Causal extension by zero ($f_0(t)=f(t)(t\ge 0),f_0(t)=0(t<0)$)

Extend a function given for nonnegative time to the real line by setting it to zero before the starting time. This turns unilateral convolution into whole-line convolution and identifies a Laplace transform slice with a Fourier transform after exponential function weighting.