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