beta, ftype] = kaiserord(bands, mag, dev, Fs);
%!   d=max(1,fix(n/10)); 
%!   if mag(length(mag))==1 && rem(d,2)==1, d=d+1; endif
%!   [h, f] = freqz(fir1(n,w,ftype,kaiser(n+1,beta),'noscale'),1,[],Fs);
%!   hm = freqz(fir1(n-d,w,ftype,kaiser(n-d+1,beta),'noscale'),1,[],Fs);
%!   plot(f,abs(hm),sprintf("r;order %d;",n-d), ...
%!      f,abs(h), sprintf("b;order %d;",n));
%!   b = ; hold on;
%!   for i=2:2:length(b), 
%!     hi=mag(i/2)+dev(1); lo=max(mag(i/2)-dev(1),0);
%!     plot([b(i-1), b(i), b(i), b(i-1), b(i-1)],[hi, hi, lo, lo, hi],"c;;");
%!   endfor; hold off;
%! endfor
%! oneplot();
%! %--------------------------------------------------------------
%! % A filter meets the specifications if its frequency response
%! % passes through the ends of the criteria boxes, and fails if
%! % it passes through the top or the bottom.  The criteria are
%! % met precisely if the frequency response only passes through
%! % the corners of the boxes.  The blue line is the filter order
%! % returned by kaiserord, and the red line is some lower filter
%! % order.  Confirm that the blue filter meets the criteria and
%! % the red line fails.

%!test error("extend demo to show detail at criteria box corners");

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