tomwalters@0: .TH RACF 1 "1 September 1993"
tomwalters@0: 
tomwalters@0: .SH NAME
tomwalters@0: racf \- recursive autocorrelation function of contiguous frames.
tomwalters@0: 
tomwalters@0: .SH SYNTAX 
tomwalters@0: racf  [arguments]  [file]
tomwalters@0: 
tomwalters@0: .SH DESCRIPTION
tomwalters@0: Autocorrelation function using a recursive "leaky integrator" filter.
tomwalters@0: For the m'th lag, the n'th recursive update is:
tomwalters@0: 
tomwalters@0: .nf
tomwalters@0:       y[n] = a.y[n-1] + (1-a).f[n].f[n-m]
tomwalters@0: .fi
tomwalters@0: 
tomwalters@0: where decay constant a = exp(-Ts/T),
tomwalters@0: Ts is the sample interval in seconds, and T  is the decay time constant in seconds.
tomwalters@0: 
tomwalters@0: The recursion computes the mean value of the product f[n].f[n-m]
tomwalters@0: within an exponential window which weights past values.
tomwalters@0: The window width parameter (eg. corresponding with the width of the
tomwalters@0: fft analysis window) is the time constant parameter.
tomwalters@0: The half life of the exponential window is given by -T.ln(0.5) = 0.693T
tomwalters@0: ie. for a given time constant, T secs, the window decays to half of its
tomwalters@0: current value in a period of 0.693T secs.
tomwalters@0: Similarly, the window decays by 99% of its initial value in about 4.6T secs.
tomwalters@0: So T can be set to accomodate an expected period.
tomwalters@0: 
tomwalters@0: The routine generates the autocovariance function.
tomwalters@0: An optional normalization (dividing each coefficient by the zeroth
tomwalters@0: coefficient) produces the autocorrelation function,
tomwalters@0: (and this is then scaled up to the range [0-1000]).
tomwalters@0: 
tomwalters@0: The output framewidth is the given maximum acf lag.
tomwalters@0: 
tomwalters@0: .SH "SEE ALSO"
tomwalters@0: options acf acgram
tomwalters@0: 
tomwalters@0: .SH COPYRIGHT
tomwalters@0: .LP
tomwalters@0: Copyright (c) Applied Psychology Unit, Medical Research Council, 1995
tomwalters@0: .LP
tomwalters@0: Permission to use, copy, modify, and distribute this software without fee 
tomwalters@0: is hereby granted for research purposes, provided that this copyright 
tomwalters@0: notice appears in all copies and in all supporting documentation, and that 
tomwalters@0: the software is not redistributed for any fee (except for a nominal 
tomwalters@0: shipping charge). Anyone wanting to incorporate all or part of this 
tomwalters@0: software in a commercial product must obtain a license from the Medical 
tomwalters@0: Research Council.
tomwalters@0: .LP
tomwalters@0: The MRC makes no representations about the suitability of this 
tomwalters@0: software for any purpose.  It is provided "as is" without express or 
tomwalters@0: implied warranty.
tomwalters@0: .LP
tomwalters@0: THE MRC DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING 
tomwalters@0: ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL 
tomwalters@0: THE A.P.U. BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES 
tomwalters@0: OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, 
tomwalters@0: WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, 
tomwalters@0: ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS 
tomwalters@0: SOFTWARE.
tomwalters@0: