|
Functions |
| MArrayN< double > | filter (MArray< double > &, MArray< double > &, MArrayN< double > &, int dim) |
| MArrayN< Complex > | filter (MArray< Complex > &, MArray< Complex > &, MArrayN< Complex > &, int dim) |
| MArrayN< float > | filter (MArray< float > &, MArray< float > &, MArrayN< float > &, int dim) |
| MArrayN< FloatComplex > | filter (MArray< FloatComplex > &, MArray< FloatComplex > &, MArrayN< FloatComplex > &, int dim) |
| template<class T > |
| MArrayN< T > | filter (MArray< T > &b, MArray< T > &a, MArrayN< T > &x, MArrayN< T > &si, int dim=0) |
| MArrayN< double > | filter (MArray< double > &, MArray< double > &, MArrayN< double > &, MArrayN< double > &, int dim) |
| MArrayN< Complex > | filter (MArray< Complex > &, MArray< Complex > &, MArrayN< Complex > &, MArrayN< Complex > &, int dim) |
| MArrayN< float > | filter (MArray< float > &, MArray< float > &, MArrayN< float > &, MArrayN< float > &, int dim) |
| MArrayN< FloatComplex > | filter (MArray< FloatComplex > &, MArray< FloatComplex > &, MArrayN< FloatComplex > &, MArrayN< FloatComplex > &, int dim) |
| template<class T > |
| MArrayN< T > | filter (MArray< T > &b, MArray< T > &a, MArrayN< T > &x, int dim=-1) |
| | DEFUN_DLD (filter, args, nargout,"-*- texinfo -*-\n\
@deftypefn {Loadable Function} {y =} filter (@var{b}, @var{a}, @var{x})\n\
@deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si})\n\
@deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, [], @var{dim})\n\
@deftypefnx {Loadable Function} {[@var{y}, @var{sf}] =} filter (@var{b}, @var{a}, @var{x}, @var{si}, @var{dim})\n\
Return the solution to the following linear, time-invariant difference\n\
equation:\n\
@iftex\n\
@tex\n\
$$\n\
\\sum_{k=0}^N a_{k+1} y_{n-k} = \\sum_{k=0}^M b_{k+1} x_{n-k}, \\qquad\n\
1 \\le n \\le P\n\
$$\n\
@end tex\n\
@end iftex\n\
@ifnottex\n\
\n\
@c Set example in small font to prevent overfull line\n\
@smallexample\n\
N M\n\
SUM a(k+1) y(n-k) = SUM b(k+1) x(n-k) for 1<=n<=length(x)\n\
k=0 k=0\n\
@end smallexample\n\
@end ifnottex\n\
\n\
@noindent\n\
where\n\
@ifnottex\n\
N=length(a)-1 and M=length(b)-1.\n\
@end ifnottex\n\
@iftex\n\
@tex\n\
$a \\in \\Re^{N-1}$, $b \\in \\Re^{M-1}$, and $x \\in \\Re^P$.\n\
@end tex\n\
@end iftex\n\
over the first non-singleton dimension of @var{x} or over @var{dim} if\n\
supplied. An equivalent form of this equation is:\n\
@iftex\n\
@tex\n\
$$\n\
y_n = -\\sum_{k=1}^N c_{k+1} y_{n-k} + \\sum_{k=0}^M d_{k+1} x_{n-k}, \\qquad\n\
1 \\le n \\le P\n\
$$\n\
@end tex\n\
@end iftex\n\
@ifnottex\n\
\n\
@c Set example in small font to prevent overfull line\n\
@smallexample\n\
N M\n\
y(n) = - SUM c(k+1) y(n-k) + SUM d(k+1) x(n-k) for 1<=n<=length(x)\n\
k=1 k=0\n\
@end smallexample\n\
@end ifnottex\n\
\n\
@noindent\n\
where\n\
@ifnottex\n\
c = a/a(1) and d = b/a(1).\n\
@end ifnottex\n\
@iftex\n\
@tex\n\
$c = a/a_1$ and $d = b/a_1$.\n\
@end tex\n\
@end iftex\n\
\n\
If the fourth argument @var{si} is provided, it is taken as the\n\
initial state of the system and the final state is returned as\n\
@var{sf}. The state vector is a column vector whose length is\n\
equal to the length of the longest coefficient vector minus one.\n\
If @var{si} is not supplied, the initial state vector is set to all\n\
zeros.\n\
\n\
In terms of the z-transform, y is the result of passing the discrete-\n\
time signal x through a system characterized by the following rational\n\
system function:\n\
@iftex\n\
@tex\n\
$$\n\
H(z) = {\\displaystyle\\sum_{k=0}^M d_{k+1} z^{-k}\n\
\\over 1 + \\displaystyle\\sum_{k+1}^N c_{k+1} z^{-k}}\n\
$$\n\
@end tex\n\
@end iftex\n\
@ifnottex\n\
\n\
@example\n\
@group\n\
M\n\
SUM d(k+1) z^(-k)\n\
k=0\n\
H(z) = ----------------------\n\
N\n\
1 + SUM c(k+1) z^(-k)\n\
k=1\n\
@end group\n\
@end example\n\
@end ifnottex\n\
@end deftypefn") |
