# Analysis¶

## Statistics of spike trains¶

brian.firing_rate(spikes)

Rate of the spike train.

brian.CV(spikes)

Coefficient of variation.

brian.correlogram(T1, T2, width=20.0 * msecond, bin=1.0 * msecond, T=None)

Returns a cross-correlogram with lag in [-width,width] and given bin size. T is the total duration (optional) and should be greater than the duration of T1 and T2. The result is in Hz (rate of coincidences in each bin).

N.B.: units are discarded. TODO: optimise?

brian.autocorrelogram(T0, width=20.0 * msecond, bin=1.0 * msecond, T=None)

Returns an autocorrelogram with lag in [-width,width] and given bin size. T is the total duration (optional) and should be greater than the duration of T1 and T2. The result is in Hz (rate of coincidences in each bin).

N.B.: units are discarded.

brian.CCF(T1, T2, width=20.0 * msecond, bin=1.0 * msecond, T=None)

Returns the cross-correlation function with lag in [-width,width] and given bin size. T is the total duration (optional). The result is in Hz**2: CCF(T1,T2)=<T1(t)T2(t+s)>

N.B.: units are discarded.

brian.ACF(T0, width=20.0 * msecond, bin=1.0 * msecond, T=None)

Returns the autocorrelation function with lag in [-width,width] and given bin size. T is the total duration (optional). The result is in Hz**2: ACF(T0)=<T0(t)T0(t+s)>

N.B.: units are discarded.

brian.CCVF(T1, T2, width=20.0 * msecond, bin=1.0 * msecond, T=None)

Returns the cross-covariance function with lag in [-width,width] and given bin size. T is the total duration (optional). The result is in Hz**2: CCVF(T1,T2)=<T1(t)T2(t+s)>-<T1><T2>

N.B.: units are discarded.

brian.ACVF(T0, width=20.0 * msecond, bin=1.0 * msecond, T=None)

Returns the autocovariance function with lag in [-width,width] and given bin size. T is the total duration (optional). The result is in Hz**2: ACVF(T0)=<T0(t)T0(t+s)>-<T0>**2

N.B.: units are discarded.

brian.total_correlation(T1, T2, width=20.0 * msecond, T=None)

Returns the total correlation coefficient with lag in [-width,width]. T is the total duration (optional). The result is a real (typically in [0,1]): total_correlation(T1,T2)=int(CCVF(T1,T2))/rate(T1)

brian.spike_triggered_average(spikes, stimulus, max_interval, dt, onset=None, display=False)

Spike triggered average reverse correlation. spikes is an array containing spike times stimulus is an array containing the stimulus max_interval (second) is the duration of the averaging window dt (second) is the sampling period onset (second) before which the spikes are discarded. Note: it will be at least as long as max_interval display (default=False) display the number of spikes processed out of the total number output the spike triggered average and the corresponding time axis