# Step-by-step calculation of rectangular window

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Paul Hinze 2022 年 7 月 6 日
コメント済み: Paul Hinze 2022 年 7 月 7 日
Dear community!
I would like to make a step-by-step calculation of synaptic input. As you can see in the attached figure, the synaptic input rises only, but my goal is that after the given time constant tau, the synaptic input declines again, with the same value as it were raised.
The goal is:
A single spike should elicit a synaptic input that last for the given time of tau. Thus, the synaptic input should go down and not up.
%% Generate Single synaptic input shape
clear
close
clc
Ninput = 3;
Lrate = 20; % input intensity (lambda) [spikes/sec]
Tleng = 50; % simulated time length [ms]
dt = 0.01; % time step [ms]
% time vector
t = (0:round(Tleng/dt)-1)*dt; % time vector
tv = (0:round(Tleng/dt)-1)*dt; % time vector
% call poisson spike generator
spikes = poisson_train(Ninput, Lrate, Tleng, dt);
spikeall = sum(spikes,1); % total number of spikes at each time step
xalpha = 0;
yalpha = 0;
% creating output vector
g = zeros(1,length(spikeall));
% initial values
x = 0;
y = 0;
% factors used for calculation
Asyn = 3.5;
tau = 1; % ms
aa = Asyn; % amplitude factor for normalizing the input
ee = (dt/tau); % decrease factor used at each time step
% step-by-step calculation
for t = 1:length(spikeall)
y = y + aa*spikeall(t);
x = ee*x + dt*y;
g(t) = x; % store data
end
figure;
set(gcf, 'Position', [100 50 900 600]); % position and size
% plotting model synaptic input
subplot(2,1,1)
plot(tv,spikeall)
title('spikes')
subplot(2,1,2)
plot(tv,g);
title('simulated synaptic input');
xlabel('time [ms]');
##### 2 件のコメント表示非表示 1 件の古いコメント
Paul Hinze 2022 年 7 月 7 日
Function for spike generation:
function spikes = poisson_train(Ninput, Lrate, Tleng, dt)
% - Input:
% Ninput number of inputs (= number of source neurons or number of repetitions)
% Lrate input intensity (lambda) [spikes/sec]
% Tleng simulated time length [ms]
% dt time step [ms]
%
% - Output:
% spikes number of Poissonian spikes at each time step
% length(spikes) = round(Tleng/dt);
%
%% time vector
t = (0:round(Tleng/dt)-1)*dt; % time vector
%% parameters for Poisson process
ldt = Lrate*dt/1000.0; % (lambda) * (delta t) [no unit]
%% main part
% take random variable of length t
rd = rand(Ninput, length(t));
% compare the random variable with the probability to get spikes
spikes = ( rd < ldt ); % output spike vector

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### 採用された回答

Jonas 2022 年 7 月 7 日
i suggest you just add the rectangular window at the specified times given by the spices and the spice amplitude:
fs=10000;
t=0:1/fs:3;
tau=0.25; tauInSamp=tau*fs;
spikeTimes= (randi(t(end)*fs+1,10,1)-1); % generate 10 spikes somewhere in the time, unit is samples
spikeVals = randi(5,10,1);
resultingSpikes=zeros(size(t));
for spikeNr=1:numel(spikeTimes)
if spikeTimes(spikeNr)+tauInSamp-1<=numel(t) % if not near the end of the allowed time frame
resultingSpikes(spikeTimes(spikeNr):spikeTimes(spikeNr)+tauInSamp-1)=resultingSpikes(spikeTimes(spikeNr):spikeTimes(spikeNr)+tauInSamp-1)+spikeVals(spikeNr);
else
resultingSpikes(spikeTimes(spikeNr):end)=resultingSpikes(spikeTimes(spikeNr):end)+spikeVals(spikeNr);
end
end
ax1=subplot(2,1,1);
stem(spikeTimes/fs,spikeVals);
ax2=subplot(2,1,2);
plot(t,resultingSpikes);
##### 2 件のコメント表示非表示 1 件の古いコメント
Paul Hinze 2022 年 7 月 7 日
Thank you Jonas

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### その他の回答 (1 件)

Jonas 2022 年 7 月 7 日
or you use the movsum function
fs=10000;
t=0:1/fs:3;
tau=0.25; tauInSamp=tau*fs;
spikeTimes= randi(numel(t),10,1); % generate 10 spikes somewhere in the time, unit is samples
spikeVals = randi(2,10,1)/2;
allSpikes=zeros(size(t));
allSpikes(spikeTimes)=spikeVals;
resultingSpikes=movsum(allSpikes,[tauInSamp-1 0]);
ax1=subplot(2,1,1);
stem(spikeTimes/fs,spikeVals);
ax2=subplot(2,1,2);
plot(t,resultingSpikes);
##### 1 件のコメント表示非表示 なし
Paul Hinze 2022 年 7 月 7 日
Wow, even withut a loop!
This will speed up my code.
Thanks a lot ;)

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