tomwalters@0: .TH FILT1 1 "1 September 1993"
tomwalters@0: 
tomwalters@0: .SH NAME
tomwalters@0: filt1 \- 1st order LP filter using an exponential smoother.
tomwalters@0: 
tomwalters@0: .SH SYNTAX 
tomwalters@0: filt1 [options] [file]
tomwalters@0: 
tomwalters@0: .SH DESCRIPTION
tomwalters@0: A recursive "leaky integrator" 1st order low-pass filter which is a shifting
tomwalters@0: exponential window which decays into the past values.
tomwalters@0: 
tomwalters@0: .SH OPTIONS
tomwalters@0: 
tomwalters@0: 1. tc
tomwalters@0: 
tomwalters@0: The time-constant parameter which controls the rate of decay and so the
tomwalters@0: size of the exponential window. For a given time constant of T seconds:
tomwalters@0: 
tomwalters@0: .nf
tomwalters@0: 	0.7T secs   is the window half--life.
tomwalters@0: 	4.6T secs   is 99% of the window's life.
tomwalters@0: .fi
tomwalters@0: 
tomwalters@0: When the time-constant parameter is given with time units (s or ms) then
tomwalters@0: it is converted to a decay constant using  a = exp(-Ts/T),
tomwalters@0: where Ts is the sample interval in seconds from the given `samplerate' option,
tomwalters@0: and T  is decay time-constant in seconds.
tomwalters@0: Otherwise the time-constant parameter is taken to be the decay constant directly.
tomwalters@0: 
tomwalters@0: With decay constant a=1 there is infinite memory because it does not decay.
tomwalters@0: With 0 < a < 1 there is a finite decaying memory.
tomwalters@0: The smaller `a', the smaller the memory (it decays faster).
tomwalters@0: With a = 0 the filter output is identical with its input.
tomwalters@0: 
tomwalters@0: 2. de
tomwalters@0: 
tomwalters@0: Two optional difference equations are provided which repsectively compute
tomwalters@0: a recursive sum (when "de=sum") and mean (when "de=mean").
tomwalters@0: The n'th recursive update is respectively:
tomwalters@0: 
tomwalters@0: .nf
tomwalters@0: 	y[n] = a.y[n-1] + x[n]                recursive sum
tomwalters@0: 	y[n] = a.y[n-1] + (1-a).x[n]          recursive mean
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 decay time-constant in seconds.
tomwalters@0: 
tomwalters@0: .SH "SEE ALSO"
tomwalters@0: options smooth
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: