Introduced singularity functions u_k(t) where u_0(t) = delta(t), u_{-1}(t) = u(t), and u_{k+r}(t) = u_k(t) * u_r(t). In particular, u_1(t) is the impulse response for the system y(t) = d(x(t))/dt and is called the unit doublet. Defined unit step response. Started an example on correcting effect of echoes on an acoustic signal (2.64).