Nothing

```
## Copyright (C) 2002 Andras Carezia
##
## 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: chebwin (n, at)
##
## Returns the filter coefficients of the n-point Dolph-Chebyshev window
## with at dB of attenuation in the stop-band of the corresponding
## Fourier transform.
##
## For the definition of the Chebyshev window, see
##
## * Peter Lynch, "The Dolph-Chebyshev Window: A Simple Optimal Filter",
## Monthly Weather Review, Vol. 125, pp. 655-660, April 1997.
## (http://www.maths.tcd.ie/~plynch/Publications/Dolph.pdf)
##
## * C. Dolph, "A current distribution for broadside arrays which
## optimizes the relationship between beam width and side-lobe level",
## Proc. IEEE, 34, pp. 335-348.
##
## The window is described in frequency domain by the expression:
##
## Cheb(n-1, beta * cos(pi * k/n))
## W(k) = -------------------------------
## Cheb(n-1, beta)
##
## with
##
## beta = cosh(1/(n-1) * acosh(10^(at/20))
##
## and Cheb(m,x) denoting the m-th order Chebyshev polynomial calculated
## at the point x.
##
## Note that the denominator in W(k) above is not computed, and after
## the inverse Fourier transform the window is scaled by making its
## maximum value unitary.
##
## See also: kaiser
## $Id: chebwin.m,v 1.4 2005/12/29 03:54:39 pkienzle Exp $
##
## Author: Andras Carezia <acarezia@uol.com.br>
## Description: Coefficients of the Dolph-Chebyshev window
chebwin <- function(n, at) {
if (!(length(n) == 1 && (n == round(n)) && (n > 0)))
stop("n has to be a positive integer")
if (!(length(at) == 1 && (at == Re(at))))
stop("at has to be a real scalar")
if (n == 1)
w <- 1
else {
# beta calculation
gamma <- 10^(-at/20)
beta <- cosh(1/(n-1) * acosh(1/gamma))
# freq. scale
k <- 0:(n-1)
x <- beta*cos(pi*k/n)
# Chebyshev window (freq. domain)
p <- cheb(n-1, x)
# inverse Fourier transform
if (n %% 2) {
w <- Re(fft(p))
M <- (n+1)/2
w <- w[1:M] / w[1]
w <- c(w[M:2], w)
} else {
# half-sample delay (even order)
p <- p * exp(1i*pi/n * (0:(n-1)))
w <- Re(fft(p))
M <- n / 2 + 1
w <- w/w[2]
w <- c(w[M:2], w[2:M])
}
}
w
}
## Copyright (C) 2002 Andras Carezia
##
## 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: cheb (n, x)
##
## Returns the value of the nth-order Chebyshev polynomial calculated at
## the point x. The Chebyshev polynomials are defined by the equations:
##
## / cos(n acos(x), |x| <= 1
## Tn(x) = |
## \ cosh(n acosh(x), |x| > 1
##
## If x is a vector, the output is a vector of the same size, where each
## element is calculated as y(i) = Tn(x(i)).
## Author: Andras Carezia <acarezia@uol.com.br>
## Description: Value of the Chebyshev polynomials
cheb <- function(n, x) {
if (!(is.numeric(n) && (n == round(n)) && (n >= 0)))
stop("n has to be a positive integer")
T <- numeric(length(x))
ind <- x <= 1
if (any(ind))
T[ind] <- cos(n * acos(as.complex(x[ind])))
ind <- x > 1
myacosh <- function(x) log(x + sqrt(x^2 - 1)) # workaround for a win32 bug in acosh
if (any(ind))
T[ind] <- cosh(n * myacosh(as.complex(x[ind])))
Re(T)
}
```

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