On generating a finite pulse or a symmetric impulse response by a generalized approximation function

In some recent applications, researchers have been facing old problems of the time-domain synthesis, like the necessity of having circuits providing particular temporal responses. In this paper, we show that a recent method suitable to approximate functions with symmetric impulse response, and other one to obtain pulses with finite duration, actually refers to the same function. Hence, it allows us to derive a generalized transfer function, which contemplates both applications. A table with explicit expressions for the transfer functions is also given.