Example #4: x(t=e A Gaussian. important in probability, optics, etc (0) at dt X0)/2 區 T e 4a (Pulse width in t).(Pulse width in o) △r△O~(l/al2)y(a12)=1 Also a gaussian Uncertainty Principle! Cannot make both△tand△ o arbitrarily smallExample #4: x(t) = e−at 2 — A Gaussian, important in probability, optics, etc. Also a Gaussian! Uncertainty Principle! Cannot make both ∆t and ∆ω arbitrarily small. (Pulse width in t)•(Pulse width in ω) ⇒ ∆t•∆ω ~ (1/a1/2)•(a1/2) = 1