In order to find the Impulse response , f(t), you need only the real part , R(ω),of the transfer function
According to the mentioned paper:
f(t)= (2/π).∫R(ω).cos(tω) dω
The limits of integration are from zero to infinity.
Thanks for your kind comments. In the meantime I could find a direct straightforward answer in the 1959 publication:
SIMPLIFED METHOD OF DETERMINING TRANSIENT RESPONSE
FROM FREQUENCY RESPONSE OF LINEAR NETWORKS AND SYSTEMS
By: Victor S . Levadi
The transfer function of a linear system is known in the sinusoidal frequency domain. It is given in its final form as a complex function of the angular frequency ω (not jω ). How to obtain the step response?
Thanks in advance.
I thank both friends for their kind help. Fortunately, and after some modifications in the equations, a solution was possible using the numerical solution of two simultaneous differential equations in two variables and one single independent variable. This was done using the NDSolve command...
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I am trying to find a closed-form (analytical) solution for the two following simultaneous integro-differential equations :
du[x]/dx= - a v[x] +b ∫〖[1-(y-x)^4 〗].(v[y]-v[x])dy
(dv[x])/dx= - f u[x] -g ∫〖[1-(y-x)^4 〗].u[y]dy
With the initial conditions:
v=e and u=0