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Initial checkin for AIM92 aimR8.2 (last updated May 1997).
author tomwalters
date Fri, 20 May 2011 15:19:45 +0100
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1 .TH RACF 1 "1 September 1993"
2
3 .SH NAME
4 racf \- recursive autocorrelation function of contiguous frames.
5
6 .SH SYNTAX
7 racf [arguments] [file]
8
9 .SH DESCRIPTION
10 Autocorrelation function using a recursive "leaky integrator" filter.
11 For the m'th lag, the n'th recursive update is:
12
13 .nf
14 y[n] = a.y[n-1] + (1-a).f[n].f[n-m]
15 .fi
16
17 where decay constant a = exp(-Ts/T),
18 Ts is the sample interval in seconds, and T is the decay time constant in seconds.
19
20 The recursion computes the mean value of the product f[n].f[n-m]
21 within an exponential window which weights past values.
22 The window width parameter (eg. corresponding with the width of the
23 fft analysis window) is the time constant parameter.
24 The half life of the exponential window is given by -T.ln(0.5) = 0.693T
25 ie. for a given time constant, T secs, the window decays to half of its
26 current value in a period of 0.693T secs.
27 Similarly, the window decays by 99% of its initial value in about 4.6T secs.
28 So T can be set to accomodate an expected period.
29
30 The routine generates the autocovariance function.
31 An optional normalization (dividing each coefficient by the zeroth
32 coefficient) produces the autocorrelation function,
33 (and this is then scaled up to the range [0-1000]).
34
35 The output framewidth is the given maximum acf lag.
36
37 .SH "SEE ALSO"
38 options acf acgram
39
40 .SH COPYRIGHT
41 .LP
42 Copyright (c) Applied Psychology Unit, Medical Research Council, 1995
43 .LP
44 Permission to use, copy, modify, and distribute this software without fee
45 is hereby granted for research purposes, provided that this copyright
46 notice appears in all copies and in all supporting documentation, and that
47 the software is not redistributed for any fee (except for a nominal
48 shipping charge). Anyone wanting to incorporate all or part of this
49 software in a commercial product must obtain a license from the Medical
50 Research Council.
51 .LP
52 The MRC makes no representations about the suitability of this
53 software for any purpose. It is provided "as is" without express or
54 implied warranty.
55 .LP
56 THE MRC DISCLAIMS ALL WARRANTIES WITH REGARD TO THIS SOFTWARE, INCLUDING
57 ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS, IN NO EVENT SHALL
58 THE A.P.U. BE LIABLE FOR ANY SPECIAL, INDIRECT OR CONSEQUENTIAL DAMAGES
59 OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS,
60 WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION,
61 ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
62 SOFTWARE.
63