/usr/share/octave/packages/signal-1.3.0/dst.m is in octave-signal 1.3.0-1.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 | ## Author: Paul Kienzle <pkienzle@users.sf.net> (2006)
## This program is granted to the public domain.
## -*- texinfo -*-
## @deftypefn {Function File} {@var{y} =} dst (@var{x})
## @deftypefnx {Function File} {@var{y} =} dst (@var{x}, @var{n})
## Computes the type I discrete sine transform of @var{x}. If @var{n} is given,
## then @var{x} is padded or trimmed to length @var{n} before computing the transform.
## If @var{x} is a matrix, compute the transform along the columns of the
## the matrix.
##
## The discrete sine transform X of x can be defined as follows:
##
## @verbatim
## N
## X[k] = sum x[n] sin (pi n k / (N+1) ), k = 1, ..., N
## n=1
## @end verbatim
##
## @seealso{idst}
## @end deftypefn
function y = dst (x, n)
if (nargin < 1 || nargin > 2)
print_usage;
endif
transpose = (rows (x) == 1);
if transpose, x = x (:); endif
[nr, nc] = size (x);
if nargin == 1
n = nr;
elseif n > nr
x = [ x ; zeros(n-nr,nc) ];
elseif n < nr
x (nr-n+1 : n, :) = [];
endif
y = fft ([ zeros(1,nc); x ; zeros(1,nc); -flipud(x) ])/-2j;
y = y(2:nr+1,:);
if isreal(x), y = real (y); endif
## Compare directly against the slow transform
## y2 = x;
## w = pi*[1:n]'/(n+1);
## for k = 1:n, y2(k) = sum(x(:).*sin(k*w)); endfor
## y = [y,y2];
if transpose, y = y.'; endif
endfunction
%!test
%! x = log(linspace(0.1,1,32));
%! y = dst(x);
%! assert(y(3), sum(x.*sin(3*pi*[1:32]/33)), 100*eps)
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