2022-08-28__Centred_STAs.jl

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# # 2022-08-28 • Centred STAs

# Center spike-triggered windows around 0 (mV) before averaging them.

# ..
#
# This is useless (in terms of increasing 'SNR' of the STA):
#
# If the current STA is this [1]:
#
# $$
# STA_{cur} = \frac{1}{N} \sum_s V[s:s+W]
# $$
#
# (where $s$ is the presynaptic spiketime, $N$ the number of such spikes, $W$ the window length, and $V$ the voltage / VI signal),
#
# then the new STA would be:
#
# $$
# STA_{new} = \frac{1}{N} \sum_s \left( V[s:s+W] - V[s] \right)
# $$
#
# In other words:
#
# $$
# STA_{new} = STA_{cur} - \frac{1}{N} \sum_s V[s] \\
#           = STA_{cur} - STA_{cur}[1]
# $$
#
# i.e. the STA waveforms would be the same as the current ones, just shifted vertically by some value (namely the average voltage at the start of the window; or, if we had rather chosen $\texttt{mean}(V[s:s+W])$ as referencing value instead of $V[s]$: the average voltage of all windows).
#
# ---
#
# [1]
# Note that this notation is more programm-y than mathy, with the $[…:…]$ slicing notation. In usual math notation we'd express it per timepoint: $STA[t] = \frac{1}{N} \sum_s V[s+t]$, with $t = 0, 1, …, W$.
#
# ---
#
# This idea would thus have no effect on connection detectability using the peak-to-peak measure (it would stay the same).
#
# Neither would it have an effect on the 'exc or inh' test, as that one already uses the $STA[1]$ as reference value.