Step-by-step calculation of rectangular window

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.

Thank you in advance for your help.

%% 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]');

[Paul Hinze]

At the end it should look like the second upper panel ;)

[Paul Hinze]

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

Answer 1

[Jonas]

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);
linkaxes([ax1 ax2],'x')

[Jonas]

note also the other, better readable solution further down the page

[Paul Hinze]

Thank you Jonas

Answer 2

[Jonas]

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);
linkaxes()

[Paul Hinze]

Wow, even withut a loop!

This will speed up my code.

Thanks a lot ;)