nnmt.lif.exp._transfer_function_shift

nnmt.lif.exp._transfer_function_shift(mu, sigma, tau_m, tau_s, tau_r, V_th_rel, V_0_rel, omegas, synaptic_filter=True)

Calcs value of transfer func for one population at given frequency omega.

Calculates transfer function according to :math:` ilde{n}` in Schuecker et al. [2015]. The expression is to first order equivalent to nnmt.lif.exp._transfer_function_taylor(). Since the underlying theory is correct to first order, the two expressions are exchangeable.

The difference here is that the linear response of the system is considered with respect to a perturbation of the input to the current I, leading to an additional low pass filtering 1/(1+i omega tau_s). Compare with the second equation of Eq. 18 and the text below Eq. 29.

Parameters:

mu[float | np.array]

Mean neuron activity of one population in V.

sigma[float | np.array]

Standard deviation of neuron activity of one population in V.

tau_m[float | np.array]

Membrane time constant in s.

tau_s[float | np.array]

Synaptic time constant in s.

tau_r[float | np.array]

Refractory time in s.

V_th_rel[float | np.array]

Relative threshold potential in V.

V_0_rel[float | np.array]

Relative reset potential in V.

omegas[float | np.array]

Input angular frequency to population in Hz.

synaptic_filterbool

Whether an additional synaptic low pass filter is to be used or not. Default is True.

Returns:

[float | np.array]

Transfer function in Hz/V.