compand

% -*- texinfo -*-
% @deftypefn {Function File} {@var{y} = } compand (@var{x}, @var{mu}, @var{V}, 'mu/compressor')
% @deftypefnx {Function File} {@var{y} = } compand (@var{x}, @var{mu}, @var{V}, 'mu/expander')
% @deftypefnx {Function File} {@var{y} = } compand (@var{x}, @var{mu}, @var{V}, 'A/compressor')
% @deftypefnx {Function File} {@var{y} = } compand (@var{x}, @var{mu}, @var{V}, 'A/expander')
%
% Compresses and expanding the dynamic range of a signal using a mu-law or
% or A-law algorithm.
%
% The mu-law compressor/expander for reducing the dynamic range, is used
% if the fourth argument of @dfn{compand} starts with 'mu/'. Whereas the
% A-law compressor/expander is used if @dfn{compand} starts with 'A/'.
% The mu-law algorithm uses the formulation
%
% @iftex
% @tex
% $$
% y = {V log (1 + \\mu / V \\|x\\|) \\over log (1 + \\mu)} sgn(x)
% $$
% @end tex
% @end iftex
% @ifinfo
% @example
%
%         V log (1 + \mu/V |x|)
%     y = -------------------- sgn(x)
%             log (1 + \mu)
%
% @end example
% @end ifinfo
%
% while the A-law algorithm used the formulation
%
% @iftex
% @tex
% $$
% y = { \\left\{  \\matrix{ {A / (1 + log A) x}, & 0 <= \\|x\\| <= V/A \\cr
%                  & \\cr  
%                  {V log (1 + log(A/V \\|x\\|) ) \\over 1 + logA}, &
%                  V/A < \\|x\\| <= V} \\right. }
% $$
% @end tex
% @end iftex
% @ifinfo
% @example
%
%         /    A / (1 + log A) x,               0 <= |x| <= V/A  
%         | 
%     y = <    V ( 1 + log (A/V |x|) )
%         |    ----------------------- sgn(x),  V/A < |x| <= V
%         \        1 + log A
% @end example
% @end ifinfo
%
% Neither converts from or to audio file ulaw format. Use mu2lin or lin2mu
% instead.
%
% @end deftypefn
% @seealso{m2ulin, lin2mu}