reverse_correlation_mv_stepfunc
REVERSE_CORRELATION_MV_STEPFUNC - Performs RC between a continuously valued signal and step function stimulus
[REV_CORR, REV_CORR_RAW, XC_STIMSIGNAL, XC_STIMSTIM] = ...
REVERSE_CORRELATION_MV_STEPFUNC(SIGNAL, SIGNAL_T, STIM_OFFSETS, STIMTIMES, STIM)
This function performs reverse correlation between a signal SIGNAL and a stimulus
STIM to obtain the best linear filter (FIR Wiener filter) that can be used to reconstruct
SIGNAL from the STIM. It achieves this by computing:
REV_CORR_RAW = Rinv * XC_STIMSIGNAL, where XC_STIMSIGNAL is the correlation between
the SIGNAL and STIM, and Rinv is the inverse of the covariance matrix R of the stimulus.
This matrix R is computed from the autocorrelation of the stimulus XC_STIMSTIM.
Further, this function offers the ability to return a filtered version of REV_CORR_RAW, which is often
necessary when the stimulus STIM is not purely white.
Inputs:
SIGNAL is the signal to be related to the stimulus
SIGNAL_T is the time of each sample in SIGNAL
STIM_OFFSETS is a list of times of SIGNAL relative to STIM over which
to compute the correlation.
The stimulus is assumed to be a step function that assumes different
values at each step. STIMTIMES is a list of the time of each step,
and STIM is a matrix of row vectors, where each column corresponds to
one stimulus variable.
In calculating the autocorrelation of the stimulus, it is assumed that each
column vector of the stimulus has the same statistics.
Outputs:
REV_CORR is the filtered reverse correlation kernel for each time lag (rows) and
each spatial component the kernel (columns).
REV_CORR is filtered according to the parameters below (typically a median filter)
in order to aid in removing the influence of a non-white stimulus.
REV_CORR has units of units('SIGNAL') / (units('STIM') * units('dt') * units('dx'))
REV_CORR_RAW is the unfiltered reverse correlation for each lag (rows) and
each spatial component of the kernel (columns).
REV_CORR_RAW has units of units('SIGNAL') / (units('STIM') * units('dt') * units('dx'))
XC_STIMSIGNAL is the correlation between SIGNAL and the STIM. Lags are in rows and
spatial components are in columns. XC_STIMSIGNAL has units of units('SIGNAL') * units('STIM')
XC_STIMSTIM is the autocorrelation of the STIM for different lags. It has units of
units('STIM')^2
Note: IF you have a theoretically-determined autocorrelation function for your stimulus,
it is highly recommended that you pass it to REVERSE_CORRELATION_MV_STEPFUNC as a
name/value pair ('xc_stimstim', myxc). This will reduce the likelihood of an unstable/garbage
solution.
See Dayan and Abbott (2005), Chapters 1-2, and any source on FIR Optimal Filtering / FIR Wiener Filtering
This function also accepts extra parameter inputs in the form of PARAMETER/VALUE
pairs that modify default behavior:
Parameter (default) | Description
----------------------------------------------------------------------------------
DoMedFilter (1) | Perform a median filter on the output to deal with
| noise due to non-white stimulus
MedFilterWidth (3) | Width of the median filter
xc_stimstim ([]) | If empty, then xc_stimstim is computed empircally from
| the stimulus. Otherwise, the xc_stimstim can be specified,
| which might be useful if the theoretical shape of the
| stimulus autocorrelation is known. xc_stimstim(1) should be
| the autocorrelation with 0 lag, xc_stimstim(2) should be the
| autocorrelation with lag 1, etc.
Rinv ([]) | The 'whitening function', determined by inverting the
| autocorrelation function. If empty, then it is calculated
| from xc_stimstim.
normalize (1) | Perform normalization of the kernel by dx and dt
normalize_xc_stimsignal (0)| Perform normalization of xc_stimsignal by dx and dt
dx (1) | Resolution of kernel in columns
dt (1) | Resolution of kernel in time
See also: STEPFUNC, DIRRFMODEL_EXAMPLE2, FIRWIENER