R/triang.R

In signal: Signal Processing

## 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:  w = triang (n)
##
## Returns the filter coefficients of a triangular window of length n.
## Unlike the bartlett window, triang does not go to zero at the edges
## of the window.  For odd n, triang(n) is equal to bartlett(n+2) except
## for the zeros at the edges of the window.

## 2001-04-07  Paul Kienzle
## * return column vector like other window functions.
## 2002-04-22  Paul Kienzle
## * peak value of 1 at 0 for even n

triang <- function(n)  {

  if (length(n) != 1 || n != trunc(n) || n < 1)
    stop("triang(n): n has to be an integer > 0")
  1 - abs(seq(-(n-1), (n-1), by = 2) / (n + n %% 2))
} 

#!error triang
#!error triang(1,2)
#!error triang([1,2])
#!assert (triang(1), 1)
#!assert (triang(2), [1; 1]/2)
#!assert (triang(3), [1; 2; 1]/2)
#!assert (triang(4), [1; 3; 3; 1]/4)
#!test
#! x = bartlett(5)
#! assert (triang(3), x(2:4))

#!demo
#! subplot(221); axis([-1, 1, 0, 1.3]); grid("on")
#! title("comparison with continuous for odd n")
#! n=7; k=(n-1)/2; t=[-k:0.1:k]/(k+1)
#! plot(t,1-abs(t),";continuous;",[-k:k]/(k+1),triang(n),"g*;discrete;")
#!
#! subplot(222); axis([-1, 1, 0, 1.3]); grid("on")
#! n=8; k=(n-1)/2; t=[-k:0.1:k]/(k+1/2)
#! title("note the higher peak for even n")
#! plot(t,1+1/n-abs(t),";continuous;",[-k:k]/(k+1/2),triang(n),"g*;discrete;")
#!
#! subplot(223); axis; grid("off")
#! title("n odd, triang(n)==bartlett(n+2)")
#! n=7
#! plot(0:n+1,bartlett(n+2),"g-*;bartlett;",triang(n),"r-+;triang;")
#!
#! subplot(224); axis; grid("off")
#! title("n even, triang(n)!=bartlett(n+2)")
#! n=8
#! plot(0:n+1,bartlett(n+2),"g-*;bartlett;",triang(n),"r-+;triang;")
#!
#! oneplot; title("")