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Initial checkin for AIM92 aimR8.2 (last updated May 1997).
author | tomwalters |
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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 |