Are impulse responses the same thing as Green's functions?

Zhipu Jin, 02-10-23

Simple answer: Yes, they are.

More details:

Green's function (GF) is a basic solution to a linear differential equation,a building block that can be used to construct many useful solutions. The exact form of the GF depends on the differential equation, the body shape, and the type of boundary conditionspresent. Green's functions are named in honor of English mathematician andphysicist George Green (1793-1841).

Impulse response is the output of a linear system with zero initial conditions and a unit impulse function as the input. The impulse response of a linear system can be used for the evaluation of the system output for any kind of input, and for the determination of the transfer function of the system.

So we can say that impulse responses are only a special kind of Green's functions.