Analysis of time-dependent linear networks

LET
$\bar f$
(an overbarred letter) denote the operator of a linear system; x(τ) an input signal, which depends on time τ and y(t) the output response, as recorded at time t. The functional relationship between x(τ) and y(t) will be written
$y = {\bar f} x. \eqno{\hbox{(1)}}$
.