# Time variant Green function

1. ### fisico30

374
Hello forum,

in the case we are in the time domain t, the Green function is a function of time.

In the translation variant case, how do we express and separate the regular time variability of the Green function from the the time variability of its functional form?

1) What is the best notation? G(t, t0) or G(t,tau), G(tau, t0) ? tau=t-t0.

(The Green function is simply the response to a delta impulse. If the delta occurs at t=0, then we get a Green function g(t). If the delta occurs later, delta(t-t0), then the green function is f(t), not equal to g(t-t0).)

2) In taking the Fourier transform of G(t, t0), we can do it with respect to t or t0 (or both).
We would get H(t,w) or H(t0,w) or H(w1, w2).... (transfer function).

what is the different between H(t,w) and H(t0,w) from a physical point of view?
In H(w1,w2) , both w1 and w2 are temporal frequencies. How are they different? Does w1 represent the frequency of the input spectral component and w2 the frequency due to the functional variability of the green function ?

Any comment, clarification, reassurance?

thanks,
fisico30