exercises for sta and reconstruction

pointprocesses/code/binnedRate.m

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+function [time, rate] = binned_rate(spike_times, bin_width, dt, t_max)
+% Calculates the firing rate with the binning method. The hist funciton is
+% used to count the number of spikes in each bin. 
+% Arguments: 
+%           spike_times, vector containing the times of the spikes.
+%           bin_width, the width of the bins in seconds.
+%           dt, the temporal resolution.
+%           t_max, the tiral duration.
+%
+% Returns two vectors containing the time and the rate.
+
+time = 0:dt:t_max-dt;
+bins = 0:bin_width:t_max;
+rate = zeros(size(time));
+
+h = hist(spike_times, bins) ./ bin_width;
+for i = 2:length(bins)
+    rate(round(bins(i - 1) / dt) + 1:round(bins(i) / dt)) = h(i);
+end

pointprocesses/code/convolutionRate.m

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+function [time, rate] = convolution_rate(spike_times, sigma, dt, t_max)
+% Calculates the firing rate with the convolution method. 
+% Arguments: 
+%           spike_times, a vector containing the spike times.
+%           sigma, the standard deviation of the Gaussian kernel in seconds.
+%           dt, the temporal resolution in seconds.
+%           t_max, the trial duration in seconds.
+%
+% Returns two vectors containing the time and the rate.
+
+time = 0:dt:t_max - dt;
+rate = zeros(size(time));
+spike_indices = round(spike_times / dt);
+rate(spike_indices) = 1;
+kernel = gauss_kernel(sigma, dt);
+
+rate = conv(rate, kernel, 'same');
+end
+
+
+function y = gauss_kernel(s, step)
+    x = -4 * s:step:4 * s;
+    y = exp(-0.5 .* (x ./ s) .^ 2) ./ sqrt(2 * pi) / s;
+end

pointprocesses/code/instantaneousRate.m

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+function [time, rate] = instantaneous_rate(spike_times, dt, t_max)
+% Function calculates the firing rate as the inverse of the interspike
+% interval.
+% Arguments:
+%            spike_times, vector containing the times of the spikes.
+%            dt, the temporal resolutions of the recording.
+%            t_max, the duration of the trial.
+%
+% Returns the vector representing time and a vector containing the rate.
+
+time = 0:dt:t_max-dt;
+rate = zeros(size(time));
+
+isis = diff([0 spike_times]);
+inst_rate = 1 ./ isis;
+spike_indices = [1 round(spike_times ./ dt)];
+
+for i = 2:length(spike_indices)
+    rate(spike_indices(i - 1):spike_indices(i)) = inst_rate(i - 1);
+end
+    
+

pointprocesses/code/reconstructStimulus.m

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+function s_est = reconstructStimulus(spike_times, sta, stim_duration, dt)
+% Function estimates the stimulus from the Spike-Triggered-Average
+% (sta).
+% Arguments:
+%         spike_times, a vector containing the spike times in seconds.
+%         sta, a vector containing the spike-triggered-average.
+%         stim_duration, the total duration of the stimulus.
+%         dt, the sampling interval given in seconds.
+%
+% Returns:
+%         the estimated stimulus.
+
+s_est = zeros(round(stim_duration / dt), 1);
+
+binary_spikes = zeros(size(s_est));
+binary_spikes(round(spike_times ./ dt)) = 1;
+
+s_est = conv(binary_spikes, sta, 'same');
+

pointprocesses/code/spikeTriggeredAverage.m

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+function [sta, std_sta, valid_spikes] = spikeTriggeredAverage(stimulus, spike_times, count, sampling_rate)
+% Function estimates the Spike-Triggered-Average (sta).
+%
+% Arguments:
+%           stimulus, a vector containing stimulus intensities
+%           as a function of time.
+%           spike_times, a vector containing the spike times 
+%           in seconds.
+%           count, the number of datapoints that are taken around
+%           the spike times.
+%           sampling_rate, the sampling rate of the stimulus.
+%
+% Returns: 
+%           the sta, a vector containing the staandard deviation and 
+%           the number of spikes taken into account.
+
+snippets = zeros(numel(spike_times), 2*count);
+valid_spikes = 1;
+for i = 1:numel(spike_times)
+    t = spike_times(i);
+    index = round(t*sampling_rate);
+    if index <= count || (index + count) > length(stimulus)
+        continue
+    end
+    snippets(valid_spikes,:) = stimulus(index-count:index+count-1);
+    valid_spikes = valid_spikes + 1;
+end
+
+snippets(valid_spikes:end,:) = [];
+
+sta = mean(snippets, 1);
+std_sta = std(snippets,[],1);