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% Transfer function of a leaky integrate and fire neuron
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% Fabrizio Gabbiani 11/03/08
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%time constant of the leaky integrate and fire neuron
tau = 30e-3; %in sec

%frequency vector in Hz=1/sec
f = 0:0.1:100;

%circular frequency
omega = 2*pi*f;

%gain equation
A = 1./sqrt(1 + tau^2 * omega.^2);

figure(1);
semilogx(f,A);
xlabel('frequency [Hz]');
ylabel('gain [normalized]');

%phase equation 
phi = atan(-tau*omega);
phi = phi*(180/pi); %converts to degrees

figure(2);
semilogx(f,phi);
xlabel('frequency [Hz]');
ylabel('phase [deg]');

%see ex4_b_g.m for real and imaginary parts